Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 51, Issue 39, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/aad6fa
Keywords
randomized benchmarking; quantum gates; Clifford gates; monomial unitary; random walks on groups; fidelity estimation
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Funding
- graduate program TopMath of the Elite Network of Bavaria
- TopMath Graduate Center of TUM Graduate School at Technische Universitat Munchen
- Technische Universitat Munchen Institute for Advanced Study
- German Excellence Initiative
- European Union Seventh Framework Programme [291763]
- Elite Network of Bavaria through the PhD programme of excellence Exploring Quantum Matter
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We investigate randomized benchmarking (RB) in a general setting with quantum gates that form a representation, not necessarily an irreducible one, of a finite group. We derive an estimate for the average fidelity, to which experimental data may then be calibrated. Furthermore, we establish that RB can be achieved by the sole implementation of quantum gates that generate the group as well as one additional arbitrary group element. In this case, we need to assume that the noise is close to being covariant. This yields a more practical approach to RB. Moreover, we show that RB is stable with respect to approximate Haar sampling for the sequences of gates. This opens up the possibility of using Markov chain Monte Carlo methods to obtain the random sequences of gates more efficiently. We demonstrate these results numerically using the well-studied example of the Clifford group as well as the group of monomial unitary matrices. For the latter, we focus on the subgroup with nonzero entries consisting of nth roots of unity, which contains T gates.
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