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REVIEW 3 major objections 6 minor 117 references

Learning the physics of open quantum systems from experiments

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This thesis claims that Bayesian inference with modern Monte Carlo sampling can characterize open quantum systems on real quantum hardware, and that the resulting estimates beat the device vendor's built-in characterization routines when…

desk verdict A well-written thesis that applies standard Bayesian/Monte Carlo machinery to real IBMQ data, but the headline claim about beating Qiskit needs more experimental support before it fully convinces. read the letter →

arxiv 2412.00078 v1 pith:RMSJULL4 submitted 2024-11-26 quant-ph

Alexandra Ramôa This is my paper · ORCID
classification quant-ph MSC 62F1565C0581P6881P50
keywords BayesianinferenceopenquantumsystemscharacterizationHamiltonianMonteCarlosequentialKrausoperatorsqubitdecoherencedevicecalibration
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This thesis argues that Bayesian inference stops being a theoretical ideal and becomes a practical characterization tool once it is paired with the right numerical samplers. The author constructs likelihood models for a single qubit undergoing spin precession, energy relaxation, and dephasing, using a Kraus-operator description of the open-system dynamics, and infers the qubit's frequency, T1 (energy decay time), and T2 (dephasing time) from measurements taken on cloud-accessible superconducting hardware. The central claim is that Hamiltonian Monte Carlo and sequential Monte Carlo with Markov kernels produce posterior estimates that are more accurate than the vendor's built-in characterization functions at the same measurement budget. A sympathetic reader would care because the approach extracts more information per measurement and returns a full posterior distribution, including an honest statement of uncertainty, rather than a single point estimate.

What carries the argument

The load-bearing object is the Kraus operator-sum representation of the qubit's evolution, a standard way of writing a noisy quantum channel as a sum over jump operators, which converts the physical model into a likelihood function the inference can evaluate. For a single qubit this representation is small enough to write analytically: a precession term exp(-i(ω/2)σ_z t), an amplitude-damping channel built from the T1 rate, and a phase-damping channel built from the T2 rate. The paper couples this likelihood to two families of samplers: Hamiltonian Monte Carlo, including the no-U-turn sampler, which uses gradient information to explore the posterior; and sequential Monte Carlo with Markov kernels, including tempered likelihood estimation, which maintains a particle cloud through a sequence of distributions. The choice of samplers is what lets the posterior be represented without a fixed grid or a Gaussian assumption, and that representation is what carries the claimed gain in accuracy.

What would settle it

Run the same four experiments on a qubit whose noise is deliberately made non-Markovian, for instance by coupling it to a two-level defect or by letting the T1 and T2 rates drift partway through the data collection, and compare the Bayesian credible intervals with independently measured parameter values. If the credible intervals exclude the independent values while the vendor's built-in routines stay close, the model-misspecification concern is confirmed. A simpler version: interleave the Bayesian characterization with a separate measurement method on the same qubit and check whether the intervals cover the independent result.

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Extended reading notes

Core claim

The paper's central discovery is that a Bayesian pipeline built around a Kraus-operator likelihood and sampled with advanced Monte Carlo outperforms the vendor's built-in characterization on real hardware. The likelihood encodes the full dynamics: a Hamiltonian rotation with unknown frequency, an amplitude-damping channel with rate 1/T1, and a phase-damping channel with rate 1/T2. On Hahn echo, T1, Ramsey, and echoed Ramsey experiments, the Bayesian posterior mean estimates of these parameters are claimed to be more accurate than the vendor's own characterization routines for the same number of measurements, while also supplying credible intervals. This is presented as evidence that the bottleneck in Bayesian quantum characterization is representation of the posterior, and that replacing particle-filter or Gaussian approximations with HMC/NUTS and sequential Monte Carlo with Markov kernels removes that bottleneck.

Load-bearing premise

The whole comparison rests on the assumption that each qubit is exactly described by the small model in Section 5.1: one fixed rotation frequency and two constant decay rates, with nothing else happening during the experiment. If real device noise drifts, depends on which gates are used, or remembers the past, the Bayesian estimates can be wrong even though they look confident.

Editorial extensions

If this is right

  • Equal measurement budgets yield better parameter estimates, so qubit calibration and drift tracking can be improved without spending more experimental time on characterization.
  • The posterior distribution provides calibrated credible intervals, so downstream control decisions can be made with a quantitative sense of how much the parameters are actually known.
  • Because the update is sequential and sample-based, the same machinery can be used online between measurements, making adaptive experiment design practically usable on real devices.
  • The likelihood-plus-sampler structure is model-agnostic: the same code path applies to any open-system model whose evolution is written in Kraus operators, not just the three channels tested here.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A practical consequence the author leaves implicit: the same pipeline could close a calibration loop, using the width of the posterior to decide automatically when a qubit needs to be recalibrated, rather than recalibrating on a fixed schedule.
  • The likelihood construction generalizes to richer noise models: adding non-Markovian degrees of freedom, such as a coupled defect or a time-dependent decay rate, would let the same inference code test whether the simple memoryless model is actually adequate, via Bayes factors or predictive checks.
  • Comparing against a second independent characterization method, for example randomized benchmarking for gate errors, would turn the reported single-device comparison into a broader test of whether the Bayesian advantage survives across qubits and error sources.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This thesis presents a Bayesian approach to learning the parameters of open quantum systems, combining Bayesian experimental design with advanced Monte Carlo methods (HMC/NUTS, SMC with MCMC kernels, and tempered likelihood estimation). The first several chapters provide an extensive tutorial on Bayesian inference and Monte Carlo sampling. The final chapter applies these methods to characterize IBMQ hardware, estimating qubit frequency, T1, and T2 from Hahn echo, energy relaxation, Ramsey, and echoed Ramsey experiments. The central empirical claim is that, for the same number of measurements, the proposed Bayesian protocol outperforms Qiskit's built-in characterization functions. The paper includes code in a GitHub repository and a thorough literature overview.

Significance. If the empirical claim were fully established, the paper would demonstrate a practically relevant advantage of advanced Monte Carlo methods for quantum device characterization, with direct implications for calibration and metrology. The theoretical review is accurate and comprehensive, the synthetic benchmarks in Chapter 4 illustrate the behavior of the algorithms, and the availability of code is a clear strength. The claim itself is falsifiable and of interest to the quantum characterization community. However, the hardware-based comparison with Qiskit is not yet supported by the reported evidence, which limits the significance of the paper in its current form.

