EAGER: QSA: Eigenstate Thermalization and the Quantum Metropolis Algorithm

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Systems of strongly interacting quantum particles are capable of realizing novel phases of quantum matter, which can exhibit astonishing emergent macroscopic properties like superfluidity, superconductivity, and long-termstorage of quantum information. Despite significant effort in simulating these systems using conventional supercomputers, progress has been limited by a fundamental barrier of computational complexity which veils an unexplored frontier of physics called the entanglement frontier. Quantum computers are naturally able to probe this frontier because they harness entanglement in their elementary operations, and so the eventual development of mature quantum computing technology will greatly advance our understanding of quantum phase transitions and enable the discovery of new phases of quantum matter with potentially transformative properties for technology and society. All of this depends on the development of efficient quantum algorithms for simulating the thermodynamic properties of quantum systems. This project investigates the quantum Metropolis algorithm, which is a quantum algorithm that directly generalizes one of the most successful 20th century paradigms for simulating classical statistical physics. By paralleling developments that occurred in the corresponding classical algorithm, this project seeks to determine general conditions which imply that a quantum computer can efficiently simulate quantum thermal properties.The main new perspective used in this project is based on a connection between physical thermalization - the process by which a physical quantum system comes into thermal equilibrium with its environment - and the behavior and convergence of the quantum Metropolis algorithm. The eigenstate thermalization hypothesis (ETH) is a prominent explanation for how physical quantum systems approach thermal equilibrium, despite their dynamical behavior being time-reversible in principle. This project connects mathematical inequalities developed in the context of the ETH directly to the transition probabilities that govern the behavior of the quantum Metropolis algorithm. This quantitative characterization of transition probabilities opens the door to establishing the first non-trivial cases of rigorously efficient (polynomial-time) quantum algorithms for simulating thermal states of some class of quantum systems that is strongly suspected to be beyond the range of efficient classical simulation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.