QuESTlink—Mathematica embiggened by a hardware-optimised quantum emulator<sup>*</sup>

Benjamin, Simon C.

doi:10.1088/2058-9565/ab8506

Cited by 38 publications

(27 citation statements)

References 11 publications

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“…I acknowledge financial support from the Glasstone Research Fellowship of the University of Oxford. The numerical modelling involved in this study made use of the Quantum Exact Simulation Toolkit (QuEST), and the recent development QuESTlink [56] which permits the user to use Mathematica as the integrated front end. I am grateful to those who have contributed to both these valuable tools.…”

Section: Acknowledgmentsmentioning

confidence: 99%

The dominant eigenvector of a noisy quantum state

Koczor

2021

New J. Phys.

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Although near-term quantum devices have no comprehensive solution for correcting errors, numerous techniques have been proposed for achieving practical value. Two works have recently introduced the very promising error suppression by derangements (ESD) and virtual distillation (VD) techniques. The approach exponentially suppresses errors and ultimately allows one to measure expectation values in the pure state as the dominant eigenvector of the noisy quantum state. Interestingly this dominant eigenvector is, however, different than the ideal computational state and it is the aim of the present work to comprehensively explore the following fundamental question: how significantly different are these two pure states? The motivation for this work is two-fold. First, comprehensively understanding the effect of this coherent mismatch is of fundamental importance for the successful exploitation of noisy quantum devices. As such, the present work rigorously establishes that in practically relevant scenarios the coherent mismatch is exponentially less severe than the incoherent decay of the fidelity—where the latter can be suppressed exponentially via the ESD/VD technique. Second, the above question is closely related to central problems in mathematics, such as bounding eigenvalues of a sum of two matrices (Weyl inequalities)—solving of which was a major breakthrough. The present work can be viewed as a first step towards extending the Weyl inequalities to eigenvectors of a sum of two matrices—and completely resolves this problem for the special case of the considered density matrices.

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Section: Acknowledgmentsmentioning

confidence: 99%

The dominant eigenvector of a noisy quantum state

Koczor

2021

New J. Phys.

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“…We simulate the quantum circuits involved in the introduced technique using the Quantum Exact Simulation Toolkit [61], and QuESTlink [62].…”

Section: Details Of Numerical Simulationmentioning

confidence: 99%

Robust quantum compilation and circuit optimisation via energy minimisation

Benjamin

2022

Quantum

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We explore a method for automatically recompiling a quantum circuit A into a target circuit B, with the goal that both circuits have the same action on a specific input i.e. B∣in⟩=A∣in⟩. This is of particular relevance to hybrid, NISQ-era algorithms for dynamical simulation or eigensolving. The user initially specifies B as a blank template: a layout of parameterised unitary gates configured to the identity. The compilation then proceeds using quantum hardware to perform an isomorphic energy-minimisation task, and an optional gate elimination phase to compress the circuit. If B is insufficient for perfect recompilation then the method will result in an approximate solution. We optimise using imaginary time evolution, and a recent extension of quantum natural gradient for noisy settings. We successfully recompile a 7-qubit circuit involving 186 gates of multiple types into an alternative form with a different topology, far fewer two-qubit gates, and a smaller family of gate types. Moreover we verify that the process is robust, finding that per-gate noise of up to 1% can still yield near-perfect recompilation. We test the scaling of our algorithm on up to 20 qubits, recompiling into circuits with up to 400 parameterized gates, and incorporate a custom adaptive timestep technique. We note that a classical simulation of the process can be useful to optimise circuits for today's prototypes, and more generally the method may enable `blind' compilation i.e. harnessing a device whose response to control parameters is deterministic but unknown.The code and resources used to generate our results are openly available online \cite{githubLink} \cite{mmaGithubLink}. A simple Mathematica demonstration of our algorithm can be found at questlink.qtechtheory.org.

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“…The numerical simulations are performed using QuESTlink [32], which is the Mathematica interface of the high-performance quantum computation simulation package QuEST [33]. The author is grateful to those who have contributed to both these valuable tools.…”

Section: Acknowledgementsmentioning

confidence: 99%

Quantum Error Mitigation using Symmetry Expansion

Cai

2021

Quantum

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Even with the recent rapid developments in quantum hardware, noise remains the biggest challenge for the practical applications of any near-term quantum devices. Full quantum error correction cannot be implemented in these devices due to their limited scale. Therefore instead of relying on engineered code symmetry, symmetry verification was developed which uses the inherent symmetry within the physical problem we try to solve. In this article, we develop a general framework named symmetry expansion which provides a wide spectrum of symmetry-based error mitigation schemes beyond symmetry verification, enabling us to achieve different balances between the estimation bias and the sampling cost of the scheme. We show that certain symmetry expansion schemes can achieve a smaller estimation bias than symmetry verification through cancellation between the biases due to the detectable and undetectable noise components. A practical way to search for such a small-bias scheme is introduced. By numerically simulating the Fermi-Hubbard model for energy estimation, the small-bias symmetry expansion we found can achieve an estimation bias 6 to 9 times below what is achievable by symmetry verification when the average number of circuit errors is between 1 to 2. The corresponding sampling cost for random shot noise reduction is just 2 to 6 times higher than symmetry verification. Beyond symmetries inherent to the physical problem, our formalism is also applicable to engineered symmetries. For example, the recent scheme for exponential error suppression using multiple noisy copies of the quantum device is just a special case of symmetry expansion using the permutation symmetry among the copies.

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QuESTlink—Mathematica embiggened by a hardware-optimised quantum emulator^*

Cited by 38 publications

References 11 publications

The dominant eigenvector of a noisy quantum state

The dominant eigenvector of a noisy quantum state

Robust quantum compilation and circuit optimisation via energy minimisation

Quantum Error Mitigation using Symmetry Expansion

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QuESTlink—Mathematica embiggened by a hardware-optimised quantum emulator*

Cited by 38 publications

References 11 publications

The dominant eigenvector of a noisy quantum state

The dominant eigenvector of a noisy quantum state

Robust quantum compilation and circuit optimisation via energy minimisation

Quantum Error Mitigation using Symmetry Expansion

Contact Info

Product

Resources

About

QuESTlink—Mathematica embiggened by a hardware-optimised quantum emulator^*