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Cited by 223Quantum Computing Algorithms and ArchitectureCold Atom Physics and Bose-Einstein CondensatesAdvanced Chemical Physics Studies

From transistor to trapped-ion computers for quantum chemistry

Open access
Yung, M.-H., Casanova, J., Mezzacapo, A., McClean, J., Lamata, L., Aspuru-Guzik, A., Solano, E.·2014·Scientific Reports
DOI 10.1038/srep03589PMC PMC5378044
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Abstract

Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper proposes a trapped-ion quantum-simulation toolkit for quantum chemistry, combining quantum-assisted variational optimization, unitary coupled-cluster states, and phonon-mode simulation. It estimates that near-term trapped-ion systems can simulate problems such as H₂ electronic structure within decoherence times and beyond classical capacity.

Key findings

  • The toolkit has two main components: a hybrid quantum-classical “quantum-assisted optimization” for ground-state energies/eigenvectors, and optimized use of trapped-ion phonon modes for molecular vibrations and spin-boson/fermion-boson problems.
  • For implementing the unitary coupled-cluster ansatz, the standard quantum-circuit treatment needs as many as 2N two-qubit gates for N fermionic modes, whereas the proposed protocol needs only two Mølmer-Sørensen gates.
  • For H₂ in a minimal STO-3G basis (two electrons, four spin-orbitals, H–H separation 0.75 Å), the Hamiltonian has 12 terms (4 local operations and 8 non-local interactions); dynamics requires 16 MS gates per Trotter step, with estimated total simulation times of about 800 μs, 1.6 ms, and 2.4 ms for n = 1, 2, and 3, within ~30 ms decoherence times.
  • Trapped-ion context cited: up to 100 quantum logic gates have been realized for six qubits, quantum simulators involving 300 ions have been demonstrated, state preparation/single- and two-qubit gates/detection fidelities are above 99%, and one-qubit measurement fidelity is 99.99%.

Methods

  • Theoretical proposal for digital-analog trapped-ion quantum simulation of electronic structure, molecular dynamics, and vibronic coupling, using Jordan-Wigner transformation, Mølmer-Sørensen gates, Suzuki-Trotter expansion, and phase estimation with one extra ancilla ion.
  • Quantum-assisted optimization prepares parameterized UCC states, measures Hamiltonian expectation values in polynomial pieces, and updates parameters via classical optimization algorithms such as gradient descent, Nelder-Mead, or quasi-Newton methods.
  • Numerical investigation estimates resources and fidelity loss for H₂ in a minimal STO-3G basis, comparing simulated and exact state fidelities and energy for the initial state |↑↑↓↓〉 across Trotter steps n = 1, 2, 3.

Limitations

  • Stated: increasing Trotter steps reduces digital approximation error but accumulates single-gate error, creating a tradeoff; classical approximate UCC can break down when the reference state is not a good solution.
  • Stated/assumed: convergence of the UCC optimization assumes the parametrization gives a smooth energy function E(T(k)) that converges for large k.
  • Evident: the numerical demonstration is limited to H₂ in a minimal basis and resource estimates; no experimental trapped-ion implementation is reported, and near-future two-qubit gate infidelities of 10⁻⁴ are predicted rather than demonstrated.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1038/srep03589

Cites

56 of 56 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 23 cited sources checked · 0 supported · 0 flagged

  • Findingreasoning

    After Jordan-Wigner transformation, the electronic Hamiltonian in second quantization becomes highly nonlocal in terms of Pauli operators.

    “Consequently, the electronic Hamiltonian in Eq. (1) becomes highly nonlocal in terms of the Pauli operators {σx, σy, σz}, i.e.,”
    Quote in the paperSubstantial claim
  • Findingnone given

    The quantum resources for measurements can be significantly reduced by dividing the measurement of the Hamiltonian into a polynomial number of small pieces.

    “Practically, the quantum resources for the measurements can be significantly reduced when we divide the measurement of the Hamiltonian into a polynomial number of small pieces 〈Hi〉 (cf Eq. (2)).”
    Quote in the paperSubstantial claim
  • Findingnone given

    The authors have developed a novel protocol to measure correlation functions of observables in trapped ions that will be crucial for the quantum simulation of quantum chemistry.

