Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions
Open accessAbstract
We propose a method of simulating efficiently many-body interacting fermion lattice models in trapped ions, including highly nonlinear interactions in arbitrary spatial dimensions and for arbitrarily distant couplings. We map products of fermionic operators onto nonlocal spin operators and decompose the resulting dynamics in efficient steps with Trotter methods, yielding an overall protocol that employs only polynomial resources. The proposed scheme can be relevant in a variety of fields such as condensed-matter or high-energy physics, where quantum simulations may solve problems intractable for classical computers.
AI snapshot
Written from the paper’s full text.
TL;DR
The paper proposes a trapped-ion protocol for quantum simulating many-body interacting fermion lattice models by mapping fermionic operators to nonlocal spin operators via Jordan-Wigner, decomposing the evolution with Trotter methods, and implementing the resulting nonlocal terms with Mølmer-Sørensen gates. It argues the protocol uses polynomial resources and can handle long-range, highly nonlinear interactions in arbitrary dimensions, with numerical Fermi-Hubbard simulations showing convergence of the Trotter approximation.
Key findings
- The protocol simulates general fermionic lattice Hamiltonians with arbitrary spatial dimension and arbitrarily distant couplings, avoiding auxiliary virtual Majorana fermions and the usual restriction to few neighbors.
- For a Fermi-Hubbard example with three lattice sites and six modes (two spins per site), the number of Hamiltonian terms scales as \(5N/2 - 4\), giving 11 terms for \(N=6\); the total number of gates per Trotter step is 33, on average 3 gates per Hamiltonian term.
- Trotter fidelity approaches 1 with increasing Trotter steps \(n_T\); for \(n_T=10\), fidelity is 0.99 in one parameter case and 0.97 in another. Supplementary fits show the error scales as \(1 - C/n_T^2\).
- The authors state that for more than \(\sim 30\) particles, foreseeable in the near future, one could simulate fermionic systems intractable for classical computers.
Methods
- Theoretical proposal in three steps: Jordan-Wigner mapping of \(N\) fermionic modes to \(N\) nonlocal spin operators; Trotter decomposition of the total evolution into exponentials of each nonlocal spin term; implementation of each exponential on \(N\) two-level trapped ions using Mølmer-Sørensen gates, local gates, and local rotations.
- Numerical validation compares exact diagonalization with Trotter-evolved dynamics for the Fermi-Hubbard Hamiltonian on three lattice sites with six modes, simulated by six two-level trapped ions, using initial state \(b^\dagger_{1\uparrow} b^\dagger_{1\downarrow}|0\rangle\).
- Supplementary analysis argues the number of elementary gates scales polynomially in the Trotter error \(\epsilon\), total evolution time \(t\), and number of fermionic modes \(N\), for bounded Hamiltonians.
Limitations
- The paper does not include a dedicated limitations section; stated caveats include that the Trotter expansion is approximate and its error decreases with more Trotter steps, and that the error analysis focuses on time-independent Hamiltonians.
- The numerical demonstration is limited to a small Fermi-Hubbard system of three lattice sites and six modes; no experimental implementation is reported.
- The text notes that current technology has realized more than 100 gates in a single experiment and that without error correction one would expect more than a thousand gates in the near future, indicating gate counts and scalability depend on future experimental capabilities.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
0 of 41 cited sources checked · 0 supported · 0 flagged
- Findingown data§ FINAL REMARKS · p. 6
The error of the Trotter expansion goes to zero polynomially in n_T.
“Thus, the error goes to zero polynomially in n T , as expected.”
Quote in the paperNot a substantial claim - Findingnone given§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3
The number of terms to be implemented scales linearly with the number of modes, 5N/2 - 4.
“Notice that the number of terms to be implemented scales linearly with the number of modes, 5 N/ 2 -4 (11 in this case, for N = 6).”
Quote in the paperSubstantial claim - Interpretationcitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
The method includes calculation of time evolutions and ground state computations, e.g., through adiabatic protocols.
“This includes the calculation of time evolutions and ground state computations, e.g. through adiabatic protocols [34].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [34] source
Not checked in the free run.
- Interpretationcitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2
Each exponential can be implemented, for arbitrary k and up to local rotations, with a Mølmer-Sørensen gate upon k ions, one local gate upon one of the ions, and the inverse Mølmer-Sørensen gate.
“Each of these exponentials can be implemented, for arbitrary k and up to local rotations, with a Mølmer-Sørensen gate upon k ions, one local gate upon one of the ions, and the inverse Mølmer-Sørensen gate [31].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [31] source
Not checked in the free run.
- Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3
The method can simulate Fröhlich Hamiltonians to recover polaron physics.
“We can simulate this kind of Hamiltonians in order to recover the polaron physics, a critical open issue for the deep understanding of correlated electrons in solids [38].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [38]
Not checked in the free run.
- Interpretationreasoning§ ANALYSIS OF THE TROTTER ERROR · p. 6
Each H_j is of the form of a product of an arbitrary number of Pauli matrices times a coupling h_j, such that its norm ||H_j|| = h_j.
“ii) each H j is always of the form of a product of arbitrary number of Pauli matrices times a coupling h j , such that its norm || H j || = h j , given that the 2-norm of a product of arbitrary number of Pauli matrices is always 1.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3
The efficient encoding of fermionic models in a lattice with arbitrarily long-range couplings is feasible.
“One of the main appeals of our method is that the efficient encoding of fermionic models in a lattice with arbitrarily long-range couplings is feasible.”
Quote in the paperSubstantial claim - Premisecitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
The Jordan-Wigner mapping establishes a correspondence between a set of fermionic operators and a set of spin operators, transforming a local Hamiltonian of fermions onto a nonlocal Hamiltonian of spins.
“This technique establishes a correspondence between a set of fermionic operators and a set of spin operators, transforming a local Hamiltonian of fermions onto a nonlocal Hamiltonian of spins.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [28] source
Not checked in the free run.
- Interpretationcitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
Each exponential of a nonlocal spin operator can be implemented in polynomial time on a set of N two-level trapped ions with a reduced number of laser pulses.
“Finally, we implement each of these exponentials in polynomial time on a set of N two-level trapped ions with a reduced number of laser pulses [31, 32].”
Quote in the paperSubstantial claim0 of 2 sources checked - Premisecitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
Only in one spatial dimension, and for couplings extended to a reduced number of neighbors, the correspondence is from a local model to a similar one.
“Only in one spatial dimension, and for couplings extended to a reduced number of neighbors, the correspondence is from a local model to a similar one [28].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [28] source
Not checked in the free run.
- Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
Quantum simulations will allow us to compute the time evolution of free and interacting fermion lattice theories with minimal experimental resources.
“Quantum simulations appear as a tool that will allow us to compute the time evolution of free and interacting fermion lattice theories with minimal experimental resources.”
Quote in the paperNot a substantial claim - Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3
The dynamics of the Fröhlich Hamiltonian term b†_{p+q} b_p (a_q + a†_{-q}) can be implemented with the technique.
“The last term contains the product b † p + q b p ( a q + a † -q ), whose dynamics can be implemented with our technique above according to Eq. (6).”
Quote in the paperSubstantial claim - Interpretationnone given§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2
The last term of the Fermi-Hubbard Hamiltonian contains the product of four fermionic operators, allowing for efficient implementation.
