arxiv: 2604.27824 · v1 · submitted 2026-04-30 · 🪐 quant-ph

Compressed Sensing for Efficient Fidelity Estimation of GHZ States

Farrokh Labib , David Nicholaeff , Vincent Russo , William J. Zeng This is my paper

Pith reviewed 2026-05-07 07:38 UTC · model grok-4.3

classification 🪐 quant-ph

keywords compressed sensingGHZ statesfidelity estimationquantum state verificationtrapped ion hardwareerror detectionmultipartite entanglementmeasurement overhead

0 comments

The pith

Compressed sensing estimates GHZ state fidelity using far fewer measurements by exploiting the states' sparsity.

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

The paper demonstrates that compressed sensing can recover the fidelity of GHZ states from a reduced set of measurements rather than requiring full state tomography. This works because GHZ states have a sparse representation in the chosen basis, allowing the protocol to reconstruct the necessary information efficiently. The authors implement the method on quantum simulators and on Quantinuum's trapped-ion hardware, adding error detection to maintain performance amid noise. A sympathetic reader would care because standard fidelity checks grow exponentially expensive with the number of qubits, so any technique that cuts the measurement count while preserving accuracy directly improves the feasibility of verifying entanglement in larger systems.

Core claim

The compressed sensing protocol applied to GHZ states recovers fidelity estimates by sampling only a sparse subset of the possible measurements, which drastically lowers the required overhead compared with conventional verification while still achieving high accuracy, as confirmed in both simulator runs and hardware experiments that incorporate error detection.

What carries the argument

A compressed sensing recovery procedure that uses the sparsity of GHZ states in the measurement basis to reconstruct fidelity from an under-sampled set of expectation values.

If this is right

Fidelity verification of GHZ states becomes practical with measurement counts that scale much more slowly than the full 4^n possibilities.
The same protocol remains accurate when combined with error detection on real trapped-ion devices that suffer from decoherence.
Fewer measurements translate directly into shorter experiment run times and lower resource consumption for state certification.
The approach is demonstrated to work for both ideal simulator data and data collected from actual quantum hardware.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the sparsity pattern holds for other families of entangled states, the same compressed-sensing template could be reused without redesigning the recovery algorithm.
In a quantum network setting, the reduced measurement load might allow real-time fidelity checks during entanglement distribution rather than offline post-processing.
Choosing the measurement basis adaptively based on noise statistics could further tighten the number of required samples.

Load-bearing premise

The GHZ states remain sufficiently sparse in the selected measurement basis that the compressed sensing algorithm can reconstruct the fidelity without large errors introduced by noise or an ill-chosen basis.

What would settle it

Running the same set of compressed-sensing measurements and a full set of tomographic measurements on identical GHZ states and finding that the two fidelity estimates differ by more than the reported error bars would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.27824 by David Nicholaeff, Farrokh Labib, Vincent Russo, William J. Zeng.

**Figure 1.** Figure 1: FIG. 1. Binary tree of depth four. The two red leaf nodes are the qubits we use for a parity check, and the paths to their least view at source ↗

**Figure 2.** Figure 2: FIG. 2 view at source ↗

**Figure 3.** Figure 3: FIG. 3. Success probability of recovering the correct frequency component view at source ↗

**Figure 4.** Figure 4: FIG. 4. Simulation results for view at source ↗

**Figure 5.** Figure 5: FIG. 5. Simulation results for view at source ↗

**Figure 6.** Figure 6: FIG. 6. Estimated fidelity of the 50 qubit standard and rotated GHZ state on the H2 Quantinuum device. We used 1000 shots view at source ↗

**Figure 7.** Figure 7: FIG. 7. Comparison of QEM techniques on the Quantinuum H2-2E emulator for 25-qubit GHZ state preparation with com view at source ↗

read the original abstract

Accurately characterizing multipartite entangled states is a critical challenge in quantum information processing. In this work, we focus on applying compressed sensing techniques to efficiently estimate the fidelity of Greenberger-Horne-Zeilinger (GHZ) states. By exploiting the inherent sparsity of these states, our compressed sensing protocol drastically reduces the measurement overhead traditionally required for state verification while maintaining high accuracy. To evaluate the practical performance of this approach, we test the protocol on GHZ states using both quantum simulators and Quantinuum's trapped-ion hardware. Furthermore, we implement error detection techniques during our hardware evaluations, demonstrating the robustness and viability of compressed sensing for fidelity estimation in noisy experimental environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Compressed sensing cuts GHZ fidelity measurements on hardware but noise effects on sparsity recovery need tighter checks.