major comments (3)
  1. [Section 5.2.2-5.2.5] The central claim that the Bayesian method 'surpasses the built-in characterization functions of Qiskit for the same number of measurements' is not supported by the evidence presented. The results appear to be reported as point estimates without error bars, repeated-run statistics, or a detailed account of the number of measurements and device drift. Without such statistics, the reported outperformance could be within shot-to-shot or day-to-day variability. A quantitative comparison with uncertainties (e.g., standard errors over repeated experiments) is needed to establish the claim.
  2. [Section 5.1.2-5.1.5 and Section 5.2.2-5.2.5] The likelihood model assumes a single qubit undergoing coherent precession plus Markovian amplitude and phase damping with constant rates. If the actual IBMQ noise is non-Markovian or time-dependent, as is typical for superconducting qubits, the posterior targets an effective, sequence-dependent decay rather than a fixed T2, and the credible intervals are likely overconfident. The manuscript does not report posterior predictive checks, validation on pulse sequences different from those used for inference, or repeated runs across qubits or days. At minimum, a posterior predictive check and a stability analysis across data subsets would be needed to shield the outperformance claim from this failure mode.
  3. [Equations (2.127), (2.129), and Section 5.2] The adaptive scheme introduces several free hyperparameters: the proportionality constant for m_k, the exponential time-spacing constant C, and the prior means and variances. The text does not state how these were chosen for the IBMQ experiments, nor does it provide a sensitivity analysis. If these were tuned on the same data used for the Qiskit comparison, the comparison is not a fair test of the two methods. Reporting the chosen values and a small sensitivity scan (or tuning on a separate calibration dataset) is necessary.
minor comments (6)
  1. [Throughout] There are numerous typos and grammatical errors (e.g., 'an monotonous', 'the the two last operations', 'a a single one') that should be corrected.
  2. [Section 5.2.1] The experimental setup should state the IBMQ device name, the qubit(s) used, the number of shots per measurement point, and whether data were collected in a single session or across multiple days; these details are essential for assessing the reproducibility of the reported advantage.
  3. [Section 5.2.2-5.2.5] The manuscript does not specify which Qiskit functions were used as baseline (e.g., version of Qiskit and the exact built-in characterization routine), making it difficult to reproduce the comparison.
  4. [Equation (2.36)] The notation 'A =∧ B' for 'A estimates B' is non-standard and could be confused with definitions; consider using a more conventional symbol or wording.
  5. [Section 1.2] Several references in the literature overview (e.g., [36], [45], [77]) are cited without explaining their specific relation to the methods compared in Chapter 5; a short sentence for each would help the reader.
  6. [Figures 2.19 and 2.20] The text refers to 'crimson curves' but the figure colors are not described in the caption; consider referring to them by line style or position.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the IBMQ benchmark is externally grounded and the central derivation is self-contained.

full rationale

The central empirical claim—that Bayesian inference using HMC/NUTS and SMC-based samplers outperforms Qiskit's built-in characterization at equal measurement count—is tested against external IBMQ hardware and against an external baseline (Qiskit). The likelihood models in Sections 5.1.2–5.1.5 are standard open-system physics (Kraus operators for amplitude and phase damping plus spin precession), not quantities defined in terms of the parameters being estimated. Section 2.4.3's optional hyperparameter sweep tunes a proportionality constant on hypothetical values drawn from the prior, which is an ex ante design choice rather than a fitted parameter renamed as a prediction. The noted equivalence between the phase-estimation and precession likelihoods is a mathematical identity used for exposition, not a re-branding of an empirical result. Citations to prior Bayesian quantum estimation literature are background and do not carry the argument; no uniqueness theorem or load-bearing self-citation is invoked. Concerns about Markovianity and constant-rate assumptions are model-misspecification or correctness risks, not circularity. The derivation chain is therefore self-contained with respect to its external benchmarks.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on two types of assumptions: standard Bayesian and Monte Carlo theory, and the physical domain assumption that IBMQ qubits follow simple Markovian noise channels. The free parameters are mostly algorithmic constants and prior hyperparameters, none of which are fitted to the final target values. No new physical entities are introduced.

free parameters (3)
  • Exponential time-spacing constant C (Eq. 2.129) = 9/8 (for unit prior domain)
    Constant chosen beforehand for the heuristic adaptive time schedule. Its value is not derived from first principles and affects the measurement sequence.
  • Proportionality constant for adaptive m_k (Eq. 2.127) = Not specified; can be optimized by hyperparameter sweep
    Section 2.4.3 explicitly allows tuning this constant via a sweep over hypothetical parameter draws, making it a fitted parameter in the control policy.
  • Priors for Hamiltonian and noise parameters (means and variances) = Not given in excerpt
    The hardware experiments require priors over qubit frequency, T1, T2, etc.; these are chosen by hand and influence the posterior, though the thesis argues they wash out with enough data.
assumptions (5)
  • domain assumption The Born rule gives outcome probabilities as squared amplitudes (Eq. 2.52-2.53).
    Used as the foundation of all likelihood models in section 2.3.2 and throughout the experimental analysis.
  • domain assumption Open quantum system dynamics are captured by Markovian amplitude-damping and phase-damping Kraus channels (sections 5.1.2-5.1.4).
    The IBMQ experiments assume the qubit can be described by these simple channels with constant rates, ignoring non-Markovianity, gate-dependent errors, and crosstalk.
  • standard math The Bernstein-von Mises theorem justifies prior-independence of posteriors for the problems considered (section 2.2.1).
    Invoked to defend flat priors; requires identifiability and smoothness conditions that are not verified for the specific device models.
  • standard math Monte Carlo estimators are unbiased and converge with M^{-1/2} (section 3.1).
    Standard Monte Carlo theory used to justify the numerical integration and sampling methods.
  • standard math Central limit theorem for shot noise scaling and Gaussian approximations (section 2.4.2).
    Used to derive the standard quantum limit scaling and to justify normality assumptions in the risk analysis.

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Cite this review

Pith. "Pith review of Learning the physics of open quantum systems from experiments." pith.science (2026). https://pith.science/paper/RMSJULL4

@misc{pith2026241200078,
  author       = {Pith},
  title        = {Pith review of: Learning the physics of open quantum systems from experiments},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RMSJULL4}},
  note         = {Machine review of arXiv:2412.00078}
}
read the original abstract

This thesis explores adaptive inference as a tool to characterize quantum systems using experimental data, with applications in sensing, calibration, control, and metrology. I propose and test algorithms for learning Hamiltonian and Kraus operators using Bayesian experimental design and advanced Monte Carlo techniques, including Sequential and Hamiltonian Monte Carlo. Application to the characterization of quantum devices from IBMQ shows a robust performance, surpassing the built-in characterization functions of Qiskit for the same number of measurements. Introductions to Bayesian statistics, experimental design, and numerical integration are provided, as well as an overview of existing literature.

Figures

Figures reproduced from arXiv: 2412.00078 by the authors.

