RQS-QuICS Special Seminar

Randomized benchmarking (RB) is a widely used strategy to assess the quality of available quantum gates in a computational context. The quality is usually expressed as an effective depolarizing error per step. RB involves applying random sequences of gates to an initial state and making a final measurement to determine the probability of an error. Current implementations of RB estimate this probability by repeating each randomly chosen sequence many times.

The demands of fault tolerance mean that a wide variety of simple and exotic noise types must be tamed for quantum devices to progress. Crucially, this means keeping up with complex correlated — or non-Markovian — effects, both with respect to the background process and to control operations. Recently, we have developed a generalised version of quantum process tomography to characterise arbitrary non-Markovian processes in practice.

Generating randomness efficiently is a key capability in both classical and quantum information processing applications. For example, Haar-random quantum states serve as primitives for applications including quantum cryptography, quantum process tomography, and randomized benchmarking. How quickly can these random states be generated? And how much randomness is really necessary for any given application? In this talk, I will address these questions in Brownian quantum circuit models, which admit a large-$N$ limit that can be solved exactly.

Randomized benchmarking protocols have become the prominent tool for assessing the quality of gates on digital quantum computing platforms.  In `classical' variants of randomized benchmarking multi-qubit gates are drawn uniformly from a finite group.  The functioning of such schemes be rigorous guaranteed under realistic assumptions.  In contrast, experimentally attractive and practically more scalable randomized benchmarking schemes often directly perform random circuits or use other non-uniform probability measures.