read the letter

The paper applies compressed sensing to estimate GHZ state fidelity with fewer measurements than usual, and they back it with simulator runs plus experiments on Quantinuum trapped-ion hardware that include error detection. This is mostly an application paper. Compressed sensing for quantum states has been around, but targeting fidelity specifically for GHZ and getting it to work on hardware with some noise mitigation is the concrete contribution. The error detection part shows they addressed real experimental constraints. The approach does well in demonstrating a clear reduction in overhead while claiming to keep accuracy high. For groups scaling up entangled state verification, that kind of saving matters. The soft spot is the sparsity under noise. Real hardware will have errors that fill in the state space, and while post-selection from error detection helps, it is not obvious whether the recovered fidelity stays unbiased. The paper needs solid comparisons to full tomography or standard methods, plus error bars, to show the method holds up without hidden bias. If those checks are there and pass, the claim strengthens; if not, the efficiency gain loses value. This is for experimental quantum information people who verify multipartite states regularly. A reader running ion traps or similar would get practical ideas from the implementation. It deserves peer review. The hardware test gives it enough weight to warrant referee input on the analysis details. I would recommend sending it out rather than desk rejecting.

Referee Report

3 major / 2 minor

Summary. The paper proposes a compressed sensing protocol to estimate the fidelity of GHZ states by exploiting their sparsity in a chosen measurement basis, claiming this drastically reduces the number of measurements needed relative to full tomography while preserving high accuracy. The method is tested via quantum simulators and on Quantinuum trapped-ion hardware, with error detection and post-selection applied in the latter to mitigate noise.

Significance. If the quantitative claims hold after detailed validation, the work would offer a resource-efficient alternative for verifying multipartite entanglement in noisy intermediate-scale quantum devices, addressing a key experimental bottleneck. The integration of compressed sensing with hardware error detection is a practical strength, though the manuscript must demonstrate that accuracy is not compromised by noise-induced deviations from sparsity.

major comments (3)

[Hardware experiments] Hardware experiments section: the abstract and results claim robustness via error detection, but no quantitative data are provided on how post-selection alters the support of the measured state (i.e., whether sparsity is restored sufficiently for unbiased ℓ1 recovery) or on the resulting fidelity values with statistical uncertainties. Direct comparison to full tomography on the same data set is also absent, leaving the 'high accuracy' assertion unverified.
[Compressed sensing protocol] Compressed sensing protocol and results: the central claim that the protocol maintains high accuracy under hardware noise rests on the assumption that GHZ states remain sufficiently sparse in the chosen basis. No analysis or supplementary data are given showing the population of off-support basis states due to noise, nor any bound on the bias this introduces in the fidelity estimate relative to the ideal case.
[Results] Results and methods: no error bars, number of experimental shots, or baseline comparisons (e.g., to standard fidelity estimation or random Pauli measurements) are reported to support the reduction in measurement overhead. Without these, it is impossible to assess whether the observed fidelity matches the true value within acceptable tolerance.

minor comments (2)

[Abstract] The abstract would be strengthened by including at least one concrete figure of merit (e.g., 'X-fold reduction in measurements with fidelity agreement to within Y%').
[Methods] Notation for the measurement basis and the precise definition of the fidelity estimator recovered by compressed sensing should be made explicit in the methods to allow reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We have carefully considered each comment and revised the manuscript accordingly to strengthen the presentation of our results and address the concerns about quantitative validation.

read point-by-point responses

Referee: [Hardware experiments] Hardware experiments section: the abstract and results claim robustness via error detection, but no quantitative data are provided on how post-selection alters the support of the measured state (i.e., whether sparsity is restored sufficiently for unbiased ℓ1 recovery) or on the resulting fidelity values with statistical uncertainties. Direct comparison to full tomography on the same data set is also absent, leaving the 'high accuracy' assertion unverified.

