Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states

Abstract

Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One example of such a hybrid quantum-classical approach is the variational quantum eigensolver (VQE) built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed among the candidates for first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even non-systematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we show how variational quantum-classical approaches fit in a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions with additional classical resources. We demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error correction codes.First conceived of by Richard Feynman [1], quantum computers have the potential to offer radical advances in solving important problems ranging from optimization and eigenvalue problems to materials design. One problem of particular recent interest is that of quantum chemistry, where quantum computers have the potential to offer an exponential speedup in the determination of physical and chemical properties [2][3][4]. This problem has received attention both because of its great practical utility, and because it is believed that it may be one of the first approaches to demonstrate the superiority of a quantum computer over currently available classical computers [5,6].Recently, there have been a number of advances in quantum chemistry on quantum computers both algorithmically and technologically. The original work utilized the quantum phase estimation algorithm [7-9] and analyzed the use of adiabatic state preparation in chemical problems. Since then, the cost of the quantum phase estimation procedure has been brought down dramatically through considerations of physical locality of interactions, chemical insights, and more general algorithmic enhancements [10][11][12][13][14]. Additionally, prototype implementations of many of these algorithms have now been verified in the lab on quantum technologies such as quantum photonics, ion traps, NMR computers, and nitrogen vacancies in diamond [15][16][17][18][19][20].While there have been significant developments in quantum hardware across a variety of platforms, many of these algorithms cannot be faithfully run on current or near-future technology. To combat this problem, a hybrid quantum classical approach was developed, with the the idea that quantum processors should only be * Corresponding author: jmcclean@lbl.gov FIG. 1. A cartoon sche...

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