Efficient quantum algorithms for testing symmetries of open quantum
systems
- URL: http://arxiv.org/abs/2309.02515v2
- Date: Thu, 16 Nov 2023 23:31:57 GMT
- Title: Efficient quantum algorithms for testing symmetries of open quantum
systems
- Authors: Rahul Bandyopadhyay, Alex H. Rubin, Marina Radulaski, Mark M. Wilde
- Abstract summary: In quantum mechanics, it is possible to eliminate degrees of freedom by leveraging symmetry to identify the possible physical transitions.
Previous works have focused on devising quantum algorithms to ascertain symmetries by means of fidelity-based symmetry measures.
We develop alternative symmetry testing quantum algorithms that are efficiently implementable on quantum computers.
- Score: 17.55887357254701
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Symmetry is an important and unifying notion in many areas of physics. In
quantum mechanics, it is possible to eliminate degrees of freedom from a system
by leveraging symmetry to identify the possible physical transitions. This
allows us to simplify calculations and characterize potentially complicated
dynamics of the system with relative ease. Previous works have focused on
devising quantum algorithms to ascertain symmetries by means of fidelity-based
symmetry measures. In our present work, we develop alternative symmetry testing
quantum algorithms that are efficiently implementable on quantum computers. Our
approach estimates asymmetry measures based on the Hilbert--Schmidt distance,
which is significantly easier, in a computational sense, than using fidelity as
a metric. The method is derived to measure symmetries of states, channels,
Lindbladians, and measurements. We apply this method to a number of scenarios
involving open quantum systems, including the amplitude damping channel and a
spin chain, and we test for symmetries within and outside the finite symmetry
group of the Hamiltonian and Lindblad operators.
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