Quantum dimension witness with a single repeated operation

TL;DR

This paper introduces a simple, feasible quantum dimension witness test using a single repeated operation, applicable to current quantum technologies, and demonstrates its implementation on IBM Quantum devices.

Contribution

The paper proposes a new null test for quantum system dimension using the method of delays with a single repeated operation, suitable for existing quantum hardware.

Findings

Test successfully demonstrated on IBM Quantum

Failure indicates non-identity of gates or extra dimensions

Weaker versions analyzed with statistical error expressions

Abstract

We present a simple null test of a dimension of a quantum system, using a single repeated operation in the method of delays, assuming that each instance is identical and independent. The test is well-suited to current feasible quantum technologies, with programed gates. We also analyze weaker versions of the test, assuming unitary or almost unitary operations and derive expressions for the statistical error. The feasibility of the test is demonstrated on IBM Quantum. The failure in one of the tested devices can indicate a lack of identity between subsequent gates or an extra dimension in the many worlds/copies model.