Figure 1.1
Figure 1.1. Diagram of the topics to be covered in this dissertation. Dashed boxes denote specific [PITH_FULL_IMAGE:figures/full_fig_p011_1_1.png] view at source ↗
Figure 2
Figure 2. represents the posterior probability density - which is proportional to [PITH_FULL_IMAGE:figures/full_fig_p020_2.png] view at source ↗
Figure 2.1
Figure 2.1. Bayesian posterior probability density for a binomial likelihood. The dashed and full ver [PITH_FULL_IMAGE:figures/full_fig_p021_2_1.png] view at source ↗
Figures from the paper (68 more)
Figure 2
Figure 2. Figure 2: figure 2.1, the answer seems obvious: we should just take the value of [PITH_FULL_IMAGE:figures/full_fig_p021_2.png]
Figure 2.2
Figure 2.2. Figure 2.2: Bayesian posterior probability density for a binomial likelihood. The dashed and full ver [PITH_FULL_IMAGE:figures/full_fig_p025_2_2.png]
Figure 2.3
Figure 2.3. Figure 2.3: Bayesian posterior probability evaluations for a binomial likelihood. The dashed line marks [PITH_FULL_IMAGE:figures/full_fig_p029_2_3.png]
Figure 2.4
Figure 2.4. Figure 2.4: Bayesian posterior probability distribution for a binomial likelihood. The dashed line [PITH_FULL_IMAGE:figures/full_fig_p029_2_4.png]
Figure 2.5
Figure 2.5. Figure 2.5: Bayesian posterior probability mass function for a binomial likelihood. The dashed line [PITH_FULL_IMAGE:figures/full_fig_p032_2_5.png]
Figure 2.6
Figure 2.6. Figure 2.6: Bayesian conjugate posterior density for a binomial likelihood and a flat prior. The dashed [PITH_FULL_IMAGE:figures/full_fig_p034_2_6.png]
Figure 2.7
Figure 2.7. Figure 2.7: Illustration of the model M1 from equation 2.67 for different values of W. The Bayes factor of M (ii) 1 relative to M (i) 1 is B = 1/2 for D = 1. What if go further, and needlessly add an entire dimension? We can lift the one-dimensional model up to two dimensions by…
Figure 2.8
Figure 2.8. Figure 2.8: Illustration of the model M2 from equation 2.70 as compared to its one-dimensional projections. Two such projections can be viewed on a scale in figure 2.7 for different values of W. The space forms a square with side W. , and the evidence becomes: P(D = 1; M2) =  b…
Figure 2.9
Figure 2.9. Figure 2.9: Diagrammatic representation of a quantum parameter estimation algorithm using Bayesian [PITH_FULL_IMAGE:figures/full_fig_p042_2_9.png]
Figure 2.10
Figure 2.10. Figure 2.10: Bloch sphere representations of spin precession for a specific initial state and for a general [PITH_FULL_IMAGE:figures/full_fig_p046_2_10.png]
Figure 2
Figure 2. Figure 2: figure 2.1) [PITH_FULL_IMAGE:figures/full_fig_p046_2.png]
Figure 2.11
Figure 2.11. Figure 2.11: Bayesian posterior probability distribution for an oscillatory likelihood. The dashed [PITH_FULL_IMAGE:figures/full_fig_p047_2_11.png]
Figure 2.12
Figure 2.12. Figure 2.12: Iterative phase estimation circuit diagram. [PITH_FULL_IMAGE:figures/full_fig_p048_2_12.png]
Figure 2
Figure 2. Figure 2: a shows the posterior distributions resulting from 100 coin flips for each coin; the one with [PITH_FULL_IMAGE:figures/full_fig_p051_2.png]
Figure 2.13
Figure 2.13. Figure 2.13: Impact of the magnitude of the parameter’s coefficient(s) in the shape of the likelihood [PITH_FULL_IMAGE:figures/full_fig_p052_2_13.png]
Figure 2.14
Figure 2.14. Figure 2.14: Binary tree illustrating the computation of the expected utility for a set of experiments [PITH_FULL_IMAGE:figures/full_fig_p054_2_14.png]
Figure 2.15
Figure 2.15. Figure 2.15: Diagrammatic representation of a quantum parameter estimation algorithm using [PITH_FULL_IMAGE:figures/full_fig_p055_2_15.png]
Figure 2.16
Figure 2.16. Figure 2.16: Diagrammatic representation of a quantum parameter estimation algorithm using [PITH_FULL_IMAGE:figures/full_fig_p056_2_16.png]
Figure 2.17
Figure 2.17. Figure 2.17: Binary trees illustrating the computation of the locally expected utility for two followed [PITH_FULL_IMAGE:figures/full_fig_p057_2_17.png]
Figure 2.18
Figure 2.18. Figure 2.18: Diagrammatic representation of a local optimization routine in the context of Bayesian [PITH_FULL_IMAGE:figures/full_fig_p058_2_18.png]
Figure 2.19
Figure 2.19. Figure 2.19: Posterior distributions for a time-dependent binomial model, for 2 sets of measurement [PITH_FULL_IMAGE:figures/full_fig_p064_2_19.png]
Figure 2.20
Figure 2.20. Figure 2.20: Posterior distributions for a time-dependent binomial model, for 2 sets of measurement [PITH_FULL_IMAGE:figures/full_fig_p065_2_20.png]
Figure 3.1
Figure 3.1. Figure 3.1: Evolution of the posterior probability distribution with the iteration number. The dashed [PITH_FULL_IMAGE:figures/full_fig_p073_3_1.png]
Figure 3
Figure 3. Figure 3: illustrates this problem, using the posteriors displayed in figure 3.1. After the first curve, [PITH_FULL_IMAGE:figures/full_fig_p074_3.png]
Figure 3.2
Figure 3.2. Figure 3.2: Illustration of the particle degeneracy/weight collapse problem, prompted by the particle [PITH_FULL_IMAGE:figures/full_fig_p075_3_2.png]
Figure 3.3
Figure 3.3. Figure 3.3: Illustration of the obtention of a weighted particle set and the necessary treatment to [PITH_FULL_IMAGE:figures/full_fig_p078_3_3.png]
Figure 3.4
Figure 3.4. Figure 3.4: Illustration of the process behind a HMC proposal (for a gaussian distribution). [PITH_FULL_IMAGE:figures/full_fig_p097_3_4.png]
Figure 3.5
Figure 3.5. Figure 3.5: Posterior probability (crimson) and log-probability (blue) for two different likelihood models [PITH_FULL_IMAGE:figures/full_fig_p105_3_5.png]
Figure 3.6
Figure 3.6. Figure 3.6: Effect of noise on the phase space trajectory for a harmonic oscillator model ( [PITH_FULL_IMAGE:figures/full_fig_p113_3_6.png]
Figure 4.1
Figure 4.1. Figure 4.1: Trajectories generated using RWM (top) and HMC (bottom) to sample from a multivariate [PITH_FULL_IMAGE:figures/full_fig_p117_4_1.png]
Figure 4.2
Figure 4.2. Figure 4.2: 3-dimensional plot of the Rosenbrock function from equation 4.1. [PITH_FULL_IMAGE:figures/full_fig_p118_4_2.png]
Figure 4.3
Figure 4.3. Figure 4.3: Trajectories generated using RWM (4.3a) and HMC (4.3b) to sample from a (bivariate) [PITH_FULL_IMAGE:figures/full_fig_p119_4_3.png]
Figure 4
Figure 4. Figure 4: b used the best known HMC variant, where the last state of the trajectory is deterministically [PITH_FULL_IMAGE:figures/full_fig_p119_4.png]
Figure 4.4
Figure 4.4. Figure 4.4: Trajectories generated using different variants of HMC to sample from a (bivariate) Rosen [PITH_FULL_IMAGE:figures/full_fig_p120_4_4.png]
