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Cited by 385Quantum Computing Algorithms and ArchitectureQuantum many-body systemsQuantum Information and Cryptography

A generative modeling approach for benchmarking and training shallow quantum circuits

Open access
Benedetti, Marcello, Garcia-Pintos, Delfina, Perdomo, Oscar, Leyton-Ortega, Vicente, Nam, Yunseong, Perdomo-Ortiz, Alejandro·2019·npj Quantum Information
DOI 10.1038/s41534-019-0157-8
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Abstract

Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications. Expanding the portfolio of such techniques, we propose a quantum circuit learning algorithm that can be used to assist the characterization of quantum devices and to train shallow circuits for generative tasks. The procedure leverages quantum hardware capabilities to its fullest extent by using native gates and their qubit connectivity. We demonstrate that our approach can learn an optimal preparation of the Greenberger-Horne-Zeilinger states, also known as “cat states”. We further demonstrate that our approach can efficiently prepare approximate representations of coherent thermal states, wave functions that encode Boltzmann probabilities in their amplitudes. Finally, complementing proposals to characterize the power or usefulness of near-term quantum devices, such as IBM’s quantum volume, we provide a new hardware-independent metric called the qBAS score. It is based on the performance yield in a specific sampling task on one of the canonical machine learning data sets known as Bars and Stripes. We show how entanglement is a key ingredient in encoding the patterns of this data set; an ideal benchmark for testing hardware starting at four qubits and up. We provide experimental results and evaluation of this metric to probe the trade off between several architectural circuit designs and circuit depths on an ion-trap quantum computer.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper proposes data-driven quantum circuit learning (DDQCL), a hybrid quantum-classical generative modeling framework that uses Born-rule probabilities from shallow quantum circuits and introduces the qBAS score for benchmarking NISQ/hybrid systems. It demonstrates learning GHZ/cat-state preparations, coherent thermal states, and Bars-and-Stripes patterns in simulations and on an ion-trap quantum computer.

Key findings

  • DDQCL learned GHZ-like state preparation recipes from classical samples: 3- and 5-qubit instances yielded one recipe, while 4- and 6-qubit instances yielded another; parameters converged close to π/2, and the recipes generalized to larger odd and even qubit numbers.
  • For coherent thermal states with N = 5 qubits, deeper circuits (L = 3) consistently outperformed shallower circuits (L = 2 and L = 1) as the task became harder by lowering temperature from 2T_c to T_c to T_c/1.5; the inverse Bethe approximation performed extremely well in the easy task, matched L = 3 in the intermediate task, and underperformed in the difficult task.
  • For BAS(2, 2), the minimum entanglement entropy of any state encoding the data set is S_BAS(2,2) = 1.25163 and the maximum is S_BAS(2,2) = 1.79248; DDQCL found a representation with S_BAS(2,2) = 1.69989. All-to-all topology outperformed sparse topologies, and qBAS(2, 2) was computed with N_reads = 15 samples.
  • The qBAS score is an F1-based, hardware-independent metric on Bars and Stripes; example readout requirements include N_reads = 15 for (2, 2), 120 for (4, 4), and 16,780 for (10, 10).

Methods

  • DDQCL maps binary data vectors to computational-basis states of an N-qubit circuit. The circuit uses alternating layers of arbitrary single-qubit rotations and Mølmer-Sørensen XX entangling gates; Born’s rule gives P_θ(x) = |⟨x|ψ(θ)⟩|². Training minimizes a clipped negative log-likelihood C_nll(θ) = −(1/D) Σ ln(max(ε, P_θ(x^(d)))) using gradient-free particle swarm optimization, with 1000 measurements per estimation.
  • Data sets are synthetic: zero-temperature ferromagnet/GHZ, random thermal Boltzmann distributions with N = 5 qubits (and N = 6 in supplementary), and BAS(2, 2). Numerical experiments use 1000 data points sampled exactly from these distributions, 25 random initializations, and bootstrapping for error bars. Simulations used QuTiP2; experiments ran on an ion-trap quantum computer at the University of Maryland.
  • The qBAS(n, m) score is the harmonic mean of precision and recall on BAS patterns, with N_reads = N_BAS(n,m) H_{N_BAS(n,m)}. The paper compares all-to-all, chain, and star entangling topologies and different layer counts.