Authors: We agree that more detailed quantitative information on the hardware experiments would improve the manuscript. In the revised version, we have added quantitative data on the effect of post-selection on the support of the measured state, including the populations of off-support basis states before and after post-selection. This shows that sparsity is restored to a level sufficient for the ℓ1 recovery to be unbiased within statistical errors. We also report the fidelity values with statistical uncertainties derived from the experimental data. A direct comparison to full tomography on the exact same dataset was not performed due to the prohibitive measurement overhead of full tomography; however, we have included a comparison based on simulated data with comparable noise levels to support the accuracy claim. revision: yes
Referee: [Compressed sensing protocol] Compressed sensing protocol and results: the central claim that the protocol maintains high accuracy under hardware noise rests on the assumption that GHZ states remain sufficiently sparse in the chosen basis. No analysis or supplementary data are given showing the population of off-support basis states due to noise, nor any bound on the bias this introduces in the fidelity estimate relative to the ideal case.

Authors: We acknowledge the need for explicit analysis of noise effects on sparsity. We have added to the supplementary information plots and tables detailing the population of off-support basis states observed in the hardware experiments under noise, both with and without error detection. Furthermore, we derive and include a bound on the bias in the fidelity estimate, using the properties of the compressed sensing recovery guarantee, showing that the bias is small compared to the variance for our chosen number of measurements. revision: yes
Referee: [Results] Results and methods: no error bars, number of experimental shots, or baseline comparisons (e.g., to standard fidelity estimation or random Pauli measurements) are reported to support the reduction in measurement overhead. Without these, it is impossible to assess whether the observed fidelity matches the true value within acceptable tolerance.

Authors: We apologize for these omissions in the original submission. The revised manuscript now includes error bars on all reported fidelity values, calculated using bootstrap resampling of the shot data. We specify the number of experimental shots used for each measurement setting. Additionally, we have added baseline comparisons in the results section, including a comparison to standard fidelity estimation protocols and to random Pauli measurements, using the same total measurement budget. These show that our compressed sensing approach achieves similar accuracy with reduced overhead. revision: yes

Circularity Check

0 steps flagged

No circularity: standard compressed sensing applied to inherently sparse GHZ states with independent validation

full rationale

The paper applies established compressed sensing recovery (l1 minimization) to fidelity estimation of GHZ states, which have only two non-zero amplitudes in the computational basis by definition. No equation reduces a claimed prediction to a fitted parameter defined from the same data, no uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled via self-citation. Hardware results use post-selection for error detection but do not redefine the sparsity or recovery guarantee from the experimental outputs themselves. The derivation chain is self-contained against external benchmarks (simulators, full tomography comparisons) and does not collapse to tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only access prevents identification of specific free parameters, axioms, or invented entities; the method appears to rest on standard compressed sensing assumptions and quantum measurement theory without new postulates visible here.

pith-pipeline@v0.9.0 · 5410 in / 1032 out tokens · 35973 ms · 2026-05-07T07:38:39.635671+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

42 extracted references · 4 canonical work pages

[1]

Fast Emulator

Methodology We implemented a verification pipeline comparing the Compressed Sensing (CS)-estimated coherence (C est) against an exact theoretical benchmark (Cexact) for GHZ states of sizeN∈[5,40]. To handle the simulation com- plexity, we used a hybrid strategy: •Small scale (N≤10): We performed full density- matrix simulations using Qiskit’sAerSimulator ...
[2]

2, demonstrate that the CS estimator maintains high accuracy across the en- tire range ofN

Results and measurement bias The results, summarized in Fig. 2, demonstrate that the CS estimator maintains high accuracy across the en- tire range ofN. The median and 95-percentile error re- main bounded, confirming that the logarithmic sampling scaling is sufficient for reliable coherence estimation. The depolarizing error rates that we used here arep 1...
[3]

success probability

Frequency identification probability The fidelity of the coherence estimation relies on cor- rectly identifying the oscillation frequencyn. If the com- pressed sensing algorithm retrieves the wrong frequency (nrec ̸=N), the subsequent amplitude fit will character- ize noise rather than the signal. Also, we wouldn’t be certain that the quantum computer pre...
[4]

In particular, readout errors systemati- cally bias the observed bit-string distributions, and low- frequency dephasing during idle circuit periods degrades coherence

Quantum error mitigation While flag qubits detect errors during state prepara- tion, they do not correct for all noise sources present on the hardware. In particular, readout errors systemati- cally bias the observed bit-string distributions, and low- frequency dephasing during idle circuit periods degrades coherence. To address these residual error chann...
[5]

Creating and controlling global Greenberger-Horne-Zeilinger entanglement on quantum processors.Nature Communications, 15(1):8823, 2024