Figure 4.5
Figure 4.5. Figure 4.5: Target bivariate smiley function (4.5a), generated using 768 gaussian kernels, and 3-d [PITH_FULL_IMAGE:figures/full_fig_p121_4_5.png]
Figure 4.6
Figure 4.6. Figure 4.6: Trajectories generated using different SMC/MCMC sampling methods to sample from a [PITH_FULL_IMAGE:figures/full_fig_p122_4_6.png]
Figure 4.7
Figure 4.7. Figure 4.7: Evolution of the sampling process through the iterations for MCMC with RWM and HMC [PITH_FULL_IMAGE:figures/full_fig_p123_4_7.png]
Figure 4
Figure 4. Figure 4: shows the results of using SMC-SIR with LWF and MCMC to learn a frequency [PITH_FULL_IMAGE:figures/full_fig_p123_4.png]
Figure 4.8
Figure 4.8. Figure 4.8: Evolution of the sampling process through the iterations for for MCMC with RWM and [PITH_FULL_IMAGE:figures/full_fig_p124_4_8.png]
Figure 4.9
Figure 4.9. Figure 4.9: Cumulative density functions obtained via MCMC with RWM and HMC move steps (4.9a) [PITH_FULL_IMAGE:figures/full_fig_p124_4_9.png]
Figure 4.10
Figure 4.10. Figure 4.10: Kernel density estimates of the posterior resulting from full data SHMC and from sub [PITH_FULL_IMAGE:figures/full_fig_p125_4_10.png]
Figure 4.11
Figure 4.11. Figure 4.11: Results of 2-dimensional inference using SIR with RWM propagation for 15 [PITH_FULL_IMAGE:figures/full_fig_p126_4_11.png]
Figure 4.12
Figure 4.12. Figure 4.12: Results of using stochastic gradients in HMC within SIR while introducing friction (4.12b) [PITH_FULL_IMAGE:figures/full_fig_p126_4_12.png]
Figure 4.13
Figure 4.13. Figure 4.13: Achieved results using random (4.13a), adaptive (4.13b) and random but increasing [PITH_FULL_IMAGE:figures/full_fig_p127_4_13.png]
Figure 4.14
Figure 4.14. Figure 4.14: Median successful results using random (4.13a), adaptive (4.13b) and random but in [PITH_FULL_IMAGE:figures/full_fig_p127_4_14.png]
Figure 4.15
Figure 4.15. Figure 4.15: Results of 4-parameter estimation (with dimensions plotted pairwise) for two variations [PITH_FULL_IMAGE:figures/full_fig_p128_4_15.png]
Figure 5.1
Figure 5.1. Figure 5.1: Bloch representations for pure and general states. [PITH_FULL_IMAGE:figures/full_fig_p131_5_1.png]
Figure 5.2
Figure 5.2. Figure 5.2: Pulse schedule for measuring T1. After the qubit is brought to the excited state | 1 ⟩ (at the time reference ∆t = 0), the probability of measuring | 1 ⟩ decays as: P(1 | ∆t) = e −∆t/T2 (5.21) This model can be used to perform inference, or to fit a curve by regressi…
Figure 5.3
Figure 5.3. Figure 5.3: Pulse schedule for measuring T ∗ 2 . The purpose of the half-pi pulses is to take the Bloch vector to the equatorial plane, where the T ∗ 2 is most relevant, and then back for the computational basis measurement. In the x basis, the function is simply: P(+ | ∆t) = 1 …
Figure 5.4
Figure 5.4. Figure 5.4: Pulse schedule for measuring T2. This is known as a Hahn echo or spin echo sequence. To prolong the coherence time still further, higher order methods can be used. Here we will use the simple circuit from 5.4, the purpose being mostly to make the coherence time more …
Figure 5.5
Figure 5.5. Figure 5.5: Pulse schedule for estimating the detuning [PITH_FULL_IMAGE:figures/full_fig_p140_5_5.png]
Figure 5.6
Figure 5.6. Figure 5.6: Pulse schedule for measuring Ω0 = Ωe0 +δmeas in an echoed Ramsey experiment. Note that δ is an experimental control determining the pulse frequency. This is a simplification of the ideas in [109], who called this type of setup a Hahn-Ramsey sequence. not be feasible …
Figure 5.7
Figure 5.7. Figure 5.7: Estimated time fluctuations of two quantities of interest for the IBMQ backend [PITH_FULL_IMAGE:figures/full_fig_p143_5_7.png]
Figure 5.8
Figure 5.8. Figure 5.8: Evolution of the standard deviation of the dephasing time [PITH_FULL_IMAGE:figures/full_fig_p144_5_8.png]
Figure 5
Figure 5. Figure 5: illustrates this fact. The only difference between graphs is the order by which the data [PITH_FULL_IMAGE:figures/full_fig_p144_5.png]
Figure 5.9
Figure 5.9. Figure 5.9: Curves produced by T2 estimates for the IBMQ device ibmq rome, using 75 different measurement times. In figure 5.9a the model of equation 5.21 was used, whereas 5.9b relaxes it to include two constants A and B [PITH_FULL_IMAGE:figures/full_fig_p145_5_9.png]
Figure 5.10
Figure 5.10. Figure 5.10: Curves produced by T2 estimates for the IBMQ device ibmq casablanca, using also estimates for A, B ̸≡ 1/2. The results were obtained using Bayesian inference (solid red line) and a curve fit (dashed black line), superposed on the data points used for the latter (gra…
Figure 5.11
Figure 5.11. Figure 5.11: Curve produced by the Qiskit coherence fitter for [PITH_FULL_IMAGE:figures/full_fig_p146_5_11.png]
Figure 5.12
Figure 5.12. Figure 5.12: Evolution of the standard deviation during the estimation of the energy relaxation time [PITH_FULL_IMAGE:figures/full_fig_p147_5_12.png]
Figure 5.13
Figure 5.13. Figure 5.13: Evolution of the standard deviations during the estimation of the detuning frequency [PITH_FULL_IMAGE:figures/full_fig_p148_5_13.png]
Figure 5.14
Figure 5.14. Figure 5.14: Curves produced by δ (labeled f) and T ∗ 2 estimates for the IBMQ device ibmq guadalupe, using 75 different measurement times. As discussed in section 5.1.4, T ∗ 2 is susceptible to large variations, so any comparison should be [PITH_FULL_IMAGE:figures/full_fig_p14…
Figure 5.15
Figure 5.15. Figure 5.15: Curve produced by the Qiskit coherence fitter for [PITH_FULL_IMAGE:figures/full_fig_p149_5_15.png]
Figure 5
Figure 5. Figure 5: a suggests that the inference results fit the data well. Expectably, the results are more [PITH_FULL_IMAGE:figures/full_fig_p150_5.png]
Figure 5.16
Figure 5.16. Figure 5.16: Ramsey experiment inference results obtained using 100 runs over the same dataset, or [PITH_FULL_IMAGE:figures/full_fig_p150_5_16.png]
Figure 5.17
Figure 5.17. Figure 5.17: Effect of inserting a refocusing pulse in a Ramsey sequence for [PITH_FULL_IMAGE:figures/full_fig_p151_5_17.png]
Figure 5.18
Figure 5.18. Figure 5.18: Evolution of the standard deviation during the inference process for adaptive (blue line) [PITH_FULL_IMAGE:figures/full_fig_p151_5_18.png]
Figure 5.19
Figure 5.19. Figure 5.19: Results of using TLE with HMC move steps to learn a detuning frequency on the IBMQ [PITH_FULL_IMAGE:figures/full_fig_p152_5_19.png]
Figure 5.20
Figure 5.20. Figure 5.20: Results of using TLE with RWM move steps and data subsampling with control variates [PITH_FULL_IMAGE:figures/full_fig_p153_5_20.png]