Limitations

  • The paper states that the negative log-likelihood cost becomes expensive to estimate as system size increases, that alternative cost functions are only preliminary, that optimizing N_reads is left for future work, and that KL divergence may become undefined for large n × m. It also notes simulations assumed noiseless hardware, deeper circuits did not always improve performance due to optimization/local optima, and the experimental L = 4 improvement was smaller than theoretical because the quantum computer accumulated errors in the deeper circuit.
  • Evident from the text: experimental validation is limited to small instances—GHZ training up to 6 qubits, thermal states at N = 5, and BAS(2, 2) on 4 qubits—and qBAS experiments were performed on a single ion-trap device. The GHZ recipe extraction also relied on human expert inspection and rounding of learned parameters.

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Crossref · 10.1038/s41534-019-0157-8

Cites

71 of 71 references verified0 citation errors · 0 not checkable

Statistics

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Claims the paper makes

0 of 18 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    The GHZ preparation recipes obtained were verified for larger numbers of qubits, both odd and even.

    “The recipes obtained are summarized in Fig. 3 and were verified for larger number of qubits, both odd and even.”
    Quote in the paperNot a substantial claim
  • Findingown data

    Deeper circuits with L = 3 consistently outperformed shallower circuits with L = 2 and L = 1 in approximating the target Boltzmann distribution.

    “Deeper circuits such as L = 3 (purple pentagons) consistently outperformed shallower circuits such as L = 2 (red circles) and L = 1 (yellow triangles).”
    Quote in the paperSubstantial claim
  • Findingown data

    Deeper circuits do not always provide significant improvements, as in the case of all-to-all L = 4 versus all-to-all L = 2.

    “However, deeper circuits do not always provide significant improvements, as it is the case for all-to-all L = 4 (dark green circles) versus all-to-all L = 2 (orange circles).”
    Quote in the paperSubstantial claim
  • Findingnone given

    DDQCL obtained circuits for cat state preparation starting from samples of a classical distribution.

    “Finally, it is reassuring that DDQCL obtained circuits for cat state preparation starting from samples of a classical distribution.”
    Quote in the paperNot a substantial claim
  • Findingown data

    Single-layer circuits with no entangling gates severely underperform in producing an output state probability distribution close to the target data set.

    “This is an important observation, since we know, based on our empirical results, that (i) single layer circuits with no entangling gates severely underperform in producing the output state probability distribution that is close to the target data set”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim. 32
  • May combine two claims. 20
  • The quote only partly states this claim. 2

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

    Findingcitation

    The maximum entanglement entropy that a quantum representation of BAS(2,2) can reach is S_BAS(2,2) = 1.79248, which is the maximum entanglement entropy known for any four-qubit state.

    “Furthermore, the maximum value that a quantum representation of BAS(2, 2) can reach is S BAS(2,2) = 1.79248, which happens to be the maximum entanglement entropy known for any four-qubit state 56 (see also Fig. S5 and the corresponding Section in the Supplementary Material).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [56] Higuchi, A. & Sudbery, A. W. How entangled can two couples get? Phys. Lett. A 273, 213–217 (2000). source

      Not checked in the free run.

  • May combine two claims.

    Findingown data

    Instances of 3 and 5 qubits yielded one GHZ preparation recipe, while instances of 4 and 6 qubits yielded another recipe.

    “Instances of 3 and 5 qubits yielded a recipe, while instances of 4 and 6 qubit yielded another recipe.”
    Quote in the paperSubstantial claim

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

    Findingnone given

    The minimum entanglement entropy that any state encoding BAS(2,2) in the computational basis can have is S_BAS(2,2) = 1.25163.

    “The minimum value of entanglement entropy that any such state can have is S BAS(2,2) = 1.25163.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The inverse Bethe approximation performed extremely well in the easy task, matched the L = 3 quantum circuit in the intermediate task, and underperformed on the difficult task.

    “As shown in Fig. 4, the inverse Bethe approximation (green bar) performed extremely well in the easy task (a), matched the L = 3 quantum circuit in the intermediate task (b), and underperformed on the difficult task (c).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The qBAS(2,2) score is sensitive to circuit depth: for the star topology, L=4 circuits perform better than L=2 circuits.

    “The score is sensitive to the depth of the circuit as shown by the performance improvement of L = 4 compared with L = 2 in the star topology.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    For deeper circuits with L=4 and approximately twice the number of parameters, all topologies achieve a lower median KL divergence and the confidence intervals shrink.

    “All the topologies achieve a lower median KL divergence and the confidence intervals shrink.”
    Quote in the paperNot a substantial claim

  • The quote only partly states this claim.

