Symmetry enhanced variational quantum spin eigensolver

Lyu, Chufan; Xu, Xusheng; Yung, Man‐Hong; Bayat, Abolfazl

doi:10.48550/arxiv.2203.02444

Cited by 4 publications

(5 citation statements)

References 91 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further works that treat symmetry-enhanced variational meth-ods are found in Refs. [21][22][23]. Another possibility outside of altering the ansatz itself to enforce symmetries is to enforce them through the optimizer via the use of additional terms in the cost function that penalize asymmetric states as in Refs.…”

mentioning

confidence: 99%

Exploiting symmetry in variational quantum machine learning

Meyer¹,

Mularski²,

Gil-Fuster³

et al. 2022

Preprint

View full text Add to dashboard Cite

Variational quantum machine learning is an extensively studied application of near-term quantum computers. The success of variational quantum learning models crucially depends on finding a suitable parametrization of the model that encodes an inductive bias relevant to the learning task. However, precious little is known about guiding principles for the construction of suitable parametrizations. In this work, we holistically explore when and how symmetries of the learning problem can be exploited to construct quantum learning models with outcomes invariant under the symmetry of the learning task. Building on tools from representation theory, we show how a standard gateset can be transformed into an equivariant gateset that respects the symmetries of the problem at hand through a process of gate symmetrization. We benchmark the proposed methods on two toy problems that feature a non-trivial symmetry and observe a substantial increase in generalization performance. As our tools can also be applied in a straightforward way to other variational problems with symmetric structure, we show how equivariant gatesets can be used in variational quantum eigensolvers.

show abstract

mentioning

confidence: 99%

Exploiting symmetry in variational quantum machine learning

Meyer¹,

Mularski²,

Gil-Fuster³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…In this section, we focus on digital VQE simulation of the ground state of the Hamiltonian (2) across its phase diagram as θ and α vary. In order to prevent the complexity of degenerate ground states in the antiferromagnetic phase, we include the Z symmetry in the cost function of the system [65] such that…”

Section: Digital Vqe Simulation Of the Ground Statementioning

confidence: 99%

“…As the average energy reaches its global minimum the output of the quantum circuit simulates the ground state of the system. VQE has also been generalized for simulating excited states through addition of penalizing terms to the cost function [54][55][56][57], subspacesearch VQE [58] and exploiting symmetries [42,[59][60][61][62][63][64][65].…”

Section: Introductionmentioning

confidence: 99%

Variational quantum simulation of long-range interacting systems

Tang¹,

Lyu²,

Li³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

Current quantum simulators suffer from multiple limitations such as short coherence time, noisy operations, faulty readout and restricted qubit connectivity. Variational quantum algorithms are the most promising approach in near-term quantum simulation to achieve quantum advantage over classical computers. Here, we explore variational quantum algorithms, with different levels of qubit connectivity, for digital simulation of the ground state of long-range interacting systems. We find that as the interaction becomes more long-ranged, the variational algorithms become less efficient, achieving lower fidelity and demanding more optimization iterations. In particular, when the system is near its criticality the efficiency is even lower. Increasing the connectivity between distant qubits improves the results, even with less quantum and classical resources. Our results show that by mixing circuit layers with different levels of connectivity one can sensibly improve the results. Interestingly, the order of layers becomes very important and grouping the layers with long-distance connectivity at the beginning of the circuit outperforms other permutations. The same design of circuits can also be used to variationally produce spin squeezed states, as a resource for quantum metrology. The quantum variational method indeed outperforms the ground state and quench dynamics approach for creating spin squeezing.

show abstract

“…In these algorithms, the complexity is divided between a quantum circuit and a classical computer, allowing a complex task to be achieved using a shallow quantum circuit. So far, VQAs have been exploited to solve a wide range of problems, including eigenvalue solvers [51][52][53][54][55][56], quantum neural networks [42,57,58], quantum adversarial machine learning [59][60][61][62], quantum approximate optimization algorithms [63], linear equation solvers [64][65][66] and quantum sensing [67][68][69]. Variational Quantum Classification (VQC) algorithms, as typical VQAs, have also been developed to solve classification problems on NISQ computers [39,41,42,60,62,[70][71][72][73][74], with some of them being experimentally demonstrated [17,62,75,76].…”

Section: Introductionmentioning

confidence: 99%

Ensemble-learning error mitigation for variational quantum shallow-circuit classifiers

Li¹,

Huang²,

Hou³

et al. 2023

Preprint

View full text Add to dashboard Cite

Classification is one of the main applications of supervised learning. Recent advancement in developing quantum computers has opened a new possibility for machine learning on such machines. However, due to the noisy performance of near-term quantum computers, we desire an approach for solving classification problems with only shallow circuits. Here, we propose two ensemble-learning classification methods, namely bootstrap aggregating and adaptive boosting, which can significantly enhance the performance of variational quantum classifiers for both classical and quantum datasets. The idea is to combine several weak classifiers, each implemented on a shallow noisy quantum circuit, to make a strong one with high accuracy. While both of our protocols substantially outperform errormitigated primitive classifiers, the adaptive boosting shows better performance than the bootstrap aggregating. In addition, its training error decays exponentially with the number of classifiers, leading to a favorable complexity for practical realization. The protocols have been exemplified for classical handwriting digits as well as quantum phase discrimination of a symmetry-protected topological Hamiltonian.

show abstract

Symmetry enhanced variational quantum spin eigensolver

Cited by 4 publications

References 91 publications

Exploiting symmetry in variational quantum machine learning

Exploiting symmetry in variational quantum machine learning

Variational quantum simulation of long-range interacting systems

Ensemble-learning error mitigation for variational quantum shallow-circuit classifiers

Contact Info

Product

Resources

About