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Works this paper leans on

117 extracted references · 79 canonical work pages

  1. [1]

    Pseudo-marginal hamiltonian monte carlo

    Johan Alenl¨ ov, Arnoud Doucet, and Fredrik Lindsten. Pseudo-marginal hamiltonian monte carlo. Journal of Machine Learning Research , 22(141):1–45, 2021

    2021

  2. [2]

    Qiskit pulse: programming quantum computers through the cloud with pulses

    Thomas Alexander, Naoki Kanazawa, Daniel J Egger, Lauren Capelluto, Christopher J Wood, Ali Javadi-Abhari, and David C McKay. Qiskit pulse: programming quantum computers through the cloud with pulses. Quantum Science and Technology, 5(4):044006, 8 2020

    2020

  3. [3]

    Alexandra R. Alves. Quantum parameter estimation via bayesian learning (masters project). https://github.com/alexandra-frca/bayesianlearning, 2021

    2021

  4. [4]

    Christophe Andrieu, Nando de Freitas, Arnaud Doucet, and Michael I. Jordan. An introduction to mcmc for machine learning. Machine Learning, 50(1):5–43, 1 2003

    2003

  5. [5]

    Christophe Andrieu and Gareth O. Roberts. The pseudo-marginal approach for efficient monte carlo computations. The Annals of Statistics , 37(2), 4 2009

    2009

  6. [6]

    Barron, Luciano Bello, Yael Ben-Haim, Daniel Bevenius, Dhruv Bhatnagar, Arjun Bhobe, Paolo Bianchini, Lev S

    MD SAJID ANIS, H´ ector Abraham, AduOffei, Rochisha Agarwal, Gabriele Agliardi, Merav Aharoni, Ismail Yunus Akhalwaya, Gadi Aleksandrowicz, Thomas Alexander, Matthew Amy, Sashwat Anagolum, Eli Arbel, Abraham Asfaw, Anish Athalye, Artur Avkhadiev, Carlos Azaus- tre, PRATHAMESH BHOLE, Abhik Banerjee, Santanu Banerjee, Will Bang, Aman Bansal, Panagiotis Bark...

    2021

  7. [7]

    Abraham Asfaw, Antonio Corcoles, Luciano Bello, Yael Ben-Haim, Mehdi Bozzo-Rey, Sergey Bravyi, Nicholas Bronn, Lauren Capelluto, Almudena Carrera Vazquez, Jack Ceroni, Richard Chen, Albert Frisch, Jay Gambetta, Shelly Garion, Leron Gil, Salvador De La Puente Gonzalez, Francis Harkins, Takashi Imamichi, Hwajung Kang, Amir h. Karamlou, Robert Loredo, David ...

    2020

  8. [8]

    Hamiltonian and Langevin Monte Carlo , pages 281–325

    Adrian Barbu and Song Zhu. Hamiltonian and Langevin Monte Carlo , pages 281–325. Springer Singapore, 02 2020

    2020

Show all 117 references
  1. [9]

    D. W. Berry, B. L. Higgins, S. D. Bartlett, M. W. Mitchell, G. J. Pryde, and H. M. Wiseman. How to perform the most accurate possible phase measurements. Physical Review A , 80(5), 11 2009

    2009

  2. [10]

    Farrell, and Andrew M

    Alexandros Beskos, Mark Girolami, Shiwei Lan, Patrick E. Farrell, and Andrew M. Stuart. Geometric MCMC for infinite-dimensional inverse problems. Journal of Computational Physics , 335:327–351, 4 2017

    2017

  3. [11]

    M. J. Betancourt. Efficient bayesian inference with hamiltonian monte carlo. https://www. youtube.com/watch?v=pHsuIaPbNbY&t=3095s, 2014

    2014

  4. [12]

    M. J. Betancourt. Adiabatic monte carlo, 2015

    2015

  5. [13]

    M. J. Betancourt. The fundamental incompatibility of hamiltonian monte carlo and data sub- sampling, 2015

    2015

  6. [14]

    M. J. Betancourt. Scalable bayesian inference with hamiltonian monte carlo. https://www. youtube.com/watch?v=jUSZboSq1zg&t=1395s, 2018. BIBLIOGRAPHY 162

    2018

  7. [15]

    A conceptual introduction to hamiltonian monte carlo, 2018

    Michael Betancourt. A conceptual introduction to hamiltonian monte carlo, 2018

    2018

  8. [16]

    Blei, Alp Kucukelbir, and Jon D

    David M. Blei, Alp Kucukelbir, and Jon D. McAuliffe. Variational inference: A review for statisticians. Journal of the American Statistical Association , 112(518):859–877, 4 2017

    2017

  9. [17]

    Bernstein–von mises theorems for gaussian regression with increasing number of regressors

    Dominique Bontemps. Bernstein–von mises theorems for gaussian regression with increasing number of regressors. The Annals of Statistics , 39(5), 10 2011

    2011

  10. [18]

    Alexander Buchholz, Nicolas Chopin, and Pierre E. Jacob. Adaptive tuning of hamiltonian monte carlo within sequential monte carlo. Bayesian Analysis, 16(3), 9 2021

    2021

  11. [19]

    Chase and J

    Bradley A. Chase and J. M. Geremia. Single-shot parameter estimation via continuous quantum measurement. Phys. Rev. A , 79:022314, 2 2009

    2009

  12. [20]

    Fox, and Carlos Guestrin

    Tianqi Chen, Emily B. Fox, and Carlos Guestrin. Stochastic gradient hamiltonian monte carlo, 2014

    2014

  13. [21]

    S. L. Cotter, G. O. Roberts, A. M. Stuart, and D. White. MCMC methods for functions: Modifying old algorithms to make them faster. Statistical Science, 28(3), 8 2013

    2013

  14. [22]

    Resource-efficient adaptive bayesian tracking of magnetic fields with a quantum sensor

    K Craigie, E M Gauger, Y Altmann, and C Bonato. Resource-efficient adaptive bayesian tracking of magnetic fields with a quantum sensor. Journal of Physics: Condensed Matter , 33(19):195801, 4 2021

    2021

  15. [23]

    Hamil- tonian monte carlo with energy conserving subsampling

    Khue-Dung Dang, Matias Quiroz, Robert Kohn, Minh-Ngoc Tran, and Mattias Villani. Hamil- tonian monte carlo with energy conserving subsampling. Journal of Machine Learning Research, 20(100):1–31, 2019

    2019

  16. [24]

    Inference with hamiltonian sequential monte carlo simulators

    Remi Daviet. Inference with hamiltonian sequential monte carlo simulators. SSRN Electronic Journal, 2016

    2016

  17. [25]

    An introduction to feynman-kac particle methods in statistical learning and rare event simulation, 2014

    Pierre del Moral. An introduction to feynman-kac particle methods in statistical learning and rare event simulation, 2014

    2014

  18. [26]