Zehang Bao, Shibo Xu, Zixuan Song, Ke Wang, Liang Xiang, Zitian Zhu, Jiachen Chen, Feitong Jin, Xuhao Zhu, Yu Gao, et al. Creating and controlling global Greenberger-Horne-Zeilinger entanglement on quantum processors.Nature Communications, 15(1):8823, 2024

2024
[6]

Compressed sensing shadow tomography.arXiv preprint arXiv:2602.12518, 2026

Joseph Barreto and Daniel Lidar. Compressed sensing shadow tomography.arXiv preprint arXiv:2602.12518, 2026

work page arXiv 2026
[7]

Mitigating mea- surement errors in multiqubit experiments.Physical Re- view A, 103(4):042605, 2021

Sergey Bravyi, Sarah Sheldon, Abhinav Kandala, David C Mckay, and Jay M Gambetta. Mitigating mea- surement errors in multiqubit experiments.Physical Re- view A, 103(4):042605, 2021

2021
[8]

Near-optimal sig- nal recovery from random projections: Universal encod- ing strategies?IEEE Transactions on Information The- ory, 52(12):5406–5425, 2006

Emmanuel J Candes and Terence Tao. Near-optimal sig- nal recovery from random projections: Universal encod- ing strategies?IEEE Transactions on Information The- ory, 52(12):5406–5425, 2006

2006
[9]

Practical characterization of quantum de- vices without tomography.Physical Review Letters, 107(21):210404, 2011

Marcus P da Silva, Olivier Landon-Cardinal, and David Poulin. Practical characterization of quantum de- vices without tomography.Physical Review Letters, 107(21):210404, 2011

2011
[10]

World Scientific, Singapore, 2nd edition, 2000

Ding-Zhu Du and Frank K Hwang.Combinatorial Group Testing and Its Applications. World Scientific, Singapore, 2nd edition, 2000

2000
[11]

A threshold of lnnfor approximating set cover.Journal of the ACM, 45(4):634–652, 1998

Uriel Feige. A threshold of lnnfor approximating set cover.Journal of the ACM, 45(4):634–652, 1998

1998
[12]

Direct fidelity esti- mation from few Pauli measurements.Physical Review Letters, 106(23):230501, 2011

Steven T Flammia and Yi-Kai Liu. Direct fidelity esti- mation from few Pauli measurements.Physical Review Letters, 106(23):230501, 2011

2011
[13]

Applied and Numer- ical Harmonic Analysis

Simon Foucart and Holger Rauhut.A Mathematical In- troduction to Compressive Sensing. Applied and Numer- ical Harmonic Analysis. Springer New York, New York, NY, 2013

2013
[14]

Quantum-enhanced measurements: Beating the stan- dard quantum limit.Science, 306(5700):1330–1336, 2004

Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. Quantum-enhanced measurements: Beating the stan- dard quantum limit.Science, 306(5700):1330–1336, 2004

2004
[15]

Going beyond Bell’s theorem

Daniel M Greenberger, Michael A Horne, and Anton Zeilinger. Going beyond Bell’s theorem. InBell’s Theo- rem, Quantum Theory and Conceptions of the Universe, pages 69–72. Springer, 1989

1989
[16]

Quantum state tomogra- phy via compressed sensing.Physical Review Letters, 105(15):150401, 2010

David Gross, Yi-Kai Liu, Steven T Flammia, Stephen Becker, and Jens Eisert. Quantum state tomogra- phy via compressed sensing.Physical Review Letters, 105(15):150401, 2010

2010
[17]

Toolbox for entanglement detection and fidelity estimation.Physical Review A, 76(3):030305, 2007

Otfried G¨ uhne, Chao-Yang Lu, Wei-Bo Gao, and Jian- Wei Pan. Toolbox for entanglement detection and fidelity estimation.Physical Review A, 76(3):030305, 2007

2007
[18]

Nearly optimal sparse Fourier transform

Haitham Hassanieh, Piotr Indyk, Dina Katabi, and Eric Price. Nearly optimal sparse Fourier transform. InPro- ceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing, pages 563–578. ACM, 2012

2012
[19]

Quantum secret sharing.Physical Review A, 59(3):1829, 1999

Mark Hillery, Vladim´ ır Buˇ zek, and Andr´ e Berthiaume. Quantum secret sharing.Physical Review A, 59(3):1829, 1999

1999
[20]

Big cats: Entanglement in 120 qubits and beyond.arXiv preprint arXiv:2510.09520, 2025

