Characterizing Error Mitigation by Symmetry Verification in QAOA
- URL: http://arxiv.org/abs/2204.05852v1
- Date: Tue, 12 Apr 2022 14:51:14 GMT
- Title: Characterizing Error Mitigation by Symmetry Verification in QAOA
- Authors: Ashish Kakkar and Jeffrey Larson and Alexey Galda and Ruslan Shaydulin
- Abstract summary: Hardware errors are a major obstacle to demonstrating quantum advantage with the quantum approximate optimization algorithm (QAOA)
Symmetry verification uses parity checks that leverage the symmetries of the objective function to be optimized.
We numerically investigate the symmetry verification on the MaxCut problem and identify the error regimes in which this approach improves the QAOA objective.
- Score: 2.9860417981482263
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Hardware errors are a major obstacle to demonstrating quantum advantage with
the quantum approximate optimization algorithm (QAOA). Recently, symmetry
verification has been proposed and empirically demonstrated to boost the
quantum state fidelity, the expected solution quality, and the success
probability of QAOA on a superconducting quantum processor. Symmetry
verification uses parity checks that leverage the symmetries of the objective
function to be optimized. We develop a theoretical framework for analyzing this
approach under local noise and derive explicit formulas for fidelity
improvements on problems with global $\mathbb{Z}_2$ symmetry. We numerically
investigate the symmetry verification on the MaxCut problem and identify the
error regimes in which this approach improves the QAOA objective. We observe
that these regimes correspond to the error rates present in near-term hardware.
We further demonstrate the efficacy of symmetry verification on an IonQ trapped
ion quantum processor where an improvement in the QAOA objective of up to
19.2\% is observed.
Related papers
- Potential and limitations of quantum extreme learning machines [55.41644538483948]
We present a framework to model QRCs and QELMs, showing that they can be concisely described via single effective measurements.
Our analysis paves the way to a more thorough understanding of the capabilities and limitations of both QELMs and QRCs.
arXiv Detail & Related papers (2022-10-03T09:32:28Z) - Symmetric Pruning in Quantum Neural Networks [111.438286016951]
Quantum neural networks (QNNs) exert the power of modern quantum machines.
QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes.
We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
arXiv Detail & Related papers (2022-08-30T08:17:55Z) - Improving the performance of quantum approximate optimization for
preparing non-trivial quantum states without translational symmetry [10.967081346848687]
We study the performance of the quantum approximate optimization algorithm (QAOA) for preparing ground states of target Hamiltonians.
We propose a generalized QAOA assisted by the parameterized resource Hamiltonian to achieve a better performance.
Our work paves the way for performing QAOA on programmable quantum processors without translational symmetry.
arXiv Detail & Related papers (2022-06-06T14:17:58Z) - Adaptive construction of shallower quantum circuits with quantum spin
projection for fermionic systems [0.0]
Current devices only allow for hybrid quantum-classical algorithms with a shallow circuit depth, such as variational quantum eigensolver (VQE)
In this study, we report the importance of the Hamiltonian symmetry in constructing VQE circuits adaptively.
We demonstrate that symmetry-projection can provide a simple yet effective solution to this problem, by keeping the quantum state in the correct symmetry space, to reduce the overall gate operations.
arXiv Detail & Related papers (2022-05-14T17:08:18Z) - General Hamiltonian Representation of ML Detection Relying on the
Quantum Approximate Optimization Algorithm [74.6114458993128]
The quantum approximate optimization algorithm (QAOA) conceived for solving optimization problems can be run on the existing noisy intermediate-scale quantum (NISQ) devices.
We solve the maximum likelihood (ML) detection problem for general constellations by appropriately adapting the QAOA.
In particular, for an M-ary Gray-mapped quadrature amplitude modulation (MQAM) constellation, we show that the specific qubits encoding the in-phase components and those encoding the quadrature components are independent in the quantum system of interest.
arXiv Detail & Related papers (2022-04-11T14:11:24Z) - Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state.
In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
arXiv Detail & Related papers (2021-12-27T21:15:35Z) - Quantum Approximate Optimization Algorithm applied to the binary
perceptron [0.46664938579243564]
We apply digitized Quantum Annealing (QA) and Quantum Approximate Optimization Algorithm (QAOA) to a paradigmatic task of supervised learning in artificial neural networks.
We provide evidence for the existence of optimal smooth solutions for the QAOA parameters, which are transferable among typical instances of the same problem.
We prove numerically an enhanced performance of QAOA over traditional QA.
arXiv Detail & Related papers (2021-12-19T18:33:22Z) - Analytical and experimental study of center line miscalibrations in M\o
lmer-S\o rensen gates [51.93099889384597]
We study a systematic perturbative expansion in miscalibrated parameters of the Molmer-Sorensen entangling gate.
We compute the gate evolution operator which allows us to obtain relevant key properties.
We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor.
arXiv Detail & Related papers (2021-12-10T10:56:16Z) - Quantifying the Impact of Precision Errors on Quantum Approximate
Optimization Algorithms [0.24629531282150877]
We show that errors in the analog implementation of QAOA circuits hinder its performance as an optimization algorithm.
Despite this significant reduction, we show that it is possible to mitigate precision errors in QAOA via digitization of the variational parameters.
arXiv Detail & Related papers (2021-09-09T18:00:03Z) - Error Mitigation for Deep Quantum Optimization Circuits by Leveraging
Problem Symmetries [2.517903855792476]
We introduce an application-specific approach for mitigating the errors in QAOA evolution by leveraging the symmetries present in the classical objective function to be optimized.
Specifically, the QAOA state is projected into the symmetry-restricted subspace, with projection being performed either at the end of the circuit or throughout the evolution.
Our approach improves the fidelity of the QAOA state, thereby increasing both the accuracy of the sample estimate of the QAOA objective and the probability of sampling the binary string corresponding to that objective value.
arXiv Detail & Related papers (2021-06-08T14:40:48Z) - Quantum-optimal-control-inspired ansatz for variational quantum
algorithms [105.54048699217668]
A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form.
Here, we show that this approach is not always advantageous by introducing ans"atze that incorporate symmetry-breaking unitaries.
This work constitutes a first step towards the development of a more general class of symmetry-breaking ans"atze with applications to physics and chemistry problems.
arXiv Detail & Related papers (2020-08-03T18:00:05Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.