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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.
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: 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
“Hence there is no real decay of the coherences present in a single ensemble member, but merely a shift in phase.”
Load-bearingStrength:plain· not yet calibratedTests✓ 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
“In Eq.(21) we can separate the effects due to thermal noise from the one due to purely quantum fluctuations.”
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).
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
“For η ∼ 1 this decay is dominated by the thermal fluctuations of the reservoir and it is therefore exponential.”
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.
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
“In (a) the coherence always decays to zero.”
Load-bearingStrength:plain· not yet calibratedTests✓ 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
“The above discussion makes it clear that U(t) induces entanglement between qubit states and field states.”
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).
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
“Our semiclassical simulations for a single quantum bit demonstrate how the full statistical result is obtained by adding the individual members of the ensemble.”
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
“In (b) the system shows a very different behaviour: the decoherence saturates to a value determined by η .”
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 all cases there is a short t region where almost no decay is present.”
Strength:plain· 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.
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
“Consequently, in order to obtain factors of N with a prescribed probability of success one has to repeat the computation k times, where k grows exponentially with L .”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: In the amplification argument, the error rate ǫ is independent of the input.
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 paper shows that Shor's algorithm, in order to be efficient from the computational complexity perspective, must be modified (i.e. supplemented with an exponentially efficient quantum error correction).”
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.
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
“Let us stress that this observation is not related to any technological limitations but is a consequence of the computational complexity requirements imposed on any realistic model of computation.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesNone of the sources cited for this claim have been checked yet.
In the paper
“As the result quantum computers can efficiently solve some problems which are believed to be intractable on any classical computer (Deutsch 1985, Deutsch and Jozsa 1992, Bernstein and Vazirani 1993, Simon 1994, Shor 1994).”
What the sources say
- Not checked yetcites Deutsch 1985
- Not checked yetcites Deutsch and Jozsa 1992
- Not checked yetcites Bernstein and Vazirani 1993
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“The most striking example is the factoring problem: to factor a number N of L digits on any classical computer requires an execution time that grows exponentially with L (approximately exp L 1 / 3 for the best known algorithms such as the Number Field Sieve (Lenstra et al. 1990)).”
What the sources say
- Not checked yetcites Lenstra et al. 1990
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“We believe that as long as the reservoir is in a thermal state, any model of decoherence will lead to the same conclusions.”
Load-bearingStrength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearA 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
“It should be noted however that U ( t ) acts as a displacement operator on the field with a displacement amplitude depending on the logic value of both qubits of the register.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“However, if one can support quantum computation with some selected coherences then a large coherence length can be utilised.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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 general the set of states which are robust against the dephasing action of the environment will depend on the specific form of qubit-environment coupling.”
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA 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
“Reservoirs with large coherence lengths introduce only asymmetry in the decoherence rates of various off-diagonal elements of the density matrix with the same Hamming distance between its indices (compare Eq. (41) with Eq. (42)).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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 a semiclassical picture if the distance between the two qubits is smaller than the correlation length of the bath they 'feel' the same fluctuation.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“Even if quantum algorithms for factorisation are not efficient from the complexity theory point of view, they may still permit factoring of numbers which are much bigger than those that can be factored using classical algorithms.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“It is precisely this entanglement which, in the fully quantised description we have adopted, is responsible for the decoherence process.”
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).
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 )) regardles the functional dependence Γ( t ).”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearA 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
“However, when we consider the effect of the thermal and vacuum fluctuations, such a semiclassical view on the interaction of the qubit with the reservoir is not adequate, and one has to apply a fully quantum approach, which we shall present next.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“It should however be pointed out that at longer timescales, when T 1 processes involving exchange of energy between qubit and environment take place, this residual coherence will disappear.”
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIn the paper
“In order to avoid possible confusions it must be stressed that the phenomenon of superdecoherence vs. subdecoherence that we have just described is not the same as the process of superradiance vs. subradiance more commonly encountered in litterature (see e.g Allen & Eberly 1975).”
What the sources say
- Not checked yetcites Allen & Eberly 1975
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA 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
“- a 'quiet' regime, for t < ω -1 c , where the fluctuations are ineffective in the decoherence process”
Load-bearingStrength:plain· not yet calibratedTests✓ 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.
In the paper
“However, it should be mentioned that in some cases populations can be more fragile than coherences.”
What the sources say
- Not checked yetcites Kimble & Mabuchi 1995
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA 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 'noiseless' encoding does not pose complexity problems since to encode L qubits we need simply 2L qubits.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearNone of the sources cited for this claim have been checked yet.
In the paper
“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).”
What the sources say
- Not checked yetcites Leggett et al. 1987
- Not checked yetcites Gardiner 1991
- Not checked yetcites Unruh 1995
Strength:plain· not yet calibratedCausal:correlational· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA 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
“From the equation above follows that the size L is bounded by”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“Technological progress in isolating quantum computers from the environment and suppressing decoherence will increase the size of the biggest number that can be factored by such computers.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“- a thermal regime, for t > T -1 , where thermal fluctuations play the major role in eroding the qubit coherence.”
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.
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
“Here again the unitary evolution produces entanglement between register states and environment states.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“- a quantum regime, for ω -1 c < t < T -1 , where the main cause of coherence loss are the quantum vacuum fluctuations”
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.
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
“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) then we are forced to conclude that reservoirs with a large coherence length can be more of a hindrance than a help.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: All coherences are equally important.
- 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.
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 a realistic scenario the probability of error ǫ ( L ) has also contributions which are due to the computer - environment coupling.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes? Based: unclearA 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 produces a reduction - or an enhancement - of the decay rates depending on whether the phase shifts on the two qubits add or subtract.”
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“From the computational complexity point of view it is irrelevant how weak this coupling is for a fixed L , it is its dependence on L which matters.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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 because the cut-off frequency ω c determines the extent of the 'quiet' regime.”
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.
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
“More generally the random phase-shifts due to the bath fluctuations of wavelength shorter than the inverse of the qubit separation are the same for both qubits.”
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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
“It is evident that the so-called quantum vacuum fluctuations will contribute to the dephasing process only for times t > ω -1 c .”
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.
In the paper
“This formal separation allows us to identify the existence of various timescales in the decoherence process (see also Unruh 1995).”
What the sources say
- Not checked yetcites Unruh 1995
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).
- 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.
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 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.
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
“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.
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
“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.
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
“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).”
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?
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]
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.
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
Flagged first, then by citations
Research works printed but not linked: 1
- Lenstra A. K. Lenstra H. W. Jr Manasse M. S. & Pollard J. M. 1990 Proc. 22th ACM Symp. j on the Theory of
Cited by
Sorted by citations
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539795293172 · Cited by 8,472
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1999) · SIAM Review · doi:10.1137/s0036144598347011 · Cited by 3,904
Lloyd, S. (1996) · Science · doi:10.1126/science.273.5278.1073 · Cited by 3,088
Good quantum error-correcting codes exist
Calderbank, A. R., & Shor, P. W. (1996) · Physical Review A · doi:10.1103/physreva.54.1098 · Cited by 2,516
Decoherence-Free Subspaces for Quantum Computation
Lidar, D. A., Chuang, I. L., & Whaley, K. B. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.2594 · Cited by 1,818
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
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.
A language model drew the claims from the paper on 2026-10-06, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-06 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
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