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Quantum computers and dissipation
Open accessAbstract
We analyse dissipation in quantum computation and its destructive impact on efficiency of quantum algorithms. Using a general model of decoherence, we study the time evolution of a quantum register of arbitrary length coupled with an environment of arbitrary coherence length. We discuss relations between decoherence and computational complexity and show that the quantum factorization algorithm must be modified in order to be regarded as efficient and realistic.
Checked 2026-10-06 · 2 references not checked yet
Overview
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Written from the paper’s full text.
TL;DR
The paper analyzes how dissipation/decoherence in quantum computers destroys quantum interference and entanglement, causing the probability of successful computation to decrease exponentially with input size \(L\). It argues that Shor’s factoring algorithm must be modified, e.g. supplemented with exponentially efficient quantum error correction, to be regarded as efficient and realistic.
Key findings
- If environmental coupling makes the error rate grow as \(\epsilon(L)=1-A\exp(-\alpha L)\), then the required number of repetitions grows as \(k(L)\approx \exp(\alpha L)\), so the randomized factoring algorithm is no longer efficient.
- In the independent-reservoir limit, the worst-case density-matrix elements decay as \(\exp\{-L\Gamma(t)\}\); for reservoirs with large coherence length, some off-diagonal elements decay as \(\exp\{-\mathrm{poly}(L)\Gamma(t)\}\), which can be more of a hindrance than a help unless selected coherences can be supported.
- Single-qubit decoherence has three regimes: a “quiet” regime for \(t<\omega_c^{-1}\), a quantum regime for \(\omega_c^{-1}<t<T^{-1}\), and a thermal regime for \(t>T^{-1}\). In one dimension at low temperature, \(\Gamma(t)\sim \omega_c^2 t^2\), then \(\sim 2\ln \omega_c t\), then \(\sim Tt\); in three dimensions the decoherence saturates to a value determined by \(\eta=\omega_c/T\).
- For two qubits, collective effects produce “subdecoherent” and “superdecoherent” states, with collective decay constants \(\Gamma_\pm(R,t)\); the paper distinguishes superdecoherence from superradiance and notes that some superradiant states are subdecoherent.
Methods
- Theoretical study of an \(L\)-qubit quantum register coupled to a thermal reservoir, using a decoherence model with Hamiltonian \(H\) containing free qubit, free environment, and qubit-environment interaction terms.
- Single-qubit decoherence is treated semiclassically via stochastic fluctuating fields and numerically simulated, then fully quantized using field modes, displacement operators, and exact expressions for the reduced density-matrix coherence.
- The analysis is extended to two qubits and then to \(L\) qubits, comparing independent reservoirs with shared reservoirs and position-dependent couplings; complexity consequences are assessed through randomized-algorithm error amplification.
Limitations
- The paper states that its model does not describe \(T_1\) processes: populations are unaffected and there is no energy exchange between qubit and environment; it notes that at longer timescales \(T_1\) processes would remove residual coherence in the three-dimensional case.
- The paper states that the semiclassical approach excludes quantum features, most notably qubit-environment entanglement, and that a fully quantum approach is needed for thermal and vacuum fluctuations.
- Evident from the text: the conclusion that any thermal-reservoir decoherence model leads to the same complexity conclusion is presented as a plausibility argument, not a proof; the analysis assumes specific coupling/density-of-states forms and does not include direct two-qubit interactions.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This is because the error rate, which is due to the interaction with the environment (a thermal reservoir), grows as an exponential function of L regardless the type and the strength of the computer - environment coupling.”
- Also stated in: § 2 Errors in Randomized Algorithms · p. 3 · boosted
“Indeed, our results show that the computer-environment interaction leads to this unwelcome exponential increase of the error rate.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The environment or reservoir is modeled as a thermal reservoir.
- Also stated in: § 2 Errors in Randomized Algorithms · p. 3 · boosted
In the paper
“In the limit of a short correlation length (i.e. coupling to the independent reservoirs) our results coincide with those by Unruh (1995).”
What the sources say
- Not checked yetcites Unruh 1995
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Let us first note that thermal fluctuations can affect the qubit dynamics only for times longer than the characteristic thermal frequency T .”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The dynamics of a single qubit plus environment is described by Hamiltonian (12).
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Expression (23) reduces to Γ( t ) ∼ ω 2 c t 2 for t < ω -1 c , Γ( t ) ∼ 2 ln ω c t for ω -1 c < t < T -1 , and Γ( t ) ∼ Tt for t > T -1 .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The frequency dependence of the density of states and coupling is assumed to be (dk/dω)G(ω)|g(ω)|^2 ∝ ω^n e^{-ω/ωc}, with n depending on the number of dimensions.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In the independent reservoir case therefore in the worst case the density matrix elements decay as exp {-L Γ( t ) } .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“As η decreases, the decay onset moves towards larger t .”
