EAGER-QAC-QSA: Variational Quantum Algorithms for Nonequilibrium Quantum Many-Body Systems

Iowa State University, Ames IA

Investigators

Abstract

Nontechnical Summary This award is made on an EAGER proposal invited through the Quantum Algorithm Challenge Dear Colleague Letter. It supports research and education to develop and implement algorithms to run on quantum computers that currently exist or will exist in the near future. A perfect quantum computer is expected to solve certain problems of practical interest much faster than any conventional computer, also called a classical computer. Examples include factoring large numbers into primes with Shor's algorithm and using Lloyd's algorithm to predict the time evolution of an interacting quantum system away from equilibrium. The latter could help in optimization and design of new biomaterials, drugs, and functional quantum