    Short course in quantum information: Lecture 8, 2005

    Ivan Deutsch. Short course in quantum information: Lecture 8, 2005

    2005

  19. [27]

    Arbitrary accu- racy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit benchmark

    Miroslav Dobˇ s ´ ıˇ cek, G¨ oran Johansson, Vitaly Shumeiko, and G¨ oran Wendin. Arbitrary accu- racy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit benchmark. Physical Review A , 76(3), 9 2007

    2007

  20. [28]

    An introduction to sequential monte carlo methods

    Arnaud Doucet, Nando Freitas, and Neil Gordon. An introduction to sequential monte carlo methods. In Sequential Monte Carlo Methods in Practice , pages 3–14. Springer New York, 2001

    2001

  21. [29]

    A tutorial on particle filtering and smoothing: Fifteen years later

    Arnaud Doucet and Adam Johansen. A tutorial on particle filtering and smoothing: Fifteen years later. Handbook of Nonlinear Filtering , 12, 01 2009

    2009

  22. [30]

    Kennedy, Brian J

    Simon Duane, A.D. Kennedy, Brian J. Pendleton, and Duncan Roweth. Hybrid monte carlo. Physics Letters B , 195(2):216–222, 1987

    1987

  23. [31]

    A. W. F. Edwards. Likelihood, expanded edition. Biometrics, 49(4):1285, 12 1993. BIBLIOGRAPHY 163

    1993

  24. [32]

    Ward Edwards, Harold Lindman, and Leonard J. Savage. Bayesian statistical inference for psychological research. Psychological Review, 70(3):193–242, 5 1963

    1963

  25. [33]

    Evans, Robin Harper, and Steven T

    Tim J. Evans, Robin Harper, and Steven T. Flammia. Scalable bayesian hamiltonian learning, 2019

    2019

  26. [34]

    Chris Ferrie, Christopher Granade, and D. Cory. Adaptive hamiltonian estimation using bayesian experimental design. AIP Conference Proceedings, 1443, 11 2011

    2011

  27. [35]

    Quantum model averaging

    Christopher Ferrie. Quantum model averaging. New Journal of Physics , 16(9):093035, 9 2014

    2014

  28. [36]

    Christopher Ferrie and Christopher E. Granade. Likelihood-free methods for quantum parameter estimation. Physical Review Letters, 112(13), 4 2014

    2014

  29. [37]

    Granade, and D

    Christopher Ferrie, Christopher E. Granade, and D. G. Cory. How to best sample a periodic probability distribution, or on the accuracy of hamiltonian finding strategies. Quantum Infor- mation Processing, 12(1):611–623, 4 2012

    2012

  30. [38]

    Richard P. Feynman. Simulating physics with computers. In Feynman and Computation , pages 133–153. CRC Press, 2002

    2002

  31. [39]

    Fiderer, Jonas Schuff, and Daniel Braun

    Lukas J. Fiderer, Jonas Schuff, and Daniel Braun. Neural-network heuristics for adaptive bayesian quantum estimation. PRX Quantum , 2(2), 4 2021

    2021

  32. [40]

    Freedman

    David A. Freedman. On the asymptotic behavior of bayes estimates in the discrete case. The Annals of Mathematical Statistics , 34(4):1386–1403, 12 1963

    1963

  33. [41]

    Freedman

    David A. Freedman. On the asymptotic behavior of bayes estimates in the discrete case II. The Annals of Mathematical Statistics , 36(2):454–456, 4 1965

    1965

  34. [42]

    The classical bloch equations.American Journal of Physics, 82(10):947–954, 10 2014

    Martin Frimmer and Lukas Novotny. The classical bloch equations.American Journal of Physics, 82(10):947–954, 10 2014

    2014

  35. [43]

    Andrew Gelman, Daniel Lee, and Jiqiang Guo. Stan. Journal of Educational and Behavioral Statistics, 40(5):530–543, 10 2015

    2015

  36. [44]

    Adaptively scaling the metropolis algorithm using ex- pected squared jumped distance

    Andrew Gelman and Cristian Pasarica. Adaptively scaling the metropolis algorithm using ex- pected squared jumped distance. SSRN Electronic Journal , 2007

    2007

  37. [45]

    Gentile, Brian Flynn, Sebastian Knauer, Nathan Wiebe, Stefano Paesani, Christo- pher E

    Antonio A. Gentile, Brian Flynn, Sebastian Knauer, Nathan Wiebe, Stefano Paesani, Christo- pher E. Granade, John G. Rarity, Raffaele Santagati, and Anthony Laing. Learning models of quantum systems from experiments. Nature Physics, 17(7):837–843, 4 2021

    2021

  38. [46]

    Giovannetti

    V. Giovannetti. Quantum-enhanced measurements: Beating the standard quantum limit. Sci- ence, 306(5700):1330–1336, 11 2004

    2004

  39. [47]

    Riemann manifold langevin and hamiltonian monte carlo methods

    Mark Girolami and Ben Calderhead. Riemann manifold langevin and hamiltonian monte carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology) , 73(2):123– 214, 3 2011

    2011

  40. [48]

    Practical bayesian tomography

    Christopher Granade, Joshua Combes, and D G Cory. Practical bayesian tomography. New Journal of Physics , 18(3):033024, 3 2016. BIBLIOGRAPHY 164

    2016

  41. [49]

    QInfer: Library for statistical inference in quantum information, 9 2016

    Christopher Granade, Christopher Ferrie, Steven Casagrande, Ian Hincks, Michal Kononenko, Thomas Alexander, and Yuval Sanders. QInfer: Library for statistical inference in quantum information, 9 2016

    2016

  42. [50]

    Structured filtering

    Christopher Granade and Nathan Wiebe. Structured filtering. New Journal of Physics , 19(8):083014, 8 2017

    2017

  43. [51]

    Robust online hamiltonian learning

    Christopher E Granade, Christopher Ferrie, Nathan Wiebe, and D G Cory. Robust online hamiltonian learning. New Journal of Physics , 14(10):103013, 10 2012

    2012

  44. [52]

    Gross, A

    R. Gross, A. Marx, and F. Deppe. Lecture notes on applied superconductivity, 10.3: control of quantum two-level systems, 2013

    2013

  45. [53]

    Variational langevin hamiltonian monte carlo for distant multi- modal sampling, 2019

    Minghao Gu and Shiliang Sun. Variational langevin hamiltonian monte carlo for distant multi- modal sampling, 2019

    2019

  46. [54]

    Subsam- pling sequential monte carlo for static bayesian models

    David Gunawan, Khue-Dung Dang, Matias Quiroz, Robert Kohn, and Minh-Ngoc Tran. Subsam- pling sequential monte carlo for static bayesian models. Statistics and Computing , 30(6):1741– 1758, 9 2020

    2020

  47. [55]

    Spin echoes

    Erwin Hahn. Spin echoes. Phys. Rev., 80:580–594, 11 1950

    1950

  48. [56]

    W. K. Hastings. Monte carlo sampling methods using markov chains and their applications. Biometrika, 57(1):97–109, 4 1970

    1970

  49. [57]

    B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde. Entanglement-free heisenberg-limited phase estimation. Nature, 450(7168):393–396, 11 2007