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- The authors state this as an assumption: The frequency dependence of the density of states and coupling is assumed to be (dk/dω)G(ω)|g(ω)|^2 ∝ ω^n e^{-ω/ωc}, with n depending on the number of dimensions.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Indeed the off-diagonal elements of the reduced density matrix of the qubit decay due to the fact that the overlap between the different field states with which the qubit becomes entangled diminishes in time.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The dynamics of a single qubit plus environment is described by Hamiltonian (12).
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“It should be noted that in the time evolution of a single member of the ensemble the amplitude for the oscillations in s x and s y remains constant.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, for large η there is an intermediate region where the vacuum fluctuations dominate and the decay is roughly linear before the thermal regime takes over.”
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes- The authors state this as an assumption: The frequency dependence of the density of states and coupling is assumed to be (dk/dω)G(ω)|g(ω)|^2 ∝ ω^n e^{-ω/ωc}, with n depending on the number of dimensions.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Expression (23) reduces to Γ( t ) ∼ ω 2 c t 2 for t < ω -1 c , Γ( t ) ∼ 2 ln ω c t for ω -1 c < t < T -1 , and Γ( t ) ∼ Tt for t > T -1 .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: The frequency dependence of the density of states and coupling is assumed to be (dk/dω)G(ω)|g(ω)|^2 ∝ ω^n e^{-ω/ωc}, with n depending on the number of dimensions.
- It may state two separate claims as one. 25
- Probably not a substantial claim. 7
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Since [ σ z , H ] = 0 the populations of the qubit density matrix, ρ ( t ) = Tr R ̺ ( t ) are not affected by the environment and the coupling with the environment in our model simply erodes quantum coherence.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The dynamics of a single qubit plus environment is described by Hamiltonian (12).
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“It is obvious that states for which i a = j a and i b = j b do not get entangled with the reservoir and therefore they mantain their coherence.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Matrix elements of the form ρ i a i a ,i b j b show no collective decay, in fact”
- Also stated in: § 5 Decoherence of Quantum Registers · p. 14 · plain
“which for i b = j b reduces to ρ i a i a ,i b i b ( t ) = ρ i a i a ,i b i b (0) while for i b = j b we have ρ i a i a ,i b j b ( t ) = ρ i a i a ,i b j b (0) e -Γ( t ) .”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Also stated in: § 5 Decoherence of Quantum Registers · p. 14 · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This means that also in our fully quantised model there is no exchange of energy between qubit and environment and consequently no T 1 type of decay takes place.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The dynamics of a single qubit plus environment is described by Hamiltonian (12).
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Collective decay is instead apparent in the matrix elements of the form ρ i a j a ,i b j b ( t ) with i a = j a , i b = j b :”
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✗ Asserted: fails✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The authors may not put it forward as true. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“These three regimes can be easily identified in Fig.(4), which shows the decoherence of a single qubit induced by a one-dimensional field for the particular choice ω c /T = 100.”
Strength:plain· not yet calibratedSingle caseTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- The authors state this as an assumption: The frequency dependence of the density of states and coupling is assumed to be (dk/dω)G(ω)|g(ω)|^2 ∝ ω^n e^{-ω/ωc}, with n depending on the number of dimensions.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Any technological progress in suppressing dissipation will, of course, help to factor bigger and bigger numbers but will not change an exponential increase of the error rate.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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In the paper
“Our analysis is quite general and covers cases where qubits interact with a single reservoir and the distance between the qubits is comparable with the correlation length of the reservoir.”
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“In contrast Shor (1994) has shown that quantum computers require an execution time that grows only as a polynomial function of L ( ≈ L 2 ).”
What the sources say
- Not checked yetcites Shor 1994
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Equation (19) is exact , i.e. no approximation has been made to obtain it.”
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- The authors state this as an assumption: The dynamics of a single qubit plus environment is described by Hamiltonian (12).
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This is not a limitation of the model since, as will became clear in the following, it describes adequately the decoherence mechanism which usually takes place on a shorter timescale than the energy dissipation.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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In the paper
“Furthermore this model is exactly soluble and allows a clear analysis of the mechanism of entanglement between qubit and environment which is believed to be at the core of most decoherence processes.”
Load-bearingStrength:boosted· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The dynamics of a single qubit plus environment is described by Hamiltonian (12).
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“When a reservoir is in a thermal state the coherences change on a much shorter time scale than populations and it is decoherence which is responsible for destroying quantum parallelism.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The environment or reservoir is modeled as a thermal reservoir.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In particular, in the limit r a ≈ r b we have ξ a k ∼ ξ b k and therefore in the 'subdecoherent' state | Φ ( -) 〉 the qubits are not entangled with the field, while in the 'superdecoherent' state | Φ (+) 〉 the qubits are collectively entangled with a coherent state with an amplitude which is twice that of the single qubit case.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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In the paper
“Indeed the conditions for the two processes to occur are quite different: superdecoherence requires the qubit to be in a region of space smaller than the coherence length of the environment, which is a much more stringent condition that the one needed for superradiance to take place, i.e. that the atoms are at a distance smaller than the wavelength of the resonant field modes.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Thus the ratio t/τ , which depends on the technology employed, determines the limits of the algorithm and it is unrealistic to assume that this ratio can be made infinite.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For reservoirs with a large coherent length the fastest decoherence will be proportional to exp( -poly ( L )Γ ′ ( t )) leading to the same unwelcome exponential increase of the error rate.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearIt may state two separate claims as one.
