Advancing Hybrid Quantum-Classical Algorithms via Mean-Operators

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.

Main text: 5 pages, 4 figures, Supplemental material: 6 pages, 5 figures

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• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Identifying phases of quantum many-body systems that are universal for quantum computation