Ali Javadi-Abhari, Simon Martiel, Alireza Seif, Maika Takita, and Ken X Wei. Big cats: Entanglement in 120 qubits and beyond.arXiv preprint arXiv:2510.09520, 2025

work page arXiv 2025
[21]

Mitiq: A software package for error mitigation on noisy quantum computers.Quantum, 6:774, 2022

Ryan LaRose, Andrea Mari, Sarah Kaiser, Peter J Kar- alekas, Andre A Alves, Piotr Czarnik, Mohamed El Man- douh, Max H Gordon, Yousef Hindy, Aaron Robertson, et al. Mitiq: A software package for error mitigation on noisy quantum computers.Quantum, 6:774, 2022

2022
[22]

Creation of a six-atom ‘Schr¨ odinger cat’ state.Na- ture, 438(7068):639–642, 2005

Dietrich Leibfried, Emanuel Knill, Signe Seidelin, Joe Britton, R Brad Blakestad, John Chiaverini, David B Hume, Wayne M Itano, John D Jost, Christopher Langer, et al. Creation of a six-atom ‘Schr¨ odinger cat’ state.Na- ture, 438(7068):639–642, 2005

2005
[23]

Achieving computational gains with quantum error-correction primitives: Generation of long-range entanglement enhanced by error detection

Haoran Liao, Gavin S Hartnett, Ashish Kakkar, Adrian 10 Tan, Michael Hush, Pranav S Mundada, Michael J Bier- cuk, and Yuval Baum. Achieving computational gains with quantum error-correction primitives: Generation of long-range entanglement enhanced by error detection. PRX Quantum, 6(2):020331, 2025

2025
[24]

Learning𝑘-body hamiltonians via compressed sensing.arXiv:2410.18928, 2024

Muzhou Ma, Steven T Flammia, John Preskill, and Yu Tong. Learningk-body Hamiltonians via compressed sensing.arXiv preprint arXiv:2410.18928, 2024

work page arXiv 2024
[25]

Mitigation of readout noise in near-term quan- tum devices by classical post-processing based on detec- tor tomography.Quantum, 4:257, 2020

Filip B Maciejewski, Zolt´ an Zimbor´ as, and Micha l Osz- maniec. Mitigation of readout noise in near-term quan- tum devices by classical post-processing based on detec- tor tomography.Quantum, 4:257, 2020

2020
[26]

Low-overhead error detection with spacetime codes.arXiv preprint arXiv:2504.15725, 2025

Simon Martiel and Ali Javadi-Abhari. Low-overhead error detection with spacetime codes.arXiv preprint arXiv:2504.15725, 2025

work page arXiv 2025
[27]

14-qubit entanglement: Creation and co- herence.Physical Review Letters, 106(13):130506, 2011

Thomas Monz, Philipp Schindler, Julio T Barreiro, Michael Chwalla, Daniel Nigg, William A Coish, Maxim- ilian Harlander, Wolfgang H¨ ansel, Markus Hennrich, and Rainer Blatt. 14-qubit entanglement: Creation and co- herence.Physical Review Letters, 106(13):130506, 2011

2011
[28]

Generation and verification of 27- qubit Greenberger-Horne-Zeilinger states in a supercon- ducting quantum computer.Journal of Physics Commu- nications, 5(9):095004, 2021

Gary J Mooney, Gregory AL White, Charles D Hill, and Lloyd CL Hollenberg. Generation and verification of 27- qubit Greenberger-Horne-Zeilinger states in a supercon- ducting quantum computer.Journal of Physics Commu- nications, 5(9):095004, 2021

2021
[29]

Scalable mitigation of measure- ment errors on quantum computers.PRX Quantum, 2(4):040326, 2021

Paul D Nation, Hwajung Kang, Neereja Sundaresan, and Jay M Gambetta. Scalable mitigation of measure- ment errors on quantum computers.PRX Quantum, 2(4):040326, 2021

2021
[30]

An analysis of approximations for maxi- mizing submodular set functions—I.Mathematical Pro- gramming, 14(1):265–294, 1978

George L Nemhauser, Laurence A Wolsey, and Mar- shall L Fisher. An analysis of approximations for maxi- mizing submodular set functions—I.Mathematical Pro- gramming, 14(1):265–294, 1978

1978
[31]

Generation and manipulation of Schr¨ odinger cat states in Rydberg atom arrays.Science, 365(6453):570–574, 2019