“The last term contains the product of four fermionic operators, allowing for efficient implementation.”
Quote in the paperSubstantial claim - Interpretationcitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
The proposed method gathers techniques that have not been previously considered for quantum simulators of fermionic lattice models.
“Our protocol consists of three steps, gathering techniques that have not been previously considered for quantum simulators of fermionic lattice models [35]:”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [35] source
Not checked in the free run.
- Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
The proposed method can efficiently simulate many-body interacting fermion lattice models in trapped ions, including highly nonlinear interactions in arbitrary spatial dimensions and arbitrarily distant couplings.
“We propose a method of simulating efficiently many-body interacting fermion lattice models in trapped ions, including highly nonlinear interactions in arbitrary spatial dimensions and for arbitrarily distant couplings.”
- Also stated in: § Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1 · plain
“Our method can simulate highly nonlinear and long-range interactions in arbitrary spatial dimensions, applying the Jordan-Wigner transformation without the usual restriction of a reduced number of neighbors, and without the need of auxiliary virtual Majorana fermions [33].”
- Also stated in: § Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 4 · plain
“In conclusion, we have introduced a method for simulating efficiently, i.e. with polynomial resources, manybody fermionic lattice models in an ion string.”
Quote in the paperSubstantial claim - Also stated in: § Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1 · plain
- Interpretationreasoning§ ANALYSIS OF THE TROTTER ERROR · p. 6
The resources needed in the protocol, including number of elementary gates and time scaling, are polynomial in the Trotter error, the total time simulated, and the total size of the system, in terms of the number of fermionic modes.
“In this Section we show that the resources needed in our protocol, including number of elementary gates and time scaling, are polynomial on the Trotter error, the total time simulated, and the total size of the system, in terms of the number of fermionic modes.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2
The operators b†_p↑ b_p'↓ σ^-_j can be mapped to a sum of products of Pauli matrices, leading to an efficient implementation.
“Notice that, e.g., the operators b † p ↑ b p ′ ↓ σ -j can be now mapped to a sum of products of Pauli matrices, leading to an efficient implementation.”
Quote in the paperSubstantial claim - Premisecitation§ ANALYSIS OF THE TROTTER ERROR · p. 6
The total number of gates needed, N_e, scales in the error ε, the total evolution time t, and the norm of the Hamiltonian H, ||H||, in the form [formula] provided ε ≤ 1 ≤ 2 m 5^{k-1} ||H|| t.
“Here, the total number of gates needed, N e , scales in the error ϵ , the total evolution time t , and the norm of the Hamiltonian H , || H || , where || . || is the 2-norm, in the form [5]”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [5] D. W. Berry, G. Ahokas, R. Cleve and Barry C. Sanders, Commun. Math. Phys. 270 , 359 (2007). source
Not checked in the free run.
- Interpretationcitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
Quantum simulations will allow us to reproduce the complete dynamics of these systems, avoiding mean field approximations as Hartree-Fock to simplify nonlinear interactions.
“Furthermore, quantum simulations will allow us to reproduce the complete dynamics of these systems, avoiding mean field approximations as Hartree-Fock to simplify nonlinear interactions [27].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [27]
Not checked in the free run.
- Interpretationcitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
The method maps products of fermionic operators onto nonlocal spin operators via the Jordan-Wigner transformation.
“We map products of fermionic operators onto nonlocal spin operators and decompose the resulting dynamics in efficient steps with Trotter methods, yielding an overall protocol that employs only polynomial resources.”
- Also stated in: § Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1 · plain
“Firstly, we map the set of N fermionic modes, via the Jordan-Wigner transformation [28], to a set of N nonlocal spin operators.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [28] source
Not checked in the free run.
- Also stated in: § Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1 · plain
- Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
The proposed protocol opens the possibility to simulate a wide range of condensed-matter and high-energy physics fermionic systems for a large number of particles.
“The proposed protocol opens the possibility to simulate a wide range of interesting condensed-matter and highenergy physics fermionic systems for a large number of particles.”
Quote in the paperSubstantial claim - Premisecitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3
The spin degrees of freedom can be encoded in long-lived electronic states of the ions.
“The spin degrees of freedom can be encoded in long-lived electronic states of the ions [5, 6, 12, 14, 19, 32, 39].”
Quote in the paperSubstantial claim0 of 7 sources checked- cites [5] D. W. Berry, G. Ahokas, R. Cleve and Barry C. Sanders, Commun. Math. Phys. 270 , 359 (2007). source
Not checked in the free run.
- cites [6] M. Suzuki, Proc. Japan Acad. B 69 , 161 (1993). source
Not checked in the free run.
- cites [12] source
Not checked in the free run.
- cites [14] source
Not checked in the free run.
- cites [19] source
Not checked in the free run.
- cites [32] source
Not checked in the free run.
- cites [39]
Not checked in the free run.
- Premisecitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
The operators b_i_k, b†_i_k can always be mapped to products of Pauli matrices using the Jordan-Wigner transformation.
“The operators b i k , b † i k can always be mapped to products of Pauli matrices, i.e., nonlocal spin operators, using the Jordan-Wigner transformation”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [28] source
Not checked in the free run.
- Interpretationcitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2
The required bosonic coupling can be implemented by using red and blue sideband interactions for each of the a_j modes in standard trapped-ion technology.
“The latter can be implemented by using a red and a blue sideband interactions for each of the a j modes in the context of standard trapped-ion technology [37].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [37]
Not checked in the free run.
- Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
The proposed method can simulate fermionic systems that are intractable for classical computers for a number of particles above ∼30.
“For a number of particles above ∼ 30, which is foreseeable in the near future, one could already simulate fermionic systems that are intractable for classical computers.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2
The exponentials of each nonlocal spin operator are efficiently implementable because their exponents consist of tensor products of k Pauli matrices.
“The exponentials of each nonlocal spin operator are efficiently implementable, given that their exponents consist of tensor products of k Pauli matrices.”
Quote in the paperSubstantial claim - Interpretationcitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2
The proposed method can simulate Kondo Hamiltonians, modelling the interaction of a Fermi sea of electrons with several magnetic impurities.
“With the proposed method, we can simulate Kondo Hamiltonians [24], modelling the interaction of a Fermi sea of electrons with several magnetic impurities at positions R j ,”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [24] source
Not checked in the free run.
- Interpretationnone given§ ANALYSIS OF THE TROTTER ERROR · p. 6
In all fermionic Hamiltonians considered, the number of nonlocal spin operators m is polynomial in N, the total number of fermionic modes.
“Notice that in all fermionic Hamiltonians we are considering, we have i) a polynomial number of nonlocal spin operators, i.e., m is polynomial in N , the total number of fermionic modes.”
Quote in the paperSubstantial claim - Premisecitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3
Without error correction, one would expect the realization of more than thousand gates in the near future.
“Indeed, without error correction, one would expect the realization of more than thousand gates in the near future [40].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [40]
Not checked in the free run.
- Interpretationcitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3
The Jordan-Wigner transformation can be applied for two and three spatial dimensions, not just for one, without employing additional virtual Majorana fermions.
“This also means that we can apply the Jordan-Wigner transformation for two and three spatial dimensions, not just for one, without employing additional virtual Majorana fermions [33].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [33] source
Not checked in the free run.
- Premisecitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
The numerical simulation of fermionic systems is, in general, a hard problem due to the huge increase of the Hilbert space dimension with the number of modes.
“The numerical simulation of fermionic systems is, in general, a hard problem due to the huge increase of the Hilbert space dimension with the number of modes [1, 21].”
Quote in the paperSubstantial claim0 of 2 sources checked - Premisecitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3
With current technology, more than 100 gates have been realized in a single experiment.
“With current technology, more than 100 gates have been realized in a single experiment [39].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [39]
Not checked in the free run.
- Interpretationnone given§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2
The bosonic operators a_j can be implemented with the vibrational modes of the ion chain.
“The bosonic operators a j can be implemented with the vibrational modes of the ion chain.”
Quote in the paperSubstantial claim - Premisecitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1
Using customized numerical methods as quantum Monte Carlo is not always possible due to the well-known sign problem.
“Using customized numerical methods as quantum Monte Carlo is not always possible due to the well-known sign problem [22, 23].”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [22]
Not checked in the free run.
- cites [23] source
Not checked in the free run.
- Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2
The coupling of arbitrary products of fermionic operators to linear sums of bosonic operators can be implemented.
“We could as well implement the coupling of arbitrary products of fermionic operators [similarly to Eq. (1)] to linear sum of bosonic operators,”
Quote in the paperSubstantial claim - Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3
For n_T=10 Trotter steps, the implementation of hundreds of gates per step will allow simulation of a wide variety of fermionic models.
“This will allow, for n T = 10 Trotter steps, the implementation of hundreds of gates per step, giving us the possibility to simulate a wide variety of fermionic models.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2
The three steps of the protocol amount to an efficient method for simulating fermionic models with long-range couplings in arbitrary dimensions with trapped ions.
“The three steps of our protocol amounts to an efficient method for simulating fermionic models with long-range couplings in arbitrary dimensions with trapped ions.”
Quote in the paperSubstantial claim - Premisecitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2
For bounded Hamiltonians, the Trotter expansion associated with the exponential of the polynomial sum of efficiently implementable nonlocal terms is efficient, i.e., it only requires polynomial resources.
“Note that for bounded Hamiltonians, the Trotter expansion associated with the exponential of the polynomial sum of efficiently implementable nonlocal terms is also efficient [2, 29, 30], i.e., it only requires polynomial resources [35].”
Quote in the paperSubstantial claim0 of 4 sources checked
- May combine two claims. 11
- Classified as probably not a substantial claim. 3
May combine two claims.
Findingreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3The number of gates in each term of the Hamiltonian is, in the worst case, linear in the number of modes, and in many cases just constant.
“At the same time, the nonlocal gates upon several ions are efficiently implementable with few lasers, such that the number of gates in each term of the Hamiltonian is, in the worst case, linear in the number of modes, and in many cases just constant.”
Quote in the paperSubstantial claimMay combine two claims.
Findingcitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3The number of gates for the highly nonlocal coupling b†_1 b_10 + b†_10 b_1 can be as small as 10 per Trotter step with the proposed method, whereas in the general case it would require about 10^6 elementary gates.
“In the general case, it would require a number of elementary gates of 2 20 ≃ 10 6 [2]. With our method, the number of gates can be as small as 10 per Trotter step, consisting of Mølmer-Sørensen gates (dark blue and green), local exp( iφ ′ σ y 2 ) gates (red), exp[ ± i ( π/ 4) ∑ i σ y i ] (yellow) and exp[ ± i ( π/ 4) ∑ i σ x i ] (cyan) gates (see Fig. 1b) [35].”
Quote in the paperSubstantial claim0 of 2 sources checkedMay combine two claims.
Findingown data§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3The fidelity of the Trotter expansion goes to 1 with the number of Trotter steps n_T, and for n_T=10 it is 0.99 (b) or 0.97 (d).
“Notice that the fidelity of the Trotter expansion goes to 1 with the number of Trotter steps n T , and for n T = 10 it is 0.99 (b) or 0.97 (d).”
Quote in the paperSubstantial claimMay combine two claims.
Findingreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3In the particular example of three lattice sites with six modes, the total number of gates per Trotter step is 33, i.e., on average 3 gates per Hamiltonian term.
“In this particular example the total number of gates per Trotter step is of 33, i.e., on average 3 gates per Hamiltonian term, which is very efficient.”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationnone given§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2The method is general and extends the hopping terms to arbitrarily distant pairs of electrons.
“Notice that our method is general and extends the hopping terms to arbitrarily distant pairs of electrons.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1The method can simulate highly nonlinear and long-range interactions in arbitrary spatial dimensions, applying the Jordan-Wigner transformation without the usual restriction of a reduced number of neighbors, and without the need of auxiliary virtual Majorana fermions.
“Our method can simulate highly nonlinear and long-range interactions in arbitrary spatial dimensions, applying the Jordan-Wigner transformation without the usual restriction of a reduced number of neighbors, and without the need of auxiliary virtual Majorana fermions [33].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [33] source
Not checked in the free run.
May combine two claims.
Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 3The mapped spin Hamiltonians are highly nonlocal but their evolution is efficiently realizable.
“Thus, the mapped spin Hamiltonians are highly nonlocal but their evolution is efficiently realizable.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationreasoning§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1The resulting dynamics are decomposed in efficient steps with Trotter methods, yielding an overall protocol that employs only polynomial resources.
“We map products of fermionic operators onto nonlocal spin operators and decompose the resulting dynamics in efficient steps with Trotter methods, yielding an overall protocol that employs only polynomial resources.”
- Also stated in: § Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1 · plain
“These three steps yield an efficient protocol that employs only polynomial resources.”
Quote in the paperSubstantial claim0 of 3 sources checked- Also stated in: § Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 1 · plain
May combine two claims.
Interpretationreasoning§ ANALYSIS OF THE TROTTER ERROR · p. 6The total norm of H is bounded by ||H|| ≤ sum ||H_j|| = sum h_j ≤ m h_max_j, and thus ||H|| is polynomial in m and in N.
“iii) the total norm of H is bounded by || H || ≤ ∑ m j =1 || H j || = ∑ m j =1 h j ≤ mh max j , where h max j is the maximum among all h ′ j s . Thus, || H || is polynomial in m , and in consecuence, also in N .”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationreasoning§ ANALYSIS OF THE TROTTER ERROR · p. 6The scaling of the number of elementary gates needed in the expansion is polynomial (a power law) in ε, t, and N, such that the method for implementing arbitrary fermionic Hamiltonians that occur in nature is efficient.
“Accordingly, we have shown that the scaling of the number of elementary gates needed in our expansion, is polynomial (more specifically, a power law) in ϵ , t , and N , such that our method for implementing arbitrary fermionic Hamiltonians that occur in nature is efficient.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Premisecitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2The Fermi-Hubbard Hamiltonian takes into account a range of effects in condensed-matter physics, as the Mott transition, and is also believed to be relevant in high-Tc superconductivity.
“The Fermi-Hubbard Hamiltonian [25] takes into account a range of effects in condensed-matter physics, as the Mott transition, and is also believed to be relevant in highT c superconductivity.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [25] source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2The Kondo Hamiltonian provides a variety of interesting features in different systems, as the minimum in the resistivity at low temperatures.
