Testing symmetry on quantum computers
- URL: http://arxiv.org/abs/2105.12758v3
- Date: Sat, 16 Sep 2023 01:50:29 GMT
- Title: Testing symmetry on quantum computers
- Authors: Margarite L. LaBorde, Soorya Rethinasamy, and Mark M. Wilde
- Abstract summary: In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks.
This paper details several quantum algorithms that test the symmetry of quantum states and channels.
- Score: 3.481985817302898
- License: http://creativecommons.org/licenses/by/4.0/
- 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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