    “Furthermore, we have also developed a novel protocol to measure correlation functions of observables in trapped ions that will be crucial for the quantum simulation of quantum chemistry.”
    Quote in the paperSubstantial claim
  • Findingnone given

    For the H2 molecule in a minimal STO-3G basis, the Hamiltonian is made up of 12 terms, including 4 local ion operations and 8 non-local interactions.

    “The Hamiltonian is made up of 12 terms, that include 4 local ion operations and 8 non-local interactions.”
    Quote in the paperSubstantial claim
  • Findingown data

    The energy of the system for the initial state |↑↑↓↓〉 can be retrieved with a small error within a reduced number of digital steps.

    “Again, one can observe how the energy can be retrieved with a small error within a reduced number of digital steps.”
    Quote in the paperSubstantial claim
  • May combine two claims. 10
  • Classified as probably not a substantial claim. 9

  • May combine two claims.

    Findingcitation

    Unitary coupled-cluster (UCC) states are particularly suitable for being the input state for quantum-assisted optimization, and each quantum state can be prepared efficiently with standard techniques in trapped ions.

    “We found that the unitary coupled-cluster (UCC) states35 are particularly suitable for being the input state for quantum-assisted optimization, where each quantum state |ψλ〉 can be prepared efficiently with standard techniques in trapped ions.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [35] Taube, A. G. & Bartlett, R. J. New perspectives on unitary coupled-cluster theory. Int. J. Quant. Chem. 106, 3393–3401 (2006). source

      Not checked in the free run.

  • May combine two claims.

    Findingreasoning

    The total simulation time is about 800 μs for the n = 1 protocol, 1.6 ms for n = 2, and 2.4 ms for n = 3.

    “the total simulation time can be assumed of about 800 μs for the n = 1 protocol, 1.6 ms and 2.4 ms for the n = 2 and n = 3 protocols.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Findingnone given

    Efficient measurement methods for the electronic Hamiltonian He are available for trapped ion systems.

    “Furthermore, efficient measurement methods for He are also available for trapped ion systems.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingcitation

    The standard quantum-circuit treatment for implementing each non-local operator involves as many as 2N two-qubit gates for simulating N fermionic modes; in our protocol one needs only two Mølmer-Sørensen gates.

    “It is remarkable that the standard quantum-circuit treatment (e.g. see Ref.47) for implementing each involves as many as 2N two-qubit gates for simulating N fermionic modes; in our protocol one needs only two Mølmer-Sørensen gates, which are straightforwardly implementable with current trapped-ion technology.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [47] Whitfield, J. D., Biamonte, J. & Aspuru-Guzik, A. Simulation of electronic structure Hamiltonians using quantum computers. Mol. Phys. 109, 735750 (2011). source

      Not checked in the free run.

  • May combine two claims.

    Findingreasoning

    To implement the dynamics for the H2 Hamiltonian, one needs 16 MS gates per Trotter step and a certain number of local rotations.

    “Therefore, to implement the dynamics, one needs 16 MS gates per Trotter step and a certain number of local rotations upon the ions.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Up to 100 quantum logic gates have been realized for six qubits with trapped ions.

    “Up to 100 quantum logic gates have been realized for six qubits with trapped ions22”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [22] Lanyon, B. P. et al. Universal digital quantum simulation with trapped ions. Science 334, 57–61 (2011). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    The fidelities of state preparation, single- and two-qubit gates, and detection in trapped-ion systems are all above 99%.

    “The fidelities of state preparation, single- and two-qubit gates, and detection, are all above 99%32.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [32] Häffner, H., Roos, C. F. & Blatt, R. Quantum computing with trapped ions. Phys. Rep. 469, 155–203 (2008). source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisecitation

    A quantum computer can efficiently solve problems of quantum systems.

    “As envisioned by Feynman4, one should be able to efficiently solve problems of quantum systems with a quantum computer.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [4] Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    Trapped-ion systems offer high-precision control over both the internal degrees of freedom of individual ions and the phonon degrees of freedom of collective motions, and high-fidelity initialization and measurement.

