Partial randomized benchmarking

TL;DR

This paper analyzes partial randomized benchmarking, showing it produces a fidelity decay as a combination of exponentials, and explores how to extract meaningful error rates for quantum gates using simplified twirling methods.

Contribution

It provides a detailed analysis of partial twirling in randomized benchmarking, revealing the decay dynamics and methods to identify error channels for two-qubit gates.

Findings

Decay of fidelity is a linear combination of exponentials.

Dominant exponential characterizes primary gate errors.

Identification of exceptional gates with multiple decay rates.

Abstract

In randomized benchmarking of quantum logical gates, partial twirling can be used for simpler implementation, better scaling, and higher accuracy and reliability. For instance, for two-qubit gates, single-qubit twirling is easier to realize than full averaging. We analyze such simplified, partial twirling and demonstrate that, unlike for the standard randomized benchmarking, the measured decay of fidelity is a linear combination of exponentials with different decay rates (3 for two qubits and single-bit twirling). The evolution with the sequence length is governed by an iteration matrix, whose spectrum gives the decay rates. For generic two-qubit gates one slowest exponential dominates and characterizes gate errors in three channels. Its decay rate is close, but different from that in the standard randomized benchmarking, and we find the leading correction. Using relations to the local invariants of two-qubit gates we identify all exceptional gates with several slow exponentials and analyze possibilities to extract their decay rates from the measured curves.