Quantum error mitigation via matrix product operators

Guo, Yang; Yang, Simon X.

doi:10.48550/arxiv.2201.00752

Cited by 2 publications

(4 citation statements)

References 42 publications

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“…Combining with the matrix product operator encoding of errors discussed in Ref. [21] has potentially only constant overhead in circuit depth if the staircase of state and MPO unitaries are aligned (in a similar manner to the interferometric measurement of topological string order parameters in Ref. [15]).…”

Section: Discussionmentioning

confidence: 99%

“…There may be advantages in combining tensor network methods with machine learning tools [18][19][20] to extract simulation results as used recently in classical numerics. Moreover, there is potentially excellent fit between tensor network simulation methods and matrix product operator-based error mitigation [21,22]. While we focus on one-dimensional matrix product states (MPS), reflecting the limitations of current devices, translations of these methods to higher dimensions have been proposed [23,24].…”

Section: Introductionmentioning

confidence: 99%

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Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Dborin,

Wimalaweera,

Barratt

et al. 2022

Preprint

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We optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states. CONTENTS I. Introduction 1 II. Results 2 A. Quantum Phase Transitions 3 B. Groundstate Optimisation 3 C. Calculating and Optimising Overlaps 5 D. Quantum Dynamics 6 III. Discussion 7 IV. Methods 8 A. Fixed-point equations 8 B. Error Mitigation Strategies 8 References 9

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Dborin,

Wimalaweera,

Barratt

et al. 2022

Preprint

View full text Add to dashboard Cite

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“…The quasi-probability method [41,42] for quantum error mitigation and its variants [23,[43][44][45] involve the simulation of the inverse of noise channels with physically implementable quantum channels. The sampling cost for implementing an HPTP map N is characterized by its physical implementability [13,15], defined as…”

Section: Physical Implementability For Mixed Unitary Mapsmentioning

confidence: 99%

“…In Supplemental Material, we provide the upper and lower bounds for the physical implementability in terms of the maximum and minimum eigenvalues of the Choi matrix [25], which may inspire efficient estimation methods for the physical implementability with numerical approaches, such as the tensor network representation [46][47][48] of a general noise channel [44], instead of solving the entire optimization problem. 9…”

Section: Physical Implementability For Mixed Unitary Mapsmentioning

confidence: 99%

Noise effects on purity and quantum entanglement in terms of physical implementability

Yang

Guo²

2022

Preprint

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Quantum decoherence due to imperfect manipulation of quantum devices is a key issue in the noisy intermediate-scale quantum (NISQ) era. Standard analyses in quantum information and quantum computation use error rates to parameterize quantum noise channels. However, there is no explicit relation between the decoherence effect induced by a noise channel and its error rate. In this work, we propose to characterize the decoherence effect of a noise channel by the physical implementability of its inverse, which is a universal parameter quantifying the difficulty to simulate the noise inverse with accessible quantum channels. We establish two concise inequalities connecting the decrease of the state purity and logarithmic negativity after a noise channel to the physical implementability of the noise inverse. Our results are numerically demonstrated on several commonly adopted two- qubit noise models. We believe that these relations contribute to the theoretical research on the entanglement properties of noise channels and provide guiding principles for quantum circuit design.

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Quantum error mitigation via matrix product operators

Cited by 2 publications

References 42 publications

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Noise effects on purity and quantum entanglement in terms of physical implementability

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