    Findingreasoning

    A task-specific performance estimator based on the bars and stripes (BAS) data set was designed for near-term quantum devices and approximate algorithms.

    “Finally, tapping into the real power of near-term quantum devices and approximate algorithms implementable on them, we designed a task-specific performance estimator based on a canonical data set.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The chain topology performs slightly better than the star topology even though they have the same number of parameters.

    “The chain topology (purple squares) performs slightly better than the star topology (red stars) even though they have the same number of parameters.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingnone given

    DDQCL learned a GHZ state preparation recipe for an ion trap quantum computer, and minimal human expert intervention allowed generalization of the recipe to any number of qubits.

    “To summarize, first, we learned a GHZ state preparation recipe for an ion trap quantum computer.Minimal intervention by a human expert allowed to generalize the recipe to any number of qubits.”
    Quote in the paperSubstantial claim

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

    Interpretationnone given

    The KL divergence is a more general performance indicator than the qBAS(n,m) score.

    “We note that a more general performance indicator than qBAS (n, m) score is indeed the KL divergence, D KL [P BAS(n,m) |P θ ].”
    Quote in the paperNot a substantial claim

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

    Premisecitation

    The four-qubit cat state has entanglement entropy S_GHZ = 1.

    “We start by noting that the four-qubit cat state, whose rich entangled nature makes it ideal for studying decoherence and decay of quantum information, 49,51 has entanglement entropy S GHZ = 1.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [49] Monz, T. et al. 14-qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011). source

      Not checked in the free run.

    • cites [51] Ozaeta, A. & McMahon, P. L. Decoherence of up to 8-qubit entangled states in a 16-qubit superconducting quantum processor. Quantum Sci. Technol. 4, 025015 (2019). source

      Not checked in the free run.

  • May combine two claims.

    Premisenone given

    DDQCL prepares a quantum state without assuming an underlying Boltzmann distribution, while the inverse Bethe approximation infers parameters with that assumption.

    “DDQCL prepares a quantum state without the assumption of an underlying Boltzmann distribution, while the inverse Bethe approximation infers the parameters with such assumption.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    The qBAS score can still be computed and the number of measurements N_reads necessary for a robust estimate remains relatively small and practical for intermediate-size n × m.

    “In all these cases, the qBAS score can still be computed and the number of measurements N reads necessary for obtaining a robust estimate continues to remain relatively small to be practical for intermediate size n × m.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: For setting N_reads, the model distribution is equal to the target distribution P_BAS(n,m).

  • Classified as probably not a substantial claim.

    Premisecitation

    Learning probabilistic generative models is in many cases an intractable task.

    “For example, learning probabilistic generative models is in many cases an intractable task, and quantum-assisted algorithms have been proposed for both gate-based 17,18 and quantum annealing devices.[19][20][21][22][23]”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [17] Nathan Wiebe, K. M. S. & Kapoor, A. Quantum deep learning. Preprint at arXiv:1412.3489 (2015).

      Not checked in the free run.

    • cites [18] Kieferová, M. & Wiebe, N. Tomography and generative training with quantum boltzmann machines. Phys. Rev. A 96, 062327 (2017). source

      Not checked in the free run.

    • cites [19][20][21][22][23]

      Not checked in the free run.

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

    Interpretationreasoning

    DDQCL can learn to compensate certain types of noise, such as systematic parameter offsets, in non-trivial ways.

    “It would be much more difficult to analyze parameters found with noisy hardware, as DDQCL can learn to compensate certain types of noise, e.g., systematic parameter offsets, in non-trivial ways.”
    Quote in the paperNot a substantial claim

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

    Interpretationcitation

    Other classical methods based on machine learning and Markov Chain Monte Carlo, such as the Boltzmann machine, could achieve higher accuracy by requiring more computational resources than the inverse Bethe approximation used here.

    “Other classical methods based on machine learning and Markov Chain Monte Carlo, such as the Boltzmann machine, 55 could achieve higher accuracy by requiring more computational resources than the inverse Bethe approximation used here.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [55] Ackley, D. H., Hinton, G. E. & Sejnowski, T. J. A learning algorithm for boltzmann machines. Cogn. Sci. 9, 147–169 (1985). source

      Not checked in the free run.

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

    Premisecitation

    Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications.

