Maximally Sensitive Sets of States

TL;DR

This paper introduces the concept of maximally sensitive sets of states, such as GHZ states, to detect coherent errors in quantum systems by exploiting their quadratic error scaling behavior.

Contribution

It defines maximally sensitive sets of states and demonstrates their use with GHZ states to identify coherent errors in quantum gates and measurements.

Findings

GHZ states form a maximally sensitive set for detecting coherent errors

The method can identify coherent errors within a constant fraction of maximum sensitivity

A simpler protocol can test for coherent error accumulation in state preparation

Abstract

Coherent errors in a quantum system can, in principle, build up much more rapidly than incoherent errors, accumulating as the square of the number of qubits in the system rather than linearly. I show that only channels dominated by a unitary rotation can display such behavior. A maximally sensitive set of states is a set such that if a channel is capable of quadratic error scaling, then it is present for at least one sequence of states in the set. I show that the GHZ states in the X, Y, and Z bases form a maximally sensitive set of states, allowing a straightforward test to identify coherent errors in a system. This allows us to identify coherent errors in gates and measurements to within a constant fraction of the maximum possible sensitivity to such errors. A related protocol with simpler circuits but less sensitivity can also be used to test for coherent errors in state preparation or if the noise in a particular circuit is accumulating coherently or not.