In the paper
“Indeed, Shor's quantum factoring algorithm is of this type; in a single run it provides factors of N with probability 1 -ǫ ( L ) and the probability of error ǫ ( L ) grows only as a polynomial function of L .”
What the sources say
- Not checked yetcites Shor 1994
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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In the paper
“While superdecoherence is due to collective entanglement between qubits and environment with no exchange of energy, superradiance is a process of collective radiation by a group of closely spaced atoms.”
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Our analysis shows that decoherence destroys quantum interference and entanglement in quantum computers, thus decreasing the probability of successful computation exponentially with the input size L .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Furthermore, it must be noted that some superradiant states are subdecoherent.”
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In the independent reservoirs limit the fastest decoherence is proportional to exp( -L Γ( t )) whereas for the reservoirs with a large coherence length there are off-diagonal elements which decay as exp( -poly ( L )Γ( t )).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“When a quantum computer is in contact with an environment, here modeled as a thermal reservoir, the resulting dissipation destroys the coherences and changes the populations (the diagonal elements).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The environment or reservoir is modeled as a thermal reservoir.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If the interaction with the environment causes an exponential increase of the error rate i.e. ǫ ( L ) = 1 -A exp( -αL ), where A and α are positive constants, then k ( L ) ≈ exp( αL ) and the randomized algorithm cannot be regarded as efficient any more!”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: In the amplification argument, the error rate ǫ is independent of the input.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“However, errors in Shor's algorithm are of purely 'mathematical' origin and correspond to the random decisions which rely on the prime number theorem (i.e. on the distribution of prime numbers).”
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Shor's algorithm, as it stands at the moment, is not robust to the environmental noise and requires modifications.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“This difference in behaviour is reminiscent of the dimensional differences observed in various models of phase transitions (Ma 1976) and is due to the suppressed influence of low frequency fluctuations in three dimensions.”
What the sources say
- Not checked yetcites Ma 1976
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
- The authors state this as an assumption: The frequency dependence of the density of states and coupling is assumed to be (dk/dω)G(ω)|g(ω)|^2 ∝ ω^n e^{-ω/ωc}, with n depending on the number of dimensions.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In this case while some coherences are not affected by the decoherence some others are destroyed more rapidly.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Also we provide a plausibility argument that any model of dissipation will lead to errors that grow exponentially with L .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearIt may state two separate claims as one.
The authors state this as an assumption.
The environment or reservoir is modeled as a thermal reservoir.
“When a quantum computer is in contact with an environment, here modeled as a thermal reservoir, the resulting dissipation destroys the coherences and changes the populations (the diagonal elements).”
The authors state this as an assumption.
The quantised environment is modeled as a continuum of field modes.
“The quantised environment is modeled as a continuum of field modes.”
The authors state this as an assumption.
At time t = 0 the combined qubit-environment state is assumed to have a specified product form involving the thermal density matrix of each field mode.
“The state of the combined system i.e. qubit + environment is described by a density operator ̺ ( t ) which at time t = 0 is assumed to be in the form”
The authors state this as an assumption.
The dynamics of a single qubit plus environment is described by Hamiltonian (12).
“We assume that the dynamics of a single qubit + environment is described by the following Hamiltonian”
The authors state this as an assumption.
In the amplification argument, the error rate ǫ is independent of the input.
“Assuming that ǫ is independent of the input the success probability of the algorithm can be amplified (boosted) arbitrarily close to 1 by repeating the computation several times.”
The authors state this as an assumption.
The frequency dependence of the density of states and coupling is assumed to be (dk/dω)G(ω)|g(ω)|^2 ∝ ω^n e^{-ω/ωc}, with n depending on the number of dimensions.
“Therefore we assume ( dk/dω ) G ( ω ) | g ( ω ) | 2 ∝ ω n e -ω/ω c .”
The authors state this as an assumption.
All coherences are equally important.
“Assuming that all coherences are equally important and that for the complexity analysis we choose the worst case (i.e. the off-diagonal element which decays at the fastest rate)”
The authors state this as an assumption.
For the complexity analysis, the worst case is chosen, i.e. the off-diagonal element which decays at the fastest rate.
“Assuming that all coherences are equally important and that for the complexity analysis we choose the worst case (i.e. the off-diagonal element which decays at the fastest rate)”
The authors state this as an assumption.
All modes of the field are in thermal equilibrium.
“We can formulate in more rigorous terms the analysis we have just sketched above by taking into account all the modes of the field in thermal equilibrium.”