“The long debated Kondo Hamiltonian provides a variety of interesting features in different systems, as the minimum in the resistivity at low temperatures [36].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [36]
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
Premisecitation§ Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions · p. 2The Fröhlich Hamiltonian models the interaction of electrons with phonons.
“The Fr¨ ohlich Hamiltonian [26] models the interaction of electrons with phonons,”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [26] source
Not checked in the free run.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Second quantized fermionic Hamiltonians are efficiently simulatable in trapped ions.
“This kind of second quantized fermionic Hamiltonians are efficiently simulatable in trapped ions23.”
From From transistor to trapped-ion computers for quantum chemistry (2014) · cites this paper as [23]
The phonon degrees of freedom in trapped-ion systems provide a natural platform for addressing spin-boson or fermion-boson-type problems through quantum simulation.
“The phonon degrees of freedom in trapped-ion systems provide a natural platform for addressing spin-boson or fermion-boson-type problems through quantum simulation233637383940.”
From From transistor to trapped-ion computers for quantum chemistry (2014) · cites this paper as [23]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Expansion of the nonlinear Hamiltonian omits an identity term
MinorExpanding the stated product produces an additional g Ij ⊗ Ij+1 / 4 term. The subsequent expression calls itself equal to the product but omits that term, which changes the Hamiltonian by a constant.
“H 2 = g ( σ z j + I j ) ⊗ ( σ z j +1 + I j +1 ) / 4”
“= gσ z j ⊗ σ z j +1 / 4 + gσ z j / 4 + gσ z j +1 / 4.”
Figure 2 panel for the second fidelity is mislabeled
MinorThe prose says panels (b) and (c) show fidelity, while the Figure 2 caption assigns the second fidelity to panel (d) and says panel (c) shows excitation numbers.
“In (b) and (c) we include the fidelity |〈 ψ ( t F ) | ψ ( t F ) T 〉| 2 as a function of the number of Trotter steps n T”
“(c) 〈 b † 2 ↓ b 2 ↓ 〉 ( t ) (dashed, blue), and 〈 b † 3 ↑ b 3 ↑ 〉 ( t ) (solid, red), for n T = 15, and (d) fidelity |〈 ψ ( t F ) | ψ ( t F ) T 〉| 2”
Cites
<i>Quantum Computation and Quantum Information</i>
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895 · see citing works
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,449 · see citing works
Mahan, G. D. (2000) · doi:10.1007/978-1-4757-5714-9 · Cited by 8,249
Mahan, G. D. (1990) · Springer eBooks · doi:10.1007/978-1-4613-1469-1 · Cited by 8,220 · see citing works
Simulating physics with computers
Feynman, R. P. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf02650179 · Cited by 7,691 · see citing works
Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W., & Bloch, I. (2002) · Nature · doi:10.1038/415039a · Cited by 5,935 · see citing works
Resistance Minimum in Dilute Magnetic Alloys
Kondo, J. (1964) · Progress of Theoretical Physics · doi:10.1143/ptp.32.37 · Cited by 3,658 · see citing works
Lloyd, S. (1996) · Science · doi:10.1126/science.273.5278.1073 · Cited by 3,088 · see citing works
Quantum dynamics of single trapped ions
Leibfried, D., Blatt, R., Monroe, C., & Wineland, D. (2003) · Reviews of Modern Physics · doi:10.1103/revmodphys.75.281 · Cited by 2,739 · see citing works
�ber das Paulische �quivalenzverbot
Jordan, P., & Wigner, E. (1928) · Zeitschrift f�r Physik · doi:10.1007/bf01331938 · Cited by 2,597 · see citing works
The Kondo Problem of Heavy Fermions
Hewson, A. C., & Coleman, P. (1994) · Physics Today · doi:10.1063/1.2808446 · Cited by 2,345 · see citing works
Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations
Troyer, M., & Wiese, U. ‐. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.170201 · Cited by 1,251 · see citing works
An open-system quantum simulator with trapped ions
Barreiro, J. T., Müller, M., Schindler, P., Nigg, D., Monz, T., Chwalla, M., Hennrich, M., Roos, C. F., Zoller, P., & Blatt, R. (2011) · Nature · doi:10.1038/nature09801 · Cited by 1,100 · see citing works
About the Pauli exclusion principle
Jordán, P., & Wigner, E. P. (1928) · Cited by 951 · see citing works
The Kondo Problem to Heavy Fermions
Hewson, A. C. (1997) · Cited by 875 · see citing works
Effective Quantum Spin Systems with Trapped Ions
Porras, D., & Cirac, J. I. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.207901 · Cited by 872 · see citing works
Weimer, H., Müller, M., Lesanovsky, I., Zoller, P., & Büchler, H. P. (2010) · Nature Physics · doi:10.1038/nphys1614 · Cited by 867 · see citing works
Sign problem in the numerical simulation of many-electron systems
Loh, E. Y., Gubernatis, J. E., Scalettar, R. T., White, S. R., Scalapino, D. J., & Sugar, R. L. (1990) · Physical Review B · doi:10.1103/physrevb.41.9301 · Cited by 801 · see citing works
Towards quantum chemistry on a quantum computer
Lanyon, B. P., Whitfield, J. D., Gillett, G. G., Goggin, M. E., Almeida, M. P., Kassal, I., Biamonte, J. D., Mohseni, M., Powell, B. J., Barbieri, M., et al. (2010) · Nature Chemistry · doi:10.1038/nchem.483 · Cited by 796 · see citing works
Quantum simulation of frustrated Ising spins with trapped ions
Kim, K., Chang, M.-S., Korenblit, S., Islam, R., Edwards, E. E., Freericks, J. K., Lin, G.-D., Duan, L.-M., & Monroe, C. (2010) · Nature · doi:10.1038/nature09071 · Cited by 750 · see citing works
Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
Abrams, D. S., & Lloyd, S. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.2586 · Cited by 745 · see citing works
Quantum simulation of the Dirac equation
Gerritsma, R., Kirchmair, G., Zähringer, F., Solano, E., Blatt, R., & Roos, C. F. (2010) · Nature · doi:10.1038/nature08688 · Cited by 725 · see citing works
Self-citationEfficient Quantum Algorithms for Simulating Sparse Hamiltonians
Berry, D. W., Ahokas, G., Cleve, R., & Sanders, B. C. (2007) · Communications in Mathematical Physics · doi:10.1007/s00220-006-0150-x · Cited by 692 · see citing works
Universal Digital Quantum Simulation with Trapped Ions
Lanyon, B. P., Hempel, C., Nigg, D., Müller, M., Gerritsma, R., Zähringer, F., Schindler, P., Barreiro, J. T., Rambach, M., Kirchmair, G., et al. (2011) · Science · doi:10.1126/science.1208001 · Cited by 613 · see citing works
Simulating a quantum magnet with trapped ions
Friedenauer, A., Schmitz, H., Glueckert, J. T., Porras, D., & Schaetz, T. (2008) · Nature Physics · doi:10.1038/nphys1032 · Cited by 602 · see citing works
Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
Lamata, L., León, J., Schätz, T., & Solano, E. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.253005 · Cited by 300 · see citing works