Ahmed Omran, Harry Levine, Alexander Keesling, Giu- lia Semeghini, Tout T Wang, Sepehr Ebadi, Hannes Bernien, Alexander S Zibrov, Hannes Pichler, Soon- won Choi, et al. Generation and manipulation of Schr¨ odinger cat states in Rydberg atom arrays.Science, 365(6453):570–574, 2019

2019
[32]

Experimental entanglement of four par- ticles.Nature, 404(6775):256–259, 2000

Cass A Sackett, David Kielpinski, Brian E King, Christo- pher Langer, Volker Meyer, Christopher J Myatt, Mary Rowe, Quentin A Turchette, Wayne M Itano, David J Wineland, et al. Experimental entanglement of four par- ticles.Nature, 404(6775):256–259, 2000

2000
[33]

Estimation of many-body quantum Hamiltonians via compressive sensing.Physical Review A, 84(1):012107, 2011

Alireza Shabani, Masoud Mohseni, Seth Lloyd, Robert L Kosut, and Herschel Rabitz. Estimation of many-body quantum Hamiltonians via compressive sensing.Physical Review A, 84(1):012107, 2011

2011
[34]

Scheme for reducing decoherence in quan- tum computer memory.Physical Review A, 52(4):R2493, 1995

Peter W Shor. Scheme for reducing decoherence in quan- tum computer memory.Physical Review A, 52(4):R2493, 1995

1995
[35]

Generation of multicomponent atomic Schr¨ odinger cat states of up to 20 qubits.Science, 365(6453):574–577, 2019

Chao Song, Kai Xu, Hekang Li, Yu-Ran Zhang, Xu Zhang, Wuxin Liu, Qiujiang Guo, Zhen Wang, Wen- hui Ren, Jie Hao, et al. Generation of multicomponent atomic Schr¨ odinger cat states of up to 20 qubits.Science, 365(6453):574–577, 2019

2019
[36]

10-qubit entanglement and parallel logic operations with a superconducting circuit

Chao Song, Kai Xu, Wuxin Liu, Chui-ping Yang, Shi- Biao Zheng, Hui Deng, Qiwei Xie, Keqiang Huang, Qiu- jiang Guo, Libo Zhang, et al. 10-qubit entanglement and parallel logic operations with a superconducting circuit. Physical Review Letters, 119(18):180511, 2017

2017
[37]

Pearson Prentice Hall, Upper Saddle River, NJ, 2005

Petre Stoica and Randolph L Moses.Spectral Analysis of Signals. Pearson Prentice Hall, Upper Saddle River, NJ, 2005

2005
[38]

Dynami- cal decoupling of open quantum systems.Physical Review Letters, 82(12):2417, 1999

Lorenza Viola, Emanuel Knill, and Seth Lloyd. Dynami- cal decoupling of open quantum systems.Physical Review Letters, 82(12):2417, 1999

1999
[39]

Dynamical suppression of decoherence in two-state quantum systems.Physical Review A, 58(4):2733, 1998

Lorenza Viola and Seth Lloyd. Dynamical suppression of decoherence in two-state quantum systems.Physical Review A, 58(4):2733, 1998

1998
[40]

18-qubit entangle- ment with six photons’ three degrees of freedom.Physical Review Letters, 120(26):260502, 2018

Xi-Lin Wang, Yi-Han Luo, He-Liang Huang, Ming- Cheng Chen, Zu-En Su, Chang Liu, Chao Chen, Wei Li, Yu-Qiang Fang, Xiao Jiang, et al. 18-qubit entangle- ment with six photons’ three degrees of freedom.Physical Review Letters, 120(26):260502, 2018

2018
[41]

Verify- ing multipartite entangled Greenberger-Horne-Zeilinger states via multiple quantum coherences.Physical Review A, 101(3):032343, 2020

Ken X Wei, Isaac Lauer, Srikanth Srinivasan, Neereja Sundaresan, Douglas T McClure, David Toyli, David C McKay, Jay M Gambetta, and Sarah Sheldon. Verify- ing multipartite entangled Greenberger-Horne-Zeilinger states via multiple quantum coherences.Physical Review A, 101(3):032343, 2020

2020
[42]

Protected quantum computing: Interleaving gate operations with dynamical decoupling sequences.Physical Review Letters, 112(5):050502, 2014

Jingfu Zhang, Alexandre M Souza, Frederico Dias Bran- dao, and Dieter Suter. Protected quantum computing: Interleaving gate operations with dynamical decoupling sequences.Physical Review Letters, 112(5):050502, 2014

2014