    2007

  50. [58]

    Ian Hincks, Thomas Alexander, Michal Kononenko, Benjamin Soloway, and David G. Cory. Hamiltonian learning with online bayesian experiment design in practice, 2018

    2018

  51. [59]

    The no-u-turn sampler: Adaptively setting path lengths in hamiltonian monte carlo

    Matthew Hoffman and Andrew Gelman. The no-u-turn sampler: Adaptively setting path lengths in hamiltonian monte carlo. Journal of Machine Learning Research , 15, 11 2011

    2011

  52. [60]

    Husz´ ar and N

    F. Husz´ ar and N. M. T. Houlsby. Adaptive bayesian quantum tomography. Phys. Rev. A , 85:052120, 5 2012

    2012

  53. [61]

    Introduction to quantum computing and quantum hardware, 2020

    IBM Quantum team. Introduction to quantum computing and quantum hardware, 2020

    2020

  54. [62]

    Qiskit summer school on quantum machine learning, 2021

    IBM Quantum team. Qiskit summer school on quantum machine learning, 2021

    2021

  55. [63]

    Theory of probability

    Harold Jeffreys. Theory of probability. Oxford University Press, 1961

    1961

  56. [64]

    Kass and Adrian E

    Robert E. Kass and Adrian E. Raftery. Bayes factors. Journal of the American Statistical Association, 90(430):773–795, 6 1995

    1995

  57. [65]

    Efficient decomposition methods for controlled-r n using a single ancillary qubit

    Taewan Kim and Byung-Soo Choi. Efficient decomposition methods for controlled-r n using a single ancillary qubit. Scientific Reports, 8(1), 4 2018

    2018

  58. [66]

    Kitaev, A

    A. Kitaev, A. Shen, and M. Vyalyi. Classical and Quantum Computation . American Mathemat- ical Society, 5 2002. BIBLIOGRAPHY 165

    2002

  59. [67]

    A. Yu. Kitaev. Quantum measurements and the abelian stabilizer problem.Electronic Colloquium on Computational Complexity , 3, 1996

    1996

  60. [68]

    Wormhole hamiltonian monte carlo, 2014

    Shiwei Lan, Jeffrey Streets, and Babak Shahbaba. Wormhole hamiltonian monte carlo, 2014

    2014

  61. [69]

    Stochastic gradient hamiltonian monte carlo with variance reduction for bayesian inference

    Zhize Li, Tianyi Zhang, Shuyu Cheng, Jun Zhu, and Jian Li. Stochastic gradient hamiltonian monte carlo with variance reduction for bayesian inference. Machine Learning, 108(8-9):1701– 1727, 7 2019

    2019

  62. [70]

    Daniel A. Lidar. Lecture notes on the theory of open quantum systems, 2020

    2020

  63. [71]

    On thinning of chains in mcmc

    William Link and Mitchell Eaton. On thinning of chains in mcmc. Methods in Ecology and Evolution, 3:112 – 115, 06 2011

    2011

  64. [72]

    Combined parameter and state estimation in simulation-based filtering

    Jane Liu and Mike West. Combined parameter and state estimation in simulation-based filtering. In Sequential Monte Carlo Methods in Practice , pages 197–223. Springer New York, 2001

    2001

  65. [73]

    S. Lloyd. Universal quantum simulators. Science, 273(5278):1073–1078, 8 1996

    1996

  66. [74]

    Lukens, Brian P

    Hsuan-Hao Lu, Joseph M. Lukens, Brian P. Williams, Poolad Imany, Nicholas A. Peters, An- drew M. Weiner, and Pavel Lougovski. A controlled-NOT gate for frequency-bin qubits. npj Quantum Information , 5(1), 3 2019

    2019

  67. [75]

    Lukens, Kody J

    Joseph M. Lukens, Kody J. H. Law, Ajay Jasra, and Pavel Lougovski. Computationally efficient bayesian quantum state tomography. In 2020 IEEE Photonics Conference (IPC) . IEEE, 9 2020

    2020

  68. [76]

    A practical and efficient approach for bayesian quantum state estimation

    Joseph M Lukens, Kody J H Law, Ajay Jasra, and Pavel Lougovski. A practical and efficient approach for bayesian quantum state estimation. New Journal of Physics , 22(6):063038, 7 2020

    2020

  69. [77]

    Rab, Giorgio Milani, Nicol` o Spagnolo, Nathan Wiebe, and Fabio Sciarrino

    Alessandro Lumino, Emanuele Polino, Adil S. Rab, Giorgio Milani, Nicol` o Spagnolo, Nathan Wiebe, and Fabio Sciarrino. Experimental phase estimation enhanced by machine learning. Physical Review Applied, 10(4), 10 2018

    2018

  70. [78]

    Efficient adaptive mcmc implementation for pseudo-bayesian quantum tomogra- phy, 2021

    The Tien Mai. Efficient adaptive mcmc implementation for pseudo-bayesian quantum tomogra- phy, 2021

    2021

  71. [79]

    Pseudo-bayesian quantum tomography with rank-adaptation

    The Tien Mai and Pierre Alquier. Pseudo-bayesian quantum tomography with rank-adaptation. Journal of Statistical Planning and Inference , 184:62–76, 5 2017

    2017

  72. [80]

    A short introduction to the lindblad master equation

    Daniel Manzano. A short introduction to the lindblad master equation. AIP Advances , 10(2):025106, 2 2020

    2020

  73. [81]

    Effective sample size for importance sam- pling based on discrepancy measures

    Luca Martino, V ´ ıctor Elvira, and Francisco Louzada. Effective sample size for importance sam- pling based on discrepancy measures. Signal Processing, 131:386–401, 2 2017

    2017

  74. [82]

    Rosenbluth, Marshall N

    Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller. Equation of State Calculations by Fast Computing Machines. The Journal of Chemical Physics, 21(6):1087–1092, 6 1953

    1953

  75. [83]

    Feynman-Kac Formulae - Genealogical and Interacting Particle Systems with Applications

    Pierre Del Moral. Feynman-Kac Formulae - Genealogical and Interacting Particle Systems with Applications. Springer New York, 2004. BIBLIOGRAPHY 166

    2004

  76. [84]

    Sequential monte carlo samplers

    Pierre Del Moral, Arnaud Doucet, and Ajay Jasra. Sequential monte carlo samplers. Journal of the Royal Statistical Society: Series B (Statistical Methodology) , 68(3):411–436, 6 2006

    2006

  77. [85]

    MCMC using hamiltonian dynamics

    Radford Neal. MCMC using hamiltonian dynamics. In Chapman & Hall/CRC Handbooks of Modern Statistical Methods. Chapman and Hall/CRC, 5 2011

    2011

  78. [86]

    Radford M. Neal. Annealed importance sampling. Statistics and Computing , 11(2):125–139, 4 2001

    2001

  79. [87]

    Nielsen and Isaac L

    Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition . Cambridge University Press, 2010

    2010

  80. [88]

    Discontinuous hamiltonian monte carlo for discrete parameters and discontinuous likelihoods

    Akihiko Nishimura, David B Dunson, and Jianfeng Lu. Discontinuous hamiltonian monte carlo for discrete parameters and discontinuous likelihoods. Biometrika, 107(2):365–380, 3 2020