Self-citationQuantum simulations with cold trapped ions
Johanning, M., Varón, A. F., & Wunderlich, C. (2009) · Journal of Physics B: Atomic, Molecular and Optical Physics · doi:10.1088/0953-4075/42/15/154009 · Cited by 208 · see citing works
Quantum Simulation of the Klein Paradox with Trapped Ions
Gerritsma, R., Lanyon, B. P., Kirchmair, G., Zähringer, F., Hempel, C., Casanova, J., García-Ripoll, J. J., Solano, E., Blatt, R., & Roos, C. F. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.060503 · Cited by 204 · see citing works
Self-citationMapping local Hamiltonians of fermions to local Hamiltonians of spins
Verstraete, F., & Cirac, J. I. (2005) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2005/09/p09012 · Cited by 196 · see citing works
Schwabl, F. (2004) · Advanced Texts in Physics · doi:10.1007/978-3-662-05418-5 · Cited by 186 · see citing works
Simulation of quantum dynamics with quantum optical systems
Jané, E., Vidal, G., Dür, W., Zoller, P., & Cirac, J. I. (2003) · Quantum Information and Computation · doi:10.26421/qic3.1-2 · Cited by 145 · see citing works
Simulating open quantum systems: from many-body interactions to stabilizer pumping
Müller, M., Hammerer, K., Zhou, Y. L., Roos, C. F., & Zoller, P. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/8/085007 · Cited by 127 · see citing works
(2008) · doi:10.1007/978-3-540-85062-5 · Cited by 110 · see citing works
Simulation of quantum dynamics with quantum optical systems
Jané, E., Vidal, G., Dür, W., Zoller, P., & Cirac, J. I. (2002) · CaltechAUTHORS (California Institute of Technology) · Cited by 107 · see citing works
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J., Lamata, L., Egusquiza, I. L., Gerritsma, R., Roos, C. F., García‐Ripoll, J. J., & Solano, E. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.260501 · Cited by 91 · see citing works
Self-citationKlein tunneling and Dirac potentials in trapped ions
Casanova, J., García-Ripoll, J. J., Gerritsma, R., Roos, C. F., & Solano, E. (2010) · Physical Review A · doi:10.1103/physreva.82.020101 · Cited by 86 · see citing works
Self-citationMapping local Hamiltonians of fermions to local Hamiltonians of spins
Verstraete, F., & Cirac, J. I. (2005) · CaltechAUTHORS (California Institute of Technology) · Cited by 85 · see citing works
Relativistic quantum mechanics with trapped ions
Lamata, L., Casanova, J., Gerritsma, R., Roos, C. F., García-Ripoll, J. J., & Solano, E. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/9/095003 · Cited by 80 · see citing works
Self-citationQuantum Simulation of the Majorana Equation and Unphysical Operations
Casanova, J., Sabín, C., León, J., Egusquiza, I. L., Gerritsma, R., Roos, C. F., García-Ripoll, J. J., & Solano, E. (2011) · Physical Review X · doi:10.1103/physrevx.1.021018 · Cited by 77 · see citing works
Self-citationHubbard-<i>U</i>band-structure methods
Albers, R. C., Christensen, N. E., & Svane, A. (2009) · Journal of Physics: Condensed Matter · doi:10.1088/0953-8984/21/34/343201 · Cited by 63 · see citing works
Designing spin-spin interactions with one and two dimensional ion crystals in planar micro traps
Welzel, J., Bautista-Salvador, A., Abarbanel, C., Wineman-Fisher, V., Wunderlich, C., Folman, R., & Schmidt-Kaler, F. (2011) · The European Physical Journal D · doi:10.1140/epjd/e2011-20098-y · Cited by 42 · see citing works
Optical Conductivity of the Holstein Polaron
Goodvin, G. L., Mishchenko, A. S., & Berciu, M. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.076403 · Cited by 38 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Georgescu, I. M., Ashhab, S., & Nori, F. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.153 · Cited by 2,932 · see citing works
“There have also been related proposals using trapped ions (Casanova et al., 2012, 2011), cavity QED systems (Barrett et al., 2013) and superconducting circuits (Marcos et al., 2013; Pedernales et al., 2013).”
BackgroundStrategies for quantum computing molecular energies using the unitary coupled cluster ansatz
Romero, J., Babbush, R., McClean, J. R., Hempel, C., Love, P. J., & Aspuru-Guzik, A. (2019) · Quantum Science and Technology · doi:10.1088/2058-9565/aad3e4 · Cited by 726 · see citing works
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator
Hempel, C., Maier, C., Romero, J., McClean, J., Monz, T., Shen, H., Jurcevic, P., Lanyon, B. P., Love, P., Babbush, R., et al. (2018) · Physical Review X · doi:10.1103/physrevx.8.031022 · Cited by 597 · see citing works
Quantum Algorithms for Quantum Field Theories
Jordan, S. P., Lee, K. S. M., & Preskill, J. P. (2012) · Science · doi:10.1126/science.1217069 · Cited by 511 · see citing works
Digital quantum simulation of fermionic models with a superconducting circuit
Barends, R., Lamata, L., Kelly, J., García-Álvarez, L., Fowler, A. G., Megrant, A., Jeffrey, E. R., White, T., Sank, D., Mutus, J., et al. (2015) · Nature Communications · doi:10.1038/ncomms8654 · Cited by 329 · see citing works
Self-citationUniversality of phase transition dynamics: Topological defects from symmetry breaking
del Campo, A., & Zurek, W. H. (2014) · International Journal of Modern Physics A · doi:10.1142/s0217751x1430018x · Cited by 364 · see citing works
Engineered Open Systems and Quantum Simulations with Atoms and Ions
Müller, M., Diehl, S., Pupillo, G., & Zoller, P. (2012) · Advances in atomic, molecular, and optical physics · doi:10.1016/b978-0-12-396482-3.00001-6 · Cited by 323 · see citing works
del Campo, A., Rams, M. M., & Zurek, W. H. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.115703 · Cited by 304 · see citing works
Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure
Shen, Y., Zhang, X., Zhang, S., Zhang, J.-N., Yung, M., & Kim, K. (2017) · Physical Review A · doi:10.1103/physreva.95.020501 · Cited by 288 · see citing works
Tomza, M., Jachymski, K., Gerritsma, R., Negretti, A., Calarco, T., Idziaszek, Z., & Julienne, P. S. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.035001 · Cited by 270 · see citing works
From transistor to trapped-ion computers for quantum chemistry
Yung, M.-H., Casanova, J., Mezzacapo, A., McClean, J., Lamata, L., Aspuru-Guzik, A., & Solano, E. (2014) · Scientific Reports · doi:10.1038/srep03589 · Cited by 221 · see citing works
Self-citationQuantum Simulation of a Lattice Schwinger Model in a Chain of Trapped Ions
Hauke, P., Marcos, D., Dalmonte, M., & Zoller, P. (2013) · Physical Review X · doi:10.1103/physrevx.3.041018 · Cited by 189 · see citing works
Quantum simulation of generic many-body open system dynamics using classical noise
Chenu, A., Beau, M., Cao, J., & del Campo, A. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.140403 · Cited by 160 · see citing works
Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives
Tacchino, F., Chiesa, A., Carretta, S., & Gerace, D. (2019) · Advanced Quantum Technologies · doi:10.1002/qute.201900052 · Cited by 155 · see citing works
Adiabatic tracking of quantum many-body dynamics
Saberi, H., Opatrný, T., Mølmer, K., & del Campo, A. (2014) · Physical Review A · doi:10.1103/physreva.90.060301 · Cited by 145 · see citing works
Global entangling gates on arbitrary ion qubits
Lu, Y., Zhang, S., Zhang, K., Chen, W., Shen, Y., Zhang, J., Zhang, J.-N., & Kim, K. (2019) · Nature · doi:10.1038/s41586-019-1428-4 · Cited by 139 · see citing works
Quantum computation of scattering in scalar quantum field theories
Jordan, S. P., Lee, K. S. M., & Preskill, J. P. (2014) · Quantum Information and Computation · doi:10.26421/qic14.11-12-8 · Cited by 199 · see citing works
Electron-Phonon Systems on a Universal Quantum Computer
Macridin, A., Spentzouris, P., Amundson, J. F., & Harnik, R. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.110504 · Cited by 120 · see citing works
Linear Optics Simulation of Quantum Non-Markovian Dynamics
Chiuri, A., Greganti, C., Mazzola, L., Paternostro, M., & Mataloni, P. (2012) · Scientific Reports · doi:10.1038/srep00968 · Cited by 122 · see citing works
Non-Abelian SU(2) Lattice Gauge Theories in Superconducting Circuits
Mezzacapo, A., Rico, E., Sabín, C., Egusquiza, I. L., Lamata, L., & Solano, E. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.240502 · Cited by 113 · see citing works
Self-citationDigital Quantum Simulation of Spin Systems in Superconducting Circuits
Heras, U. L., Mezzacapo, A., Lamata, L., Filipp, S., Wallraff, A. J., & Solano, E. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.200501 · Cited by 114 · see citing works
Self-citationEmulating Solid-State Physics with a Hybrid System of Ultracold Ions and Atoms
Bissbort, U., Cocks, D., Negretti, A., Idziaszek, Z., Calarco, T., Schmidt‐Kaler, F., Hofstetter, W., & Gerritsma, R. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.080501 · Cited by 111 · see citing works
Digital Quantum Rabi and Dicke Models in Superconducting Circuits
Mezzacapo, A., Las Heras, U., Pedernales, J. S., DiCarlo, L., Solano, E., & Lamata, L. (2014) · Scientific Reports · doi:10.1038/srep07482 · Cited by 111 · see citing works
Self-citationDigital-analog quantum simulations with superconducting circuits
Lamata, L., Parra-Rodriguez, A., Sanz, M., & Solano, E. (2018) · Advances in Physics X · doi:10.1080/23746149.2018.1457981 · Cited by 98 · see citing works
Self-citationDigital quantum computation of fermion-boson interacting systems
Macridin, A., Spentzouris, P., Amundson, J. F., & Harnik, R. (2018) · Physical Review A · doi:10.1103/physreva.98.042312 · Cited by 94 · see citing works
Fermion-Fermion Scattering in Quantum Field Theory with Superconducting Circuits
García-Álvarez, L., Casanova, J., Mezzacapo, A., Egusquiza, I. L., Lamata, L., Romero, G., & Solano, E. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.070502 · Cited by 83 · see citing works
Self-citationQuantum Computation of Scattering in Scalar Quantum Field Theories
Jordan, S. P., Lee, K. S. M., & Preskill, J. P. (2014) · CaltechAUTHORS (California Institute of Technology) · Cited by 85 · see citing works
Davoudi, Z., Linke, N. M., & Pagano, G. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.043072 · Cited by 81 · see citing works
Digital Quantum Simulation of the Holstein Model in Trapped Ions
Mezzacapo, A., Casanova, J., Lamata, L., & Solano, E. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.200501 · Cited by 75 · see citing works
Self-citationEfficient Quantum Algorithm for Computing n -time Correlation Functions
Pedernales, J. S., Candia, R. D., Egusquiza, I. L., Casanova, J., & Solano, E. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.020505 · Cited by 71 · see citing works
Self-citationDigital-Analog Quantum Simulation of Spin Models in Trapped Ions
Arrazola, Í., Pedernales, J. S., Lamata, L., & Solano, E. (2016) · Scientific Reports · doi:10.1038/srep30534 · Cited by 70 · see citing works
Self-citationDemon-like algorithmic quantum cooling and its realization with quantum optics
Xu, J., Yung, M., Xu, X.-Y., Boixo, S., Zhou, Z.-W., Li, C., Aspuru‐Guzik, A., & Guo, G. (2014) · Nature Photonics · doi:10.1038/nphoton.2013.354 · Cited by 66 · see citing works
Analog quantum simulation of chemical dynamics
MacDonell, R. J., Dickerson, C. E., Birch, C. J. T., Kumar, A., Edmunds, C., Biercuk, M. J., Hempel, C., & Kassal, I. (2021) · Chemical Science · doi:10.1039/d1sc02142g · Cited by 66 · see citing works
Many-Body Interactions with Tunable-Coupling Transmon Qubits
Mezzacapo, A., Lamata, L., Filipp, S., & Solano, E. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.050501 · Cited by 63 · see citing works
Self-citationQuantum Simulator for Transport Phenomena in Fluid Flows
Mezzacapo, A., Sanz, M., Lamata, L., Egusquiza, I. L., Succi, S., & Solano, E. (2015) · Scientific Reports · doi:10.1038/srep13153 · Cited by 58 · see citing works
Self-citationEfficient quantum simulation of fermionic and bosonic models in trapped ions
Lamata, L., Mezzacapo, A., Casanova, J., & Solano, E. (2014) · EPJ Quantum Technology · doi:10.1140/epjqt9 · Cited by 54 · see citing works
Self-citationQubit regularization of the O(3) sigma model
Singh, H., & Shailesh Chandrasekharan, A. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.100.054505 · Cited by 54 · see citing works
Qubit Regularization of Asymptotic Freedom
Tanmoy Bhattacharya, A., Buser, A. J., Shailesh Chandrasekharan, A., Gupta, R., & Singh, H. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.172001 · Cited by 52 · see citing works
Variational Quantum Simulation for Quantum Chemistry
Li, Y., Hu, J., Zhang, X., Song, Z., & Yung, M. (2019) · Advanced Theory and Simulations · doi:10.1002/adts.201800182 · Cited by 51 · see citing works
Multidimensional synthetic chiral-tube lattices via nonlinear frequency conversion
Wang, K., Bell, B. A., Solntsev, A. S., Neshev, D. N., Eggleton, B. J., & Sukhorukov, A. A. (2020) · Light: Science & Applications · doi:10.1038/s41377-020-0299-7 · Cited by 52 · see citing works
Trapped-ion quantum simulation of tunable-range Heisenberg chains
Graß, T., & Lewenstein, M. (2014) · EPJ Quantum Technology · doi:10.1140/epjqt8 · Cited by 56 · see citing works
Few-qubit quantum-classical simulation of strongly correlated lattice fermions
Kreula, J. M., García-Álvarez, L., Lamata, L., Clark, S. R., Solano, E., & Jaksch, D. (2016) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-016-0049-1 · Cited by 51 · see citing works
Self-citationNonlinear quantum Rabi model in trapped ions
