Quantum Physics

Understanding quantum noise is an essential step towards building practical quantum information processing systems. Pauli noise is a useful model widely applied in quantum benchmarking, quantum error mitigation, and quantum error correction. Despite previous research, the problem of how to learn a Pauli noise model self-consistently, completely, and efficiently has remained open. In this talk, I will introduce a framework of gate-set Pauli noise learning that aims at addressing this problem. The framework treats initialization, measurement, and a set of quantum gates to suffer from unknown Pauli noise channels, which are allowed to have customized locality constraints. The goal is to learn all the Pauli noise channels using only those noisy operations. I will first introduce a theory on the “learnability” of Pauli noise model, i.e., what information is fundamentally identifiable within the model and what is not. This is established using tools from algebraic graph theory and ideas from gate set tomography; I will then discuss a sample-efficient procedure to learn all learnable information of a Paul noise model to any desired precision; Finally, I will demonstrate how to apply our theoretic framework for concrete practical gate set and noise assumptions, and discuss the potential impact on quantum error mitigation and other applications.

Abstract: Randomness is a powerful resource for information-processing applications. For example, classical randomness is essential for modern information security and underpins many cryptographic schemes. Similarly, quantum randomness can protect quantum information against noise or eavesdroppers who wish to access or manipulate that information. These observations raise a set of related questions: How quickly and efficiently can we generate quantum randomness? How much quantum randomness is necessary for a given task? What can we use quantum randomness for? In this talk, I address these questions using all-to-all Brownian circuits, a family of random quantum circuits for which exact results can often be obtained via mean-field theory. I will first demonstrate that all-to-all Brownian circuits form k-designs in a time that scales linearly with k. I will then discuss how these circuits can be applied to study Heisenberg-limited metrology and quantum advantage. In particular, I will discuss a time-reversal protocol that can achieve Heisenberg-limited precision in cavity QED and trapped ion setups; I will also discuss the application of these circuits to studying classical spoofing algorithms for the linear cross-entropy benchmark, a popular measure of quantum advantage.