    2020

  81. [89]

    Paesani, A

    S. Paesani, A. A. Gentile, R. Santagati, J. Wang, N. Wiebe, D. P. Tew, J. L. O’Brien, and M. G. Thompson. Experimental bayesian quantum phase estimation on a silicon photonic chip. Physical Review Letters, 118(10), 3 2017

    2017

  82. [90]

    Quantum Theory: Concepts and Methods

    Asher Peres, editor. Quantum Theory: Concepts and Methods . Springer Netherlands, 2002

    2002

  83. [91]

    Lecture notes for ph219/cs219: Quantum information, chapter 2, 2015

    John Preskill. Lecture notes for ph219/cs219: Quantum information, chapter 2, 2015

    2015

  84. [92]

    Lecture notes for ph219/cs219: Quantum information, chapter 3, 2018

    John Preskill. Lecture notes for ph219/cs219: Quantum information, chapter 3, 2018

    2018

  85. [93]

    Speeding up mcmc by efficient data subsampling

    Matias Quiroz, Robert Kohn, Mattias Villani, and Minh-Ngoc Tran. Speeding up mcmc by efficient data subsampling. Journal of the American Statistical Association , 114:1–35, 03 2018

    2018

  86. [94]

    The extended liu and west filter: Parameter learning in markov switching stochastic volatility models

    Maria Paula Rios and Hedibert Freitas Lopes. The extended liu and west filter: Parameter learning in markov switching stochastic volatility models. In State-Space Models, pages 23–61. Springer New York, 2013

    2013

  87. [95]

    Wiecki, and Christopher Fonnesbeck

    John Salvatier, Thomas V. Wiecki, and Christopher Fonnesbeck. Probabilistic programming in python using pymc3. PeerJ Computer Science , 2:e55, April 2016

    2016

  88. [96]

    Santagati, A

    R. Santagati, A. A. Gentile, S. Knauer, S. Schmitt, S. Paesani, C. Granade, N. Wiebe, C. Os- terkamp, L. P. McGuinness, J. Wang, M. G. Thompson, J. G. Rarity, F. Jelezko, and A. Laing. Magnetic-field learning using a single electronic spin in diamond with one-photon readout at...

    2019

  89. [97]

    Bartlett, and Howard M

    Alexandr Sergeevich, Anushya Chandran, Joshua Combes, Stephen D. Bartlett, and Howard M. Wiseman. Characterization of a qubit hamiltonian using adaptive measurements in a fixed basis. Physical Review A , 84(5), 11 2011

    2011

  90. [98]

    Sivaganesan

    S. Sivaganesan. Sensitivity of some posterior summaries when the prior is unimodal with specified quantiles. Canadian Journal of Statistics , 19(1):57–65, 3 1991

    1991

  91. [99]

    L. F. South, A. N. Pettitt, and C. C. Drovandi. Sequential monte carlo samplers with independent markov chain monte carlo proposals. Bayesian Analysis, 14(3), 9 2019

    2019

  92. [100]

    Joshua S. Speagle. A conceptual introduction to markov chain monte carlo methods, 2020. BIBLIOGRAPHY 167

    2020

  93. [101]

    Svore, Matthew B

    Krysta M. Svore, Matthew B. Hastings, and Michael Freedman. Faster phase estimation. Quan- tum Information and Computation , 14(3&4):306–328, 3 2014

    2014

  94. [102]

    Stan modeling language users guide and reference manual 2.27, 2021

    Stan Development Team. Stan modeling language users guide and reference manual 2.27, 2021

    2021

  95. [103]

    Lectures on Kinetic Theory

    David Tong. Lectures on Kinetic Theory . University of Cambridge, 2012

    2012

  96. [104]

    Quantum metrology from a quantum information science perspective

    G´ eza T´ oth and Iagoba Apellaniz. Quantum metrology from a quantum information science perspective. Journal of Physics A: Mathematical and Theoretical , 47(42):424006, 10 2014

    2014

  97. [105]

    M. N. Tran, R. Kohn, M. Quiroz, and M. Villani. The block pseudo-marginal sampler, 2017

    2017

  98. [106]

    A. W. van der Vaart. Asymptotic Statistics . Cambridge University Press, 10 1998

    1998

  99. [107]

    Model Comparison and the Principle of Parsimony

    Joachim Vandekerckhove, Dora Matzke, and Eric-Jan Wagenmakers. Model Comparison and the Principle of Parsimony . Oxford University Press, 12 2015

    2015

  100. [108]

    Oliphant, Matt Haberland, Tyler Reddy, David Cour- napeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, St´ efan J

    Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cour- napeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, St´ efan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nel- ...

    2020

  101. [109]

    Vitanov, Timm F

    Nikolay V. Vitanov, Timm F. Gloger, Peter Kaufmann, Delia Kaufmann, Thomas Collath, M. Tanveer Baig, Michael Johanning, and Christof Wunderlich. Fault-tolerant hahn-ramsey interferometry with pulse sequences of alternating detuning. Physical Review A , 91(3), 3 2015

    2015

  102. [110]

    Gentile, Nathan Wiebe, Maurangelo Petruzzella, Jeremy L

    Jianwei Wang, Stefano Paesani, Raffaele Santagati, Sebastian Knauer, Antonio A. Gentile, Nathan Wiebe, Maurangelo Petruzzella, Jeremy L. O’Brien, John G. Rarity, Anthony Laing, and et al. Experimental quantum hamiltonian learning. Nature Physics, 13(6):551–555, 3 2017

    2017

  103. [111]

    Warne, Ruth E

    David J. Warne, Ruth E. Baker, and Matthew J. Simpson. A practical guide to pseudo- marginal methods for computational inference in systems biology. Journal of Theoretical Biology, 496:110255, 7 2020

    2020

  104. [112]

    Efficient bayesian phase estimation

    Nathan Wiebe and Chris Granade. Efficient bayesian phase estimation. Physical Review Letters, 117(1), 6 2016

    2016

  105. [113]

    Nathan Wiebe, Christopher Granade, Christopher Ferrie, and D. G. Cory. Hamiltonian learning and certification using quantum resources. Physical Review Letters, 112(19), 5 2014

    2014

  106. [114]

    Quantum hamiltonian learning using imperfect quantum resources

    Nathan Wiebe, Christopher Granade, Christopher Ferrie, and David Cory. Quantum hamiltonian learning using imperfect quantum resources. Physical Review A , 89(4), 4 2014

    2014

  107. [115]

    Quantum state estimation when qubits are lost: a no-data-left-behind approach

    Brian P Williams and Pavel Lougovski. Quantum state estimation when qubits are lost: a no-data-left-behind approach. New Journal of Physics , 19(4):043003, 4 2017

    2017

  108. [116]

    Zwiebach

    B. Zwiebach. Two state systems, 2013. BIBLIOGRAPHY 168

    2013

  109. [117]

    P´ erez-Delgado, and Pieter Kok

    Marcin Zwierz, Carlos A. P´ erez-Delgado, and Pieter Kok. General optimality of the heisenberg limit for quantum metrology. Physical Review Letters, 105(18), 10 2010

    2010

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.