Cheng, X.-H., Arrazola, Í., Pedernales, J. S., Lamata, L., Chen, X., & Solano, E. (2018) · Physical Review A · doi:10.1103/physreva.97.023624 · Cited by 51 · see citing works
Self-citationCounterdiabatic driving of the quantum Ising model
Damski, B. (2014) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2014/12/p12019 · Cited by 50 · see citing works
Kerman, A. J. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/12/123011 · Cited by 46 · see citing works
Noise-Resilient Quantum Computing with a Nitrogen-Vacancy Center and Nuclear Spins
Casanova, J., Wang, Z.-Y., & Plenio, M. B. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.130502 · Cited by 47 · see citing works
Self-citationDigital-analog quantum simulation of generalized Dicke models with superconducting circuits
Lamata, L. (2017) · Scientific Reports · doi:10.1038/srep43768 · Cited by 46 · see citing works
Self-citationControlling quantum critical dynamics of isolated systems
del Campo, A., & Sengupta, K. (2015) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2015-02350-4 · Cited by 40 · see citing works
Kreula, J. M., Clark, S. R., & Jaksch, D. (2016) · Scientific Reports · doi:10.1038/srep32940 · Cited by 49 · see citing works
Li, Z., Liu, X., Wang, H., Ashhab, S., Cui, J., Chen, H., Peng, X., & Du, J. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.090504 · Cited by 42 · see citing works
Hexagonal plaquette spin–spin interactions and quantum magnetism in a two-dimensional ion crystal
Nath, R., Dalmonte, M., Glaetzle, A. W., Zoller, P., Schmidt‐Kaler, F., & Gerritsma, R. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/6/065018 · Cited by 40 · see citing works
Symmetry criteria for quantum simulability of effective interactions
Zimborás, Z., Zeier, R., Schulte‐Herbrüggen, T., & Burgarth, D. K. (2015) · Physical Review A · doi:10.1103/physreva.92.042309 · Cited by 40 · see citing works
Quantum Simulation of Dissipative Processes without Reservoir Engineering
Candia, R. D., Pedernales, J. S., del Campo, A., Solano, E., & Casanova, J. (2015) · Scientific Reports · doi:10.1038/srep09981 · Cited by 42 · see citing works
Self-citationQuantum simulations of relativistic quantum physics in circuit QED
Pedernales, J. S., Di Candia, R., Ballester, D., & Solano, E. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/5/055008 · Cited by 40 · see citing works
Self-citationNicola, F. D., Sansoni, L., Crespi, A., Ramponi, R., Osellame, R., Giovannetti, V., Fazio, R., Mataloni, P., & Sciarrino, F. (2014) · Physical Review A · doi:10.1103/physreva.89.032322 · Cited by 38 · see citing works
Analog quantum simulation of generalized Dicke models in trapped ions
Aedo, I., & Lamata, L. (2018) · Physical Review A · doi:10.1103/physreva.97.042317 · Cited by 38 · see citing works
Self-citationDigital Simulation of Topological Matter on Programmable Quantum Processors
Mei, F., Guo, Q., Yu, Y.-F., Xiao, L., Zhu, S.-L., & Jia, S. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.160503 · Cited by 39 · see citing works
Digital quantum simulation of Floquet topological phases with a solid-state quantum simulator
Chen, B., Li, S., Hou, X., Ge, F., Zhou, F., Qian, P., Mei, F., Jia, S., Xu, N., & Shen, H. (2020) · Photonics Research · doi:10.1364/prj.404163 · Cited by 35 · see citing works
A dynamic systems approach to fermions and their relation to spins
Zimborás, Z., Zeier, R., Keyl, M., & Schulte‐Herbrüggen, T. (2014) · EPJ Quantum Technology · doi:10.1140/epjqt11 · Cited by 34 · see citing works
Pulsed dynamical decoupling for fast and robust two-qubit gates on trapped ions
Arrazola, Í., Casanova, J., Pedernales, J. S., Wang, Z.-Y., Solano, E., & Plenio, M. B. (2018) · Physical Review A · doi:10.1103/physreva.97.052312 · Cited by 29 · see citing works
Self-citationQuantum Simulation of Dissipative Processes without Reservoir Engineering
Di Candia, R., Simón Pedernales, J. J., Del Campo, A., Solano, E., & Casanova Marcos, J. (2015) · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · Cited by 39 · see citing works
Self-citationZhang, X., Zhang, K., Shen, Y., Zhang, S., Zhang, J.-N., Yung, M.-H., Casanova, J., Pedernales, J. S., Lamata, L., Solano, E., et al. (2018) · Nature Communications · doi:10.1038/s41467-017-02507-y · Cited by 30 · see citing works
Self-citationLinear and Logarithmic Time Compositions of Quantum Many-Body Operators
Motzoi, F., Kaicher, M., & Wilhelm, F. K. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.160503 · Cited by 29 · see citing works
Fermionic models with superconducting circuits
Heras, U. L., García-Álvarez, L., Mezzacapo, A., Solano, E., & Lamata, L. (2015) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-015-0021-5 · Cited by 26 · see citing works
Self-citationQPlayer: Lightweight, scalable, and fast quantum simulator
Jin, K., & Cha, G. (2022) · ETRI Journal · doi:10.4218/etrij.2021-0442 · Cited by 25 · see citing works
Quantum Simulation of Tunneling in Small Systems
Sornborger, A. T. (2012) · Scientific Reports · doi:10.1038/srep00597 · Cited by 25 · see citing works
Simulating para-Fermi oscillators
Alderete, C. H., & Rodríguez-Lara, B. M. (2018) · Scientific Reports · doi:10.1038/s41598-018-29771-2 · Cited by 23 · see citing works
Cooling of many-body systems via selective interactions
Grimaudo, R., Lamata, L., Solano, E., & MESSINA, A. (2018) · Physical Review A · doi:10.1103/physreva.98.042330 · Cited by 20 · see citing works
Self-citationLinear-algebraic bath transformation for simulating complex open quantum systems
Huh, J., Mostame, S., Fujita, T., Yung, M., & Aspuru‐Guzik, A. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/12/123008 · Cited by 20 · see citing works
A Study on Fast Gates for Large-Scale Quantum Simulation with Trapped Ions
Taylor, R. L., Bentley, C. D., Pedernales, J. S., Lamata, L., Solano, E., Carvalho, A. R. R., & Hope, J. J. (2017) · Scientific Reports · doi:10.1038/srep46197 · Cited by 19 · see citing works
Self-citationError-transparent evolution: the ability of multi-body interactions to bypass decoherence
Vy, O., Wang, X., & Jacobs, K. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/5/053002 · Cited by 18 · see citing works
Superconducting circuit architecture for digital-analog quantum computing
Yu, J., Retamal, J. C., Sanz, M., Solano, E., & Albarrán-Arriagada, F. (2022) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-022-00129-y · Cited by 18 · see citing works
Self-citationPolaronic effects in one- and two-band quantum systems
Yin, T., Cocks, D., & Hofstetter, W. (2015) · Physical Review A · doi:10.1103/physreva.92.063635 · Cited by 18 · see citing works
Quantum Simulation of Noncausal Kinematic Transformations