    “The power of trapped ions for quantum simulation is manifested by the high-precision control over both the internal degrees of freedom of the individual ions and the phonon degrees of freedom of the collective motions of the trapped ions, and the high-fidelity initialization and measurement3233.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [32] Häffner, H., Roos, C. F. & Blatt, R. Quantum computing with trapped ions. Phys. Rep. 469, 155–203 (2008). source

      Not checked in the free run.

    • cites [33] Leibfried, D., Blatt, R., Monroe, C. & Wineland, D. Quantum dynamics of single trapped ions.. Rev. Mod. Phys. 75, 281–324 (2003). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    The number of terms in the electronic Hamiltonian He scales polynomially in N, and the integrals {hpq, hpqrs} can be numerically calculated by a classical computer with polynomial resources.

    “Therefore, the number of terms in He scales polynomially in N, and the integrals {hpq, hpqrs} can be numerically calculated by a classical computer with polynomial resources9.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [9] Aspuru-Guzik, A., Dutoi, A. D., Love, P. J. & Head-Gordon, M. Simulated quantum computation of molecular energies. Science 309, 1704–7 (2005). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Quantum simulators involving 300 ions have been demonstrated.

    “and quantum simulators involving 300 ions have been demonstrated34.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [34] Britton, J. W. et al. Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins. Nature 484, 489–492 (2012). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given

    The simulation of the electronic Hamiltonian can still be made efficient with trapped ions.

    “Nevertheless, the simulation can still be made efficient with trapped ions, as we shall discuss below.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Interpretationnone given

    The proposed quantum simulation toolkit for quantum chemistry with trapped ions has advantages: efficient electronic simulation, the possibility of interacting electronic and vibrational degrees of freedom, and increasing scalability provided by trapped-ion systems.

    “This paradigm in quantum simulations has several advantages: an efficient electronic simulation, the possibility of interacting electronic and vibrational degrees of freedom, and the increasing scalability provided by trapped-ion systems.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given

    After locating the local minima of the ground and excited states, vibronic coupling for the electronic structure can be further studied.

    “After locating the local minima of the ground and excited states, vibronic coupling for the electronic structure can be further studied (see Supplementary Material).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    Trapped-ion two-qubit gates are predicted to achieve in the near future infidelities of 10^-4, making the use of these protocols feasible.

    “Trapped-ion two-qubit gates are predicted to achieve in the near future infidelities of 10−4, thus making the use of these protocols feasible50.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [50] Kirchmair, G. et al. Deterministic entanglement of ions in thermal states of motion. New J. Phys. 11, 023002 (2009). source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Interpretationreasoning

    Quantum simulations of quantum chemistry problems could reach realistic conditions for finite bosonic and fermionic mode numbers.

    “It is noteworthy to mention that, contrary to the continuous of modes required for full-fledged quantum field theories, quantum simulations of quantum chemistry problems could reach realistic conditions for finite bosonic and fermionic mode numbers.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given

    The energy obtained from UCC is a variational upper bound of the exact ground-state energy.

    “The energy obtained from UCC, namely is a variational upper bound of the exact ground-state energy.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisereasoning

    Approximate UCC methods rely on the assumption that the reference state |Φ〉 is a good solution, and in many cases this assumption is not valid and the use of approximate UCC breaks down.

    “Naturally, one has to rely on approximate methods3546 to truncate the series and keep track of finite numbers of terms. Therefore, in order to make good approximations by perturbative methods, i.e., assuming T is small, one implicitly assumes that the reference state |Φ〉 is a good solution to the problem. However, in many cases, such an assumption is not valid and the use of approximate UCC breaks”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [35] Taube, A. G. & Bartlett, R. J. New perspectives on unitary coupled-cluster theory. Int. J. Quant. Chem. 106, 3393–3401 (2006). source

      Not checked in the free run.

    • cites [46] Kutzelnigg, W. Error analysis and improvements of coupled-cluster theory. Theor. Chim. Acta 80, 349–386 (1991). source

      Not checked in the free run.

18 of 18

  • The authors state this as an assumption.

    The parametrization of UCC gives a smooth function for E(T(k)).

    “Finally, as a valid assumption for general cases, we assume our parametrization of UCC gives a smooth function for E (T(k)).”
1 of 1

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?