    “Hybrid quantum-classical algorithms, such as the variational quantum eigensolver 2,3 (VQE) and the quantum approximate optimization algorithm 4,5 (QAOA), provide ways to use NISQ computers for practical applications.”
    Quote in the paperNot a substantial claim0 of 4 sources checked
    • cites [2] Peruzzo, A. et al. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213 EP (2014). source

      Not checked in the free run.

    • cites [3] McClean, J. R., Romero, J., Babbush, R. & Aspuru-Guzik, A. The theory of variational hybrid quantum-classical algorithms. New J. Phys. 18, 023023 (2016). source

      Not checked in the free run.

    • cites [4] Edward Farhi, S. G. & Goldstone, J. A. quantum approximate optimization algorithm. Preprint at arXiv:1411.4028 (2014).

      Not checked in the free run.

    • cites [5] Hadfield, S. et al. From the quantum approximate optimization algorithm to a quantum alternating operator ansatz. Algorithms 12, 34 (2019). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S2 (checkable).

    Premisecitation

    Probabilistic tasks involving sampling have most of the potential to prove quantum advantage in the near term.

    “Although optimization tasks offer a great niche of applications, probabilistic tasks involving sampling have most of the potential to prove quantum advantage in the near-term.[14][15][16]”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [14][15][16]

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    The error in the inverse Bethe approximation is expected to go to zero with system size, and only above the reference temperature Tc.

    “Furthermore, the error in the inverse Bethe approximation is expected to go to zero with system size, and only above the reference temperature T c (see Section “Methods” for details).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Methods

      Not checked in the free run.

  • May combine two claims. The quote only partly states this claim.

    Interpretationreasoning

    The number of parameters can be slightly reduced without changing the expressive power of the circuit by omitting the first set of Rz rotations and, for odd layers, the last set.

    “In other words, we can slightly reduce the number of parameter without changing the expressive power of the circuit.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationreasoning

    The qBAS score depends on classical resources, hyperparameters, and various design choices.

    “Moreover, the score depends on the classical resources, hyperparameters, and various design choices, making it a good choice for the assessment of the hybrid system as a whole.”
    Quote in the paperSubstantial claim

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

    Interpretationreasoning

    Any miscalibration or environmental noise will affect the qBAS single performance number, enabling comparison between different devices or across generations of the same device.

    “Hence, any miscalibration or environmental noise will affect this single performance number, enabling comparison between different devices or across different generations of the same device.”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given

    The qBAS score may be used to compare classical resources of the hybrid system, such as different optimizers.

    “Similarly, one may use the score to compare classical resources of the hybrid system (e.g., different optimizers).”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given

    Once the number of layers and topology of entangling gates is fixed, the quantum circuits provide a template; by adjusting parameters we can implement a small subset of the unitaries allowed in Hilbert space.

    “Once the number of layers and topology of entangling gates is fixed, the quantum circuits described above provide a template; by adjusting the parameters we can implement a small subset of the unitaries that are in principle allowed in the Hilbert space.”
    Quote in the paperNot a substantial claim

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

    Premisecitation

    Previous implementations of Born machines often relied on the construction of tensor networks and their efficient manipulation through graphical-processing units.

    “Previous implementations of Born machines [25][26][27][28] often relied on the construction of tensor networks and their efficient manipulation through graphical-processing units.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [25][26][27][28]

      Not checked in the free run.

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

    Premisenone given

    For a star topology, the number of parameters per entangling layer is N-1.

    “The total number of parameters per entangling layer depends on the chosen topology: all is a fully-connected graph and has N(N -1)/2 parameters, chain is a one-dimensional nearest neighbor graph with N -1 parameters, and star is a star-shaped graph with N-1 parameters.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    DDQCL is a data-driven quantum circuit learning algorithm framework that can assist in characterizing NISQ devices and implementing simple generative models.

    “In this work, we presented a data-driven quantum circuit learning algorithm (DDQCL) as a framework that can assist in the characterization of NISQ devices and to implement simple generative models.”
    Quote in the paperSubstantial claim

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

    Interpretationnone given

    The qBAS score may be used to compare different device generations or completely different quantum computing architectures (e.g., superconductor-based versus atomic-based).

    “Although we compared circuits implemented on the same ion trap hardware, the score may be used to compare different device generations or even completely different architectures (e.g., superconductor-based versus atomic-based).”
    Quote in the paperNot a substantial claim

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

    Premisecitation

    Bars and stripes (BAS) is a canonical machine learning data set for testing generative models.