Alvarez-Rodriguez, U., Casanova, J., Lamata, L., & Solano, E. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.090503 · Cited by 17 · see citing works
Self-citationApplications + Practical Conceptualization + Mathematics = fruitful Innovation
Anderssen, R., Broadbridge, P., Fukumoto, Y., Kajiwara, K., Takagi, T., Verbitskiy, E. A., & Wakayama, M. (2015) · Mathematics for industry · doi:10.1007/978-4-431-55342-7 · Cited by 20 · see citing works
Simulating neutrino oscillations on a superconducting qutrit
Nguyen, H. C., Bach, B. G., Nguyen, T. D., Tran, D. M., Nguyen, H. Q., & Nguyen, H. Q. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.023013 · Cited by 14 · see citing works
Micromotion-enhanced fast entangling gates for trapped-ion quantum computing
Ratcliffe, A. K., Oberg, L. M., & Hope, J. J. (2020) · Physical Review A · doi:10.1103/physreva.101.052332 · Cited by 14 · see citing works
A digital quantum simulation of the Agassi model
Pérez-Fernández, P., Arias, J. M., García-Ramos, J. E., & Lamata, L. (2022) · Physics Letters B · doi:10.1016/j.physletb.2022.137133 · Cited by 13 · see citing works
Self-citationQuantum computing and neuroscience for 6G/7G networks: Survey
Glisic, S., & Lorenzo, B. (2024) · Intelligent Systems with Applications · doi:10.1016/j.iswa.2024.200346 · Cited by 15 · see citing works
Sáiz, Á., García-Ramos, J. E., Arias, J. M., Lamata, L., & Pérez-Fernández, P. (2022) · Physical Review C · doi:10.1103/physrevc.106.064322 · Cited by 11 · see citing works
Self-citationEntanglement measures in ion-trap quantum simulators without full tomography
Pedernales, J. S., Candia, R. D., Schindler, P., Monz, T., Hennrich, M., Casanova, J., & Solano, E. (2014) · Physical Review A · doi:10.1103/physreva.90.012327 · Cited by 11 · see citing works
Self-citationTopological qubits with Majorana fermions in trapped ions
Mezzacapo, A., Casanova, J., Lamata, L., & Solano, E. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/3/033005 · Cited by 11 · see citing works
Self-citationSpacetime symmetric qubit regularization of the asymptotically free two-dimensional O(4) model
Zhou, A. J., Singh, H., Tanmoy Bhattacharya, A., Shailesh Chandrasekharan, A., & Gupta, R. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.054510 · Cited by 10 · see citing works
Probabilistic eigensolver with a trapped-ion quantum processor
Zhang, J.-N., Arrazola, Í., Casanova, J., Lamata, L., Kim, K., & Solano, E. (2020) · Physical Review A · doi:10.1103/physreva.101.052333 · Cited by 9 · see citing works
Self-citationQuantum weak and modular values in enlarged Hilbert spaces
Ho, L. B., & Imoto, N. (2018) · Physical Review A · doi:10.1103/physreva.97.012112 · Cited by 9 · see citing works
Quantum Simulations with Circuit Quantum Electrodynamics
Romero, G., Solano, E., & Lamata, L. (2017) · Quantum science and technology · doi:10.1007/978-3-319-52025-4_7 · Cited by 8 · see citing works
Self-citationVoltage-controlled Hubbard spin transistor
Yousefjani, R., Bose, S., & Bayat, A. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.043142 · Cited by 7 · see citing works
Khan, A., Yoshimura, B., & Freericks, J. K. (2015) · Physical Review A · doi:10.1103/physreva.92.043405 · Cited by 7 · see citing works
Experimenting quantum phenomena on NISQ computers using high level quantum programming
Tran, D. M., Duy, N. V., Ho, L. B., & Nguyen, H. Q. (2022) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-022-00126-1 · Cited by 7 · see citing works
Grimaudo, R., Vitanov, N. V., de Castro, A. S. M., Valenti, D., & MESSINA, A. (2022) · Fortschritte der Physik · doi:10.1002/prop.202200010 · Cited by 8 · see citing works
Error-mitigated quantum simulation of interacting fermions with trapped ions
Chen, W., Zhang, S., Zhang, J., Su, X., Lu, Y., Zhang, K., Qiao, M., Li, Y., Zhang, J.-N., & Kim, K. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00784-8 · Cited by 8 · see citing works
Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian
Mukhopadhyay, P., Stetina, T. F., & Wiebe, N. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.010345 · Cited by 6 · see citing works
Digital-analog counterdiabatic quantum optimization with trapped ions
Kumar, S., Hegade, N. N., de Oliveira, M. H., Solano, E., Cadavid, A. G., & Albarrán-Arriagada, F. (2024) · Quantum Science and Technology · doi:10.1088/2058-9565/ad8b64 · Cited by 6 · see citing works
Self-citationImproving direct state measurements by using rebits in real enlarged Hilbert spaces
Ho, L. B. (2018) · Physics Letters A · doi:10.1016/j.physleta.2018.10.047 · Cited by 6 · see citing works
Time and spatial parity operations with trapped ions
Cheng, X.-H., Alvarez-Rodriguez, U., Lamata, L., Chen, X., & Solano, E. (2015) · Physical Review A · doi:10.1103/physreva.92.022344 · Cited by 5 · see citing works
Self-citationEnhancing the Charging Capacity of Many‐Body Quantum Batteries through Landau–Zener Driving
Siddique, S. A., Ali, M. M., & Sen, A. (2025) · Advanced Quantum Technologies · doi:10.1002/qute.202500098 · Cited by 4 · see citing works
Switchable particle statistics with an embedding quantum simulator
Cheng, X.-H., Arrazola, Í., Pedernales, J. S., Lamata, L., Chen, X., & Solano, E. (2017) · Physical Review A · doi:10.1103/physreva.95.022305 · Cited by 4 · see citing works
Self-citationQuantum simulation of pairing Hamiltonians with nearest-neighbor-interacting qubits
Wang, Z., Gu, X. Q., Wu, L.-A., & Liu, Y.-X. (2016) · Physical Review A · doi:10.1103/physreva.93.062301 · Cited by 4 · see citing works
Implementation strategies for multiband quantum simulators of real materials
Hague, J. P., & MacCormick, C. (2017) · Physical Review A · doi:10.1103/physreva.95.033636 · Cited by 4 · see citing works
Quantum Multi-Round Resonant Transition Algorithm
Yang, F., Chen, X., Zhao, D., Wei, S., Wen, J., Wang, H., Xin, T., & Long, G. (2022) · Entropy · doi:10.3390/e25010061 · Cited by 3 · see citing works
- Authors
- Casanova, J., Mezzacapo, A., Lamata, L., & Solano, E.
- Affiliations
- University of the Basque Country (ES)
- Ikerbasque (ES)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2012-05-10
- Volume
- 108
- Issue
- 19
- Pages
- 190502-190502
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2088422359
- Cited by
- 118
- References
- 42
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 7 · 2023: 2 · 2022: 11 · 2021: 6 · 2020: 6 · 2019: 8 · 2018: 14 · 2017: 8 · 2016: 5 · 2015: 16 · 2014: 19 · 2013: 7 · 2012: 6
- FWCI
- 15.11
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum simulation, trapped ions, Trotter decomposition, long-range coupling, quantum many-body systems
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-07.
Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-07.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