  • The UCC ansatz adds quantum correlations to the Hartree-Fock approximation and is inefficient to represent on a classical computer.

    “They arose from the quantum chemistry-specific observation that the unitary coupled cluster (UCC) ansatz (Taube and Bartlett, 2006), which adds quantum correlations to the Hartree-Fock approximation, is inefficient to represent on a classical computer (Yung et al. , 2014).”

    From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Yung et al., 2014

  • In practice, it has been observed that δ = 10^-10 is more than sufficient to retain quantitatively accurate results in molecular calculation with GTOs.

    “In practice, it has been observed that δ = 10 -10 is more than sufficient to retain quantitatively accurate results in molecular calculation with GTOs 79,306,347 .”

    From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [347]

  • Electronic structure Hamiltonians by definition have O(N^4) terms; in a local basis the number of non-negligible terms scales as O(N^2), and advanced techniques can evaluate these contributions in O(N) time.

    “As noted before, the electronic structure Hamiltonians by definition have O ( N 4 ) terms, however, in a local basis the number of non-negligible terms scale as O ( N 2 ) and advanced techniques can evaluate these contributions in O ( N ) time. This is the basis of linear scaling methods employed in quantum chemistry 79,347 .”

    From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [347]

  • Quantum algorithms can be expressed as polynomial-sized quantum circuits built from two-qubit unitary gates.

    “It is well-known that quantum algorithms can be expressed as polynomial-sized quantum circuits built from two-qubit unitary gates [15].”

    From Validating quantum computers using randomized model circuits (2019) · cites this paper as [15]

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Related

Authors
Yung, M.-H., Casanova, J., Mezzacapo, A., McClean, J., Lamata, L., Aspuru-Guzik, A., & Solano, E.
Affiliations
  • Harvard University (US)
  • University of the Basque Country (ES)
  • Ikerbasque (ES)
Corresponding author
Solano, E.
ORCID
Venue
Scientific Reports
Publisher
Springer Science and Business Media LLC
Published
2014-01-07
Volume
4
Issue
1
Pages
3589-3589
ISSN
2045-2322 (ISSN-L)
DOI
10.1038/srep03589
PMC
PMC5378044
OpenAlex
W2157120748
Semantic Scholar
7ba2e32f72c284933a6502c4c926734a6eb62368
Cited by
221
References
55
Citations by year
2026: 3 · 2025: 6 · 2024: 22 · 2023: 22 · 2022: 30 · 2021: 42 · 2020: 30 · 2019: 17 · 2018: 11 · 2017: 8 · 2016: 10 · 2015: 7 · 2014: 11 · 2013: 2
FWCI
11.95
Type
journal article
Language
en
Open access
Licence
Locations
  • Scientific Reports (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (submittedVersion, cc-by)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
  • Digital Access to Scholarship at Harvard (DASH) (Harvard University) (submittedVersion, cc-by)
  • Communities in ADDI (Universidad del Pais Vasco) (submittedVersion, other-oa)
  • Communities in ADDI (University of the Basque Country) (submittedVersion, cc-by)
  • Hispana (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (DE-FG02-97ER25308, 1037992)
  • U.S. Department of Defense
  • U.S. Department of Energy (DEFG0297ER25308, DE‐FG02‐, FG02-97ER25308)
  • National Natural Science Foundation of China (61061130540, 61033001)
  • Eusko Jaurlaritza (IT-472-10, IT472, UPV/EHU UFI 11/55)
  • Euskal Herriko Unibertsitatea (11/55, UPV/EHU UFI 11/55, UFI 11/55)
  • Defense Threat Reduction Agency (HDTRA1-10-1-0046, HDTRA1)
  • National Key Research and Development Program of China (61033001, 2011CBA00301, 2011CBA00300, 2011CBA00301, 2011CBA00300)
  • Division of Chemistry
  • Air Force Office of Scientific Research (FA 9550-12-1-0046, FA9550-, FA9550-12, FA9550‐12‐1)
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 › Advanced Chemical Physics Studies
Keywords
trapped-ion quantum computing, molecular electronic structure, molecular dynamics, vibronic coupling, quantum control

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