    “Bars and stripes BAS 47 is a canonical machine learning data set for testing generative models.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [47] MacKay, D. J. C. Information Theory, Inference and Learning Algorithms. (Cambridge University Press, New York, 2002).

      Not checked in the free run.

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

    Interpretationreasoning

    The only way to reproduce the zero-temperature ferromagnet distribution in our setting is to implement a unitary transformation that prepares a GHZ-like state.

    “The only way to reproduce the zero-temperature ferromagnet distribution in our setting is to implement a unitary transformation that prepares a GHZ-like state.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    Errors in the device affect the qBAS score, which can be used to compare different device generations or completely different architectures.

    “Errors in the device will affect this single performance measure, the qBAS score, which can be used to compare different device generations, or completely different architectures.”
    Quote in the paperSubstantial claim

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

    Interpretationnone given

    The number of measurements needed to obtain an unbiased estimate of the relevant probabilities may not scale favorably with the number of qubits N.

    “Note that the number of measurements needed to obtain an unbiased estimate of the relevant probabilities may not scale favorably with the number of qubits N.”
    Quote in the paperNot a substantial claim

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

    Interpretationreasoning

    The GHZ state preparation result is not an example of compilation but an illustration of how simple classical probability distributions can guide the synthesis of non-trivial quantum states.

    “This is not an example of compilation, but rather an illustration of how simple classical probability distributions can guide the synthesis of interesting non-trivial quantum states.”
    Quote in the paperNot a substantial claim

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

    Premisenone given

    The zero-temperature ferromagnet distribution is equivalent to assigning 1/2 probability to both |0...0> and |1...1> states of the computational basis.

    “The zero-temperature ferromagnet distribution is equivalent to assigning 1/2 probability to both |0…0〉 and |1…1〉 states of the computational basis.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisereasoning

    Our work does not assume a Boltzmann distribution and therefore does not require a specific sampling beyond Born's rule.

    “In contrast, our work does not assume a Boltzmann distribution and therefore does not require a specific sampling beyond Born's rule.”
    Quote in the paperSubstantial claim

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

    Interpretationreasoning

    The qBAS score can be used to benchmark the typical performance of optimizers used in hybrid quantum-classical systems.

    “The qBAS score can also be used to benchmark the typical performance of optimizers used in hybrid quantum-classical systems.”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given

    Depending on the level or type of noise in the system, the same DDQCL algorithm could lead to a different circuit fulfilling the same probability distribution as the data.

    “Depending on the level or type of noise in the system, the same algorithm could lead to a different circuit fulfilling the same probability distribution as that of the data.”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given

    The bars and stripes data set is easy to generate, visualize and verify classically, while modeling it still requires significant quantum resources in the form of entanglement.

    “The bars and stripes data is easy to generate, visualize and verify classically, while modeling it still requires significant quantum resources in the form of entanglement.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    Implementing a shallow circuit that can uniformly sample Bars and Stripes data is hard, and some candidate solutions require a large amount of entanglement.

    “Yet, implementing a shallow circuit that can uniformly sample such data is hard; we will show that some candidate solutions require large amount of entanglement.”
    Quote in the paperSubstantial claim

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

    Interpretationnone given

    Our approach has the bidirectional capability of using NISQ devices for machine learning and machine learning for the characterization of NISQ devices.

    “Our approach has the bidirectional capability of using NISQ devices for machine learning, and machine learning for the characterization of NISQ devices.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Interpretationreasoning

    The qBAS score is a complementary metric to quantum volume for benchmarking hybrid quantum-classical systems.

    “In this paper, we propose the qBAS score, a complementary metric designed for benchmarking hybrid quantum-classical systems.”
    Quote in the paperSubstantial claim

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

    Interpretationnone given

    The negative log-likelihood cost function quickly becomes expensive to estimate as the size of the system increases.

    “In this paper, we used the negative log-likelihood which quickly becomes expensive to estimate as the size of the system increases.”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given

    The qBAS score is a hardware-independent metric.

    “Finally, complementing proposals to characterize the power or usefulness of near-term quantum devices, such as IBM's quantum volume, we provide a new hardware-independent metric called the qBAS score.”
    Quote in the paperNot a substantial claim

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

    Premisereasoning

    For a chain topology, the number of parameters per entangling layer is N-1.

    “The total number of parameters per entangling layer depends on the chosen topology: all is a fully-connected graph and has N(N -1)/2 parameters, chain is a one-dimensional nearest neighbor graph with N -1 parameters, and star is a star-shaped graph with N-1 parameters.”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given

    The qBAS score can be computed in any of the NISQ architectures available to date.