The authors state this as an assumption.
The position-dependent couplings have the form g_a k = g_k e^{i k·r_a} and g_b k = g_k e^{i k·r_b}.
“If we suppose g a k = g k e i k · r a and g b k = g k e i k · r b , then, in the continuum limit, the collective decay rates are”
The authors state this as an assumption.
There is no direct interaction between the two qubits.
“In (25) we are not considering any direct interaction between the two qubits which would be necessary for the conditional dynamics (Barenco et al 1995).”
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In the citing paper
“Noise, decoherence, and manufacturing problems make constructing large-scale quantum computers difficult 9-13 .”
From Experimental realization of a quantum algorithm (1998) · cites this paper as [13]
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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.
Conflicting year for the Deutsch and Jozsa citation
MinorThe text cites Deutsch and Jozsa as a 1992 work, but the corresponding reference lists 1989.
“(Deutsch 1985, Deutsch and Jozsa 1992, Bernstein and Vazirani 1993, Simon 1994, Shor 1994)”
“Deutsch, D. & Jozsa, R. 1989 Proc. Roy. Soc. A439 , pp. 553-558.”
Citations
Cites
Dynamics of the dissipative two-state system
Leggett, A. J., Chakravarty, S., Dorsey, A. T., Fisher, M. P. A., Garg, A., & Zwerger, W. (1987) · Reviews of Modern Physics · doi:10.1103/revmodphys.59.1 · Cited by 5,109 · cited 1×
“Hamiltonian (12) is equivalent to the one introduced in connection with the tunnelling problem (Leggett et al. 1987, Gardiner 1991) and used to model decoherence in quantum computers (Unruh 1995).”
MethodQuantum theory, the Church–Turing principle and the universal quantum computer
Deutsch, D. (1985) · Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences · doi:10.1098/rspa.1985.0070 · Cited by 4,597
Distribution functions in physics: Fundamentals
Hillery, M. S., O’Connell, R. F., Scully, M. O., & Wigner, E. P. (1984) · Physics Reports · doi:10.1016/0370-1573(84)90160-1 · Cited by 2,932
Rapid solution of problems by quantum computation
Deutsch, D., & Jozsa, R. (1992) · Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences · doi:10.1098/rspa.1992.0167 · Cited by 2,700
Optical resonance and two-level atoms
Allen, L., & Eberly, J. H. (1975) · Cited by 2,549
Optical Resonance and Two-level Atoms
Garside, B. K. (1975) · Optica Acta International Journal of Optics · doi:10.1080/713819009 · Cited by 2,364
Modern Theory Of Critical Phenomena
Ma, S.-K. (2018) · Routledge eBooks · doi:10.4324/9780429498886 · Cited by 2,089
Modern Theory of Critical Phenomena
Osborn, H. (1977) · Physics Bulletin · doi:10.1088/0031-9112/28/4/035 · Cited by 1,934
Cohen-Tannoudji, C. N., & Laloë, F. (1977) · Cited by 1,886
Distribution Functions in Physics: Fundamentals
Hillery, M. S., O’Connell, R. F., Scully, M. O., & Wigner, E. P. (1997) · Springer eBooks · doi:10.1007/978-3-642-59033-7_28 · Cited by 1,803
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- Lenstra A. K. Lenstra H. W. Jr Manasse M. S. & Pollard J. M. 1990 Proc. 22th ACM Symp. j on the Theory of
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Items 301–400 of 878
Universal quantum computation in a neutral-atom decoherence-free subspace
Brion, E., Pedersen, L. H., Mølmer, K., Chutia, S., & Saffman, M. E. (2007) · Physical Review A · doi:10.1103/physreva.75.032328 · Cited by 28
Additivity of decoherence measures for multiqubit quantum systems
Fedichkin, L. E., Fedorov, A., & Vladimir Privman, A. (2004) · Physics Letters A · doi:10.1016/j.physleta.2004.06.021 · Cited by 28
Spatially correlated qubit errors and burst-correcting quantum codes
Vatan, F., Roychowdhury, V., & Anantram, M. P. (1999) · IEEE Transactions on Information Theory · doi:10.1109/18.771250 · Cited by 28
Relaxation of Shallow Donor Electron Spin Due to Interaction with Nuclear Spin Bath
Saykin, S., Mozyrsky, D., & Vladimir Privman, A. (2002) · Nano Letters · doi:10.1021/nl0255552 · Cited by 29
Quantum signatures in nonlinear gravitational waves
Guerreiro, T., Coradeschi, F., Frassino, A. M., West, J. R., & Schioppa, E. J. (2022) · Quantum · doi:10.22331/q-2022-12-19-879 · Cited by 32
Domínguez, F. D., & Álvarez, G. A. (2021) · Physical Review A · doi:10.1103/physreva.104.062406 · Cited by 28
Simple non-Markovian microscopic models for the depolarizing channel of a single qubit
