Advancing Hybrid Quantum-Classical Algorithms via Mean-Operators

TL;DR

This paper introduces a mean-operator-theory that enhances hybrid quantum-classical algorithms, significantly reducing quantum operations needed for preparing complex entangled many-body states, and is applicable to current quantum simulation platforms.

Contribution

The paper proposes a novel mean-operator-theory that combines hybrid algorithms with mean-field concepts to overcome qubit and operation limitations in quantum simulations.

Findings

Reduces quantum operations for entangled state preparation

Expresses mean-operators as time-evolution operators

Applicable to neutral atom and ion quantum simulators

Abstract

Entanglement in quantum many-body systems is the key concept for future technology and science, opening up a possibility to explore uncharted realms in an enormously large Hilbert space. The hybrid quantum-classical algorithms have been suggested to control quantum entanglement of many-body systems, and yet their applicability is intrinsically limited by the numbers of qubits and quantum operations. Here we propose a theory which overcomes the limitations by combining advantages of the hybrid algorithms and the standard mean-field-theory in condensed matter physics, named as mean-operator-theory. We demonstrate that the number of quantum operations to prepare an entangled target many-body state such as symmetry-protected-topological states is significantly reduced by introducing a mean-operator. We also show that a class of mean-operators is expressed as time-evolution operators and our theory is directly applicable to quantum simulations with $^{87}$Rb neutral atoms or trapped $^{40}$Ca$^+$ ions.