Multiple-basis representation of quantum states

TL;DR

This paper introduces a new hybrid quantum-classical state representation called multiple-basis representation, which enhances the simulation of quantum states using current hardware by combining states sparse in different bases.

Contribution

It proposes a novel multiple-basis representation for quantum states, analyzing its expressivity and potential applications in near-term quantum computing.

Findings

Includes matrix-product states and stabilizer states as special cases

Enables approximation of ground states and simulation of deeper circuits

Provides a tomographical protocol for state description

Abstract

Classical simulation of quantum physics is a central approach to investigating physical phenomena. Quantum computers enhance computational capabilities beyond those of classical resources, but it remains unclear to what extent existing limited quantum computers can contribute to this enhancement. In this work, we explore a new hybrid, efficient quantum-classical representation of quantum states, the multiple-basis representation. This representation consists of a linear combination of states that are sparse in some given and different bases, specified by quantum circuits. Such representation is particularly appealing when considering depth-limited quantum circuits within reach of current hardware. We analyze the expressivity of multiple-basis representation states depending on the classical simulability of their quantum circuits. In particular, we show that multiple-basis representation states include, but are not restricted to, both matrix-product states and stabilizer states. Furthermore, we find cases in which this representation can be used, namely approximation of ground states, simulation of deeper computations by specifying bases with shallow circuits, and a tomographical protocol to describe states as multiple-basis representations. We envision this work to open the path of simultaneous use of several hardware-friendly bases, a natural description of hybrid computational methods accessible for near-term hardware.