Testing Symmetry On Quantum Computers

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Margarite L. LaBorde¹, Soorya Rethinasamy^2,1, and Mark M. Wilde^3,1

¹Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA
²School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14850, USA
³School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14850, USA

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Abstract

Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian realizing a time evolution are not useful for timekeeping during that evolution, and bipartite states that are highly extendible are not strongly entangled and thus not useful for basic tasks like teleportation. Motivated by this perspective, this paper details several quantum algorithms that test the symmetry of quantum states and channels. For the case of testing Bose symmetry of a state, we show that there is a simple and efficient quantum algorithm, while the tests for other kinds of symmetry rely on the aid of a quantum prover. We prove that the acceptance probability of each algorithm is equal to the maximum symmetric fidelity of the state being tested, thus giving a firm operational meaning to these latter resource quantifiers. Special cases of the algorithms test for incoherence or separability of quantum states. We evaluate the performance of these algorithms on choice examples by using the variational approach to quantum algorithms, replacing the quantum prover with a parameterized circuit. We demonstrate this approach for numerous examples using the IBM quantum noiseless and noisy simulators, and we observe that the algorithms perform well in the noiseless case and exhibit noise resilience in the noisy case. We also show that the maximum symmetric fidelities can be calculated by semi-definite programs, which is useful for benchmarking the performance of these algorithms for sufficiently small examples. Finally, we establish various generalizations of the resource theory of asymmetry, with the upshot being that the acceptance probabilities of the algorithms are resource monotones and thus well motivated from the resource-theoretic perspective.

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► BibTeX data

@article{LaBorde2023testingsymmetry, doi = {10.22331/q-2023-09-25-1120}, url = {https://doi.org/10.22331/q-2023-09-25-1120}, title = {Testing symmetry on quantum computers}, author = {LaBorde, Margarite L. and Rethinasamy, Soorya and Wilde, Mark M.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1120}, month = sep, year = {2023}<br /> }

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[5] Zachary P. Bradshaw, Margarite L. LaBorde, and Mark M. Wilde, “Cycle index polynomials and generalized quantum separability tests”, Proceedings of the Royal Society of London Series A 479 2274, 20220733 (2023).

[6] Denis Lacroix, Edgar Andres Ruiz Guzman, and Pooja Siwach, “Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers”, European Physical Journal A 59 1, 3 (2023).

[7] Margarite L. LaBorde, “A Menagerie of Symmetry Testing Quantum Algorithms”, arXiv:2305.14560, (2023).

[8] Zachary P. Bradshaw and Margarite L. LaBorde, “Quantum entanglement & purity testing: A graph zeta function perspective”, Physics Letters A 481, 128993 (2023).

[9] Aby Philip, Soorya Rethinasamy, Vincent Russo, and Mark M. Wilde, “Schrödinger as a Quantum Programmer: Estimating Entanglement via Steering”, arXiv:2303.07911, (2023).

[10] Zachary P. Bradshaw and Christophe Vignat, “Dubious Identities: A Visit to the Borwein Zoo”, arXiv:2307.05565, (2023).

[11] Rahul Bandyopadhyay, Alex H. Rubin, Marina Radulaski, and Mark M. Wilde, “Efficient quantum algorithms for testing symmetries of open quantum systems”, arXiv:2309.02515, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-09-25 14:52:18). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2023-09-25 14:52:16: Could not fetch cited-by data for 10.22331/q-2023-09-25-1120 from Crossref. This is normal if the DOI was registered recently.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2023-09-25-1120/

Time Stamp: September 25, 2023

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