Fonseca-Romero, K. M., & Franco, R. L. (2012) · Physica Scripta · doi:10.1088/0031-8949/86/06/065004 · Cited by 27
Quantum non-Markovian reservoirs of atomic condensates engineered via dipolar interactions
Yuan, J.-B., Xing, H., Kuang, L., & Yi, S. (2017) · Physical Review A · doi:10.1103/physreva.95.033610 · Cited by 28
Decoherence in Grover’s quantum algorithm: Perturbative approach
Azuma, H. (2002) · Physical Review A · doi:10.1103/physreva.65.042311 · Cited by 27
Analysis of the quantum Zeno effect for quantum control and computation
Dominy, J. M., Paz-Silva, G. A., Rezakhani, A. T., & Lidar, D. A. (2013) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/46/7/075306 · Cited by 27
Topological features in ion-trap holonomic computation
Pachos, J. K. (2002) · Physical Review A · doi:10.1103/physreva.66.042318 · Cited by 28
Causal structure in the presence of sectorial constraints, with application to the quantum switch
Ormrod, N., Vanrietvelde, A., & Barrett, J. (2023) · Quantum · doi:10.22331/q-2023-06-01-1028 · Cited by 26
Quantum dense coding and dynamics of information over Bloch channels
METWALLY, N. (2011) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/44/5/055305 · Cited by 26
Kamleitner, I., & Shnirman, A. (2011) · Physical Review B · doi:10.1103/physrevb.84.235140 · Cited by 26
Caneva, T., Calarco, T., & Montangero, S. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/9/093041 · Cited by 26
The dynamical-decoupling-based spatiotemporal noise spectroscopy
Krzywda, J. A., Szańkowski, P., & Cywiński, Ł. (2019) · New Journal of Physics · doi:10.1088/1367-2630/ab0ce7 · Cited by 28
Dynamics of collective decoherence and thermalization
Merkli, M., Berman, G. P., & Sigal, I. M. (2008) · Annals of Physics · doi:10.1016/j.aop.2008.07.004 · Cited by 26
Overcoming quantum noise in optical fibers
Wu, L.-A., & Lidar, D. A. (2004) · Physical Review A · doi:10.1103/physreva.70.062310 · Cited by 26
Perturbative expansions for the fidelities and spatially correlated dissipation of quantum bits
Duan, L.-M., & Guo, G. (1997) · Physical Review A · doi:10.1103/physreva.56.4466 · Cited by 26
Quantum computing in a macroscopic dark period
Tregenna, B., Beige, A., & Knight, P. L. (2002) · Physical Review A · doi:10.1103/physreva.65.032305 · Cited by 27
Three-particle QKD protocol against a collective noise
Huang, W., Guo, F.-Z., Huang, Z., Wen, Q., & Zhu, F.-C. (2010) · Optics Communications · doi:10.1016/j.optcom.2010.08.073 · Cited by 25
Unveiling noiseless clusters in complex quantum networks
Cabot, A., Galve, F., Eguı́luz, V. M., Klemm, K., Maniscalco, S., & Zambrini, R. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0108-9 · Cited by 25
Phase diffusion in quantum dissipative systems
Banerjee, S., & Srikanth, R. (2007) · Physical Review A · doi:10.1103/physreva.76.062109 · Cited by 28
Improving the Coherence Time of a Quantum System via a Coupling to a Short-Lived System
Matsuzaki, Y., Zhu, X., Kakuyanagi, K., Toida, H., Shimo-Oka, T., Mizuochi, N., Nemoto, K., Semba, K., Munro, W. J., Yamaguchi, H., et al. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.120501 · Cited by 25
Cooperative Effects in Closely Packed Quantum Emitters with Collective Dephasing
Venkatesh, B. P., Juan, M. L., & Romero‐Isart, O. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.033602 · Cited by 25
Distinguishing between Quantum and Classical Markovian Dephasing Dissipation
Seif, A., Wang, Y.-X., & Clerk, A. A. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.070402 · Cited by 26
Robust and reliable transfer of a qubit state through an XY spin chain
Wang, Z.-M., Bishop, C. A., Byrd, M., Shao, B., & Zou, J. (2009) · Physical Review A · doi:10.1103/physreva.80.022330 · Cited by 25
Universal quantum computation in decoherence-free subspaces with hot trapped ions
Aolita, L., Davidovich, L., Kim, K., & Häffner, H. (2007) · Physical Review A · doi:10.1103/physreva.75.052337 · Cited by 25
Ion-trap quantum computing in the presence of cooling
Beige, A. (2004) · Physical Review A · doi:10.1103/physreva.69.012303 · Cited by 26
Qubit decoherence and non-Markovian dynamics at low temperatures via an effective spin-boson model
Shiokawa, K., & Hu, B. L. (2004) · Physical Review A · doi:10.1103/physreva.70.062106 · Cited by 25
Quantum regression in dephasing phenomena
Lonigro, D., & Chruściński, D. (2022) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ac6a2d · Cited by 26
