Noisy Quantum Computation Modeled by Quantum Walk: Universality without Ancillas

TL;DR

This paper extends the quantum walk model to noisy, open quantum systems, enabling efficient simulation of NISQ computers without ancillas and providing insights into entanglement and noise effects.

Contribution

It introduces a novel quantum walk framework for open noisy systems that avoids explicit purification and ancillas, improving efficiency and access to entanglement properties.

Findings

Models unitary and nonunitary operations in noisy quantum systems

Provides an efficient linear-in-runtime implementation

Enables direct analysis of entanglement in open systems

Abstract

The universal quantum computation model based on quantum walk by Childs has opened the door for a new way of studying the limitations and advantages of quantum computation, as well as for its intermediate-term simulation. In recent years, the growing interest in noisy intermediate-scale quantum computers (NISQ) has lead to intense efforts being directed at understanding the computational advantages of open quantum systems. In this work, we extend the quantum walk model to open noisy systems in order to provide such a tool for the study of NISQ computers. Our method does not use explicit purification, and allows to ignore the environment degrees of freedom and obtain a much more efficient implementation (linear rather than exponential in the runtime), which employs no ancillas hence provides direct access to the entanglement properties of the system. In our scheme, the quantum walk amplitudes represent elements of the density matrix rather than the wavefunction of a pure state. Despite the non-trivial manifestation of the normalization requirement in this setting, we model the application of general unitary gates and nonunitary channels, with an explicit implementation protocol for channels that are commonly used in noise models.