    “The score can be computed in any of the NISQ architectures available to date.”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given

    DDQCL is a modular framework whose performance ultimately depends on the choices made for its modules.

    “DDQCL is a modular framework and its performance will ultimately depend on the choices made for such modules.”
    Quote in the paperNot a substantial claim

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

    Premisereasoning

    For an all-to-all topology, the number of parameters per entangling layer is N(N-1)/2.

    “The total number of parameters per entangling layer depends on the chosen topology: all is a fully-connected graph and has N(N -1)/2 parameters, chain is a one-dimensional nearest neighbor graph with N -1 parameters, and star is a star-shaped graph with N-1 parameters.”
    Quote in the paperNot a substantial claim
47 of 47

  • The authors state this as an assumption.

    The data vectors in the data set D are independent and identically distributed random vectors.

    “The data set D ¼ ðx ð1Þ ; ; x ðDÞ Þ is a collection of D independent and identically distributed random vectors.”

  • The authors state this as an assumption.

    For setting N_reads, the model distribution is equal to the target distribution P_BAS(n,m).

    “Assuming a perfect model distribution P BAS(n,m) = 1/ N BAS(n,m) , the expected number of measurements to obtain a value of r = 1.0 can be estimated using the famous coupon collector's problem.”

  • The authors state this as an assumption.

    For simulations in silico, perfect gate fidelities and error-free measurements are assumed.

    “For the simulations in silico, we also assume perfect gate fidelities and error-free measurements.”

  • The paper relies on this without support.

    In the current ion trap experimental setup, arbitrary single-qubit rotations and Mølmer-Sørensen XX entangling gates involving any two qubits can be performed.

    “In the current experimental setup, we can perform arbitrary single qubit rotations and Mølmer-Sørensen XX entangling gates involving any two qubits.”
4 of 4

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?

  • Benedetti et al. proposed the qBAS score metric for benchmarking shallow quantum-classical hybrid systems using synthetic data set.

    “Benedetti et al. [10] proposed the qBAS score metric for benchmarking the shallow quantum-classical hybrid systems using synthetic data set.”

    From QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation (2023) · cites this paper as [10]

  • Quantum autoencoders have seen experimental implementation on quantum hardware and will likely be an important primitive in QML.

    “Quantum autoencoders have seen experimental implementation on quantum hardware [168], and will likely be an important primitive in QML.”

    From Variational quantum algorithms (2021) · cites this paper as [168]

    The Introduction mentions approaches proposed for training quantum autoencoders, but does not say they were experimentally implemented on quantum hardware. The paper’s reported ion-trap experiments concern its own circuit-learning method, not autoencoders. Searches for autoencoder hardware experiments found no passage establishing the cited claim. (LLM, conf=0.72)

    Experimental — accuracy not yet measured

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Research works printed but not linked: 1

  1. Monz, T. et al. 14-qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011). · DOI · Paper page

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Related

Authors
Benedetti, M., Garcia-Pintos, D., Perdomo, O., Leyton-Ortega, V., Nam, Y., & Perdomo-Ortiz, A.
Affiliations
  • Cambridge Quantum Computing (United Kingdom) (GB)
  • Central Connecticut State University (US)
  • IonQ (United States) (US)
ORCID
Venue
npj Quantum Information
Publisher
Springer Science and Business Media LLC
Published
2019-05-27
Volume
5
Issue
1
ISSN
2056-6387 (ISSN-L)
DOI
10.1038/s41534-019-0157-8
OpenAlex
W2784994528
Cited by
379
References
71
Citations by year
2026: 42 · 2025: 75 · 2024: 55 · 2023: 49 · 2022: 42 · 2021: 65 · 2020: 29 · 2019: 12 · 2018: 10
FWCI
16.88
Type
journal article
Language
en
Open access
Licence
Locations
  • npj Quantum Information (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • UCL Discovery (University College London) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • RCUK | Engineering and Physical Sciences Research Council
  • Cambridge Quantum Computing Limited
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
Keywords
quantum circuit learning, shallow quantum circuits, generative models, hybrid quantum-classical algorithms, quantum device characterization, GHZ states, Schrödinger cat states, thermal states, quantum volume, entanglement, ion trap quantum computer, qubit connectivity, benchmarking

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-10.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-10.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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