Entanglement in dissipative dynamics of identical particles
Marzolino, U. (2013) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/104/40004 · Cited by 24
Symmetry Protection of Photonic Entanglement in the Interaction with a Single Nanoaperture
Büse, A., Juan, M. L., Tischler, N., D’Ambrosio, V., Sciarrino, F., Marrucci, L., & Molina‐Terriza, G. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.173901 · Cited by 24
Reduced dynamics and the master equation of open quantum systems
Ban, M., Kitajima, S., & Shibata, F. (2010) · Physics Letters A · doi:10.1016/j.physleta.2010.03.066 · Cited by 24
Communication via an entangled coherent quantum network
Allati, A. E., Hassouni, Y., & METWALLY, N. (2011) · Physica Scripta · doi:10.1088/0031-8949/83/06/065002 · Cited by 24
Phonon sidebands of color centers in hexagonal boron nitride
Khatri, P., Luxmoore, I. J., & Ramsay, A. J. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.125305 · Cited by 23
Influence of phase damping on nonclassical properties of the two-mode Jaynes Cummings model
Hessian, H. A., & Ritsch, H. (2002) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/35/22/305 · Cited by 23
Generation of arbitrary four-photon polarization-entangled decoherence-free states
Gong, Y.-X., Zou, X., Niu, X.-L., Li, J., Huang, Y., & Guo, G. (2008) · Physical Review A · doi:10.1103/physreva.77.042317 · Cited by 23
Quantum remote sensing under the effect of dephasing
Okane, H., Hakoshima, H., Takeuchi, Y., Seki, Y., & Matsuzaki, Y. (2021) · Physical Review A · doi:10.1103/physreva.104.062610 · Cited by 23
Luchnikov, I. A., Kiktenko, E. O., Gavreev, M. A., Ouerdane, H., Filippov, S. N., & Fedorov, A. K. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.043002 · Cited by 23
Decoherence of an n -Qubit Quantum Memory
Gorin, T., Pineda, C., & Seligman, T. H. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.240405 · Cited by 24
Bath-induced band decay of a Hubbard lattice gas
Chen, D., Meldgin, C., & DeMarco, B. (2014) · Physical Review A · doi:10.1103/physreva.90.013602 · Cited by 23
The multiplicative domain in quantum error correction
Choi, M.-D., Johnston, N., & Kribs, D. W. (2009) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/42/24/245303 · Cited by 27
Robust control of decoherence in realistic one-qubit quantum gates
Protopopescu, V., Perez, R., Helon, C. D., & Schmulen, J. (2003) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/36/8/314 · Cited by 24
Decoherence in a N -qubit solid-state quantum register
Ischi, B., Hilke, M., & Dubé, M. (2005) · Physical Review B · doi:10.1103/physrevb.71.195325 · Cited by 23
SHORT-TIME DECOHERENCE AND DEVIATION FROM PURE QUANTUM STATES
PRIVMAN, V. (2002) · Modern Physics Letters B · doi:10.1142/s0217984902003920 · Cited by 23
Quantum metrology with generalized cat states
Tatsuta, M., Matsuzaki, Y., & Shimizu, A. (2019) · Physical Review A · doi:10.1103/physreva.100.032318 · Cited by 24
Calvani, D., Cuccoli, A., Gidopoulos, N. I., & Verrucchi, P. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1217776110 · Cited by 22
Entanglement-induced electron coherence in a mesoscopic ring with two magnetic impurities
Ciccarello, F., Palma, G. M., & Zarcone, M. (2007) · Physical Review B · doi:10.1103/physrevb.75.205415 · Cited by 22
Self-citationEntanglement generation and protection by detuning modulation
Paternostro, M., Tame, M., Palma, G. M., & Kim, M. S. (2006) · Physical Review A · doi:10.1103/physreva.74.052317 · Cited by 22
Self-citationDecoherence by engineered quantum baths
Rossini, D., Calarco, T., Giovannetti, V., Montangero, S., & Fazio, R. (2006) · CERN Document Server (European Organization for Nuclear Research) · Cited by 22
Quantum gambling using two nonorthogonal states
Hwang, W. Y., Ahn, D., & Hwang, S. W. (2001) · Physical Review A · doi:10.1103/physreva.64.064302 · Cited by 22
Popovic, M., Mitchison, M. T., & Goold, J. (2023) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2023.0040 · Cited by 27
Invasiveness of nonequilibrium pure-dephasing quantum thermometry
Albarelli, F., Paris, M. G. A., Vacchini, B., & Smirne, A. (2023) · Physical Review A · doi:10.1103/physreva.108.062421 · Cited by 22
Vanrietvelde, A., Kristjánsson, H., & Barrett, J. (2021) · Quantum · doi:10.22331/q-2021-07-13-503 · Cited by 37
Numerical evaluation and robustness of the quantum mean-force Gibbs state
Chiu, Y.-F., Strathearn, A., & Keeling, J. (2022) · Physical Review A · doi:10.1103/physreva.106.012204 · Cited by 22
Abdel‐Khalek, S., Berrada, K., & Eleuch, H. (2015) · Annals of Physics · doi:10.1016/j.aop.2015.06.015 · Cited by 21
Basic Properties of Quantum Automata
Gudder, S. (2000) · Foundations of Physics · doi:10.1023/a:1003649201735 · Cited by 21
Collective decoherence of nuclear spin clusters
Fedorov, A., & Fedichkin, L. E. (2006) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/18/12/005 · Cited by 21
Thermodynamics and the quantum speed limit in the non-Markovian regime
Das, A., Bera, A., Chakraborty, S., & Chruściński, D. (2021) · Physical Review A · doi:10.1103/physreva.104.042202 · Cited by 20
Quantum-information methods for quantum gravity laboratory-based tests
Marletto, C., & Vedral, V. (2025) · Reviews of Modern Physics · doi:10.1103/revmodphys.97.015006 · Cited by 36
Measurement of two-qubit states by a two-island single-electron transistor
Tanamoto, T., & Hu, X. (2004) · Physical Review B · doi:10.1103/physrevb.69.115301 · Cited by 20
Dynamically stabilized decoherence-free states in non-Markovian open fermionic systems
Xiong, H.-N., Zhang, W.-M., Tu, M. W.-Y., & Braun, D. (2012) · Physical Review A · doi:10.1103/physreva.86.032107 · Cited by 20
Internal decoherence in nano-object interferometry due to phonons
Henkel, C., & Folman, R. (2022) · AVS Quantum Science · doi:10.1116/5.0080503 · Cited by 20
Phase-diffusion pattern in quantum-nondemolition systems
Banerjee, S., Ghosh, J., & Ghosh, R. (2007) · Physical Review A · doi:10.1103/physreva.75.062106 · Cited by 22
Decoherence-free quantum-information processing using dipole-coupled qubits
Brooke, P. G. (2007) · Physical Review A · doi:10.1103/physreva.75.022320 · Cited by 20
Gudder, S. (1999) · International Journal of Theoretical Physics · doi:10.1023/a:1026663432352 · Cited by 20
Scalable ion trap quantum computation in decoherence-free subspaces with pairwise interactions only
Brown, K. R., Vala, J., & Whaley, K. B. (2003) · Physical Review A · doi:10.1103/physreva.67.012309 · Cited by 20
Fidelity of asymmetric dephasing channels
Dajka, J., Mierzejewski, M., & Łuczka, J. (2009) · Physical Review A · doi:10.1103/physreva.79.012104 · Cited by 20
Bath-Assisted Cooling of Spins
ALLAHVERDYAN, A. E., Gracià, R. S., & Nieuwenhuizen, T. M. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.260404 · Cited by 20
Combined error correction techniques for quantum computing architectures
Byrd, M., & Lidar, D. A. (2003) · Journal of Modern Optics · doi:10.1080/09500340308235203 · Cited by 20
Quantum State Transfer with Spin ChainsPreprint
Burgarth, D. K. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0704.1309 · Cited by 20
Slicing the Fock space for state production and protection
Rossetti, R. F., Neto, G. D. D. M., Prado, F. O., Brito, F., & Moussa, M. H. Y. (2014) · Physical Review A · doi:10.1103/physreva.90.033840 · Cited by 19
Maintaining quantum coherence in the presence of noise through state monitoring
Konrad, T., & Uys, H. (2012) · Physical Review A · doi:10.1103/physreva.85.012102 · Cited by 19
Xia, Y., Song, J., Song, H., & Zhang, S. (2008) · Journal of the Optical Society of America B · doi:10.1364/josab.26.000129 · Cited by 19
Parallel decoherence in composite quantum systems
Dugić, M., & Jeknić-Dugić, J. (2012) · Pramana · doi:10.1007/s12043-012-0296-3 · Cited by 19
Bettelli, S. (2004) · Physical Review A · doi:10.1103/physreva.69.042310 · Cited by 19
Quantum Interleaver: Quantum Error Correction for Burst Error
Kawabata, S. (2000) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.69.3540 · Cited by 19
Quantum computing with mixed states
Siomau, M., & Fritzsche, S. (2011) · The European Physical Journal D · doi:10.1140/epjd/e2011-20070-y · Cited by 20
Conservation-law-induced quantum limits for physical realizations of the quantum NOT gate
Karasawa, T., & Ozawa, M. (2007) · Physical Review A · doi:10.1103/physreva.75.032324 · Cited by 19
Efficient schemes for reducing imperfect collective decoherences
Hwang, W.-Y., Lee, H., Ahn, D., & Hwang, S. (2000) · Physical Review A · doi:10.1103/physreva.62.062305 · Cited by 19
Information backflow may not indicate quantum memory
Banacki, M., Marciniak, M., Horodecki, K., & Horodecki, P. (2023) · Physical Review A · doi:10.1103/physreva.107.032202 · Cited by 18
Thermometry by correlated dephasing of impurities in a one-dimensional Fermi gas
Brattegard, S., & Mitchison, M. T. (2024) · Physical Review A · doi:10.1103/physreva.109.023309 · Cited by 20
Spectral density classification for environment spectroscopy
Barr, J., Zicari, G., Ferraro, A., & Paternostro, M. (2024) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ad2cf1 · Cited by 18
Non-Markovian dynamics of a nanomechanical resonator measured by a quantum point contact
Chen, P., Jian, C.-C., & Goan, H. (2011) · Physical Review B · doi:10.1103/physrevb.83.115439 · Cited by 18
Haikka, P., & Maniscalco, S. (2014) · Open Systems & Information Dynamics · doi:10.1142/s1230161214400058 · Cited by 18
Dynamics of entanglement of two electron spins interacting with nuclear spin baths in quantum dots
Bragar, I., & Cywiński, Ł. (2015) · Physical Review B · doi:10.1103/physrevb.91.155310 · Cited by 19
Suppressing phonon decoherence of high performance single-photon sources in nanophotonic waveguides
Dreeßen, C. L., Ouellet-Plamondon, C., Tighineanu, P., Zhou, X., Midolo, L., Sørensen, A. S., & Lodahl, P. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aadbb8 · Cited by 18
Perturbation theory for Lindblad superoperators for interacting open quantum systems
Shishkov, V. Y., Andrianov, E. S., Пухов, А. А., Vinogradov, A. P., & Lisyansky, A. A. (2020) · Physical Review A · doi:10.1103/physreva.102.032207 · Cited by 18
Effective Hamiltonian approach to open systems and its applications
Huang, X. L., Yi, X. X., Wu, C., Feng, X., Yu, S., & Oh, C. H. (2008) · Physical Review A · doi:10.1103/physreva.78.062114 · Cited by 19
Reducing quantum control for spin–spin entanglement distribution
Ciccarello, F., Paternostro, M., Palma, G. M., & Zarcone, M. (2009) · New Journal of Physics · doi:10.1088/1367-2630/11/11/113053 · Cited by 18
Self-citationZhang, J., Peng, X., Rajendran, N., & Suter, D. (2007) · Physical Review A · doi:10.1103/physreva.75.042314 · Cited by 18
Limits on the decay rate of quantum coherence and correlation
Oi, D. K. L., & Schirmer, S. G. (2012) · Physical Review A · doi:10.1103/physreva.86.012121 · Cited by 17
Exotic entanglement for non-Hermitian Jaynes–Cummings Hamiltonians
Frith, T. (2020) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/abbd53 · Cited by 17
Decoherence of interacting qubits in contact with a common environment
Ban, M. (2010) · The European Physical Journal D · doi:10.1140/epjd/e2010-00108-6 · Cited by 17
Simulating a single-qubit channel using a mixed-state environment
Narang, G., & Arvind (2007) · Physical Review A · doi:10.1103/physreva.75.032305 · Cited by 17
Reexamination of the decoherence of spin registers
Tuziemski, J., Lampo, A., Lewenstein, M., & Korbicz, J. K. (2019) · Physical Review A · doi:10.1103/physreva.99.022122 · Cited by 17
Dynamics of a chlorophyll dimer in collective and local thermal environments
Merkli, M., Berman, G. P., Sayre, R. T., Gnanakaran, S., Könenberg, M., Nesterov, A. I., & Song, H. (2016) · Journal of Mathematical Chemistry · doi:10.1007/s10910-016-0593-z · Cited by 19
Ultrafast optical signature of quantum superpositions in a nanostructure
Rodríguez, F. J., Quiroga, L., & Johnson, N. F. (2002) · Physical review. B, Condensed matter · doi:10.1103/physrevb.66.161302 · Cited by 17
Gheorghiu-Svirschevski, S. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.64.051907 · Cited by 17
Metadata
- Authors
- Palma, G. M., Suominen, K., & EKERT, A. K.
- Affiliations
- University of Oxford (GB)
- University of Helsinki (FI)
- Venue
- Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- Publisher
- The Royal Society
- Published
- 1996-12-31
- Volume
- 452
- Issue
- 1946
- Pages
- 567-584
- ISSN
- 1364-5021 (ISSN-L)
- 1471-2946
- OpenAlex
- W2157754228
- Cited by
- 899
- References
- 15
- Citations by year
- 2026: 10 · 2025: 25 · 2024: 22 · 2023: 26 · 2022: 29 · 2021: 22 · 2020: 23 · 2019: 32 · 2018: 34 · 2017: 35 · 2016: 38 · 2015: 31 · 2014: 29 · 2013: 37 · 2012: 25
- FWCI
- 26.76
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (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 › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum computing, energy dissipation, decoherence, quantum registers, environment coupling, computational complexity, quantum factoring, Shor's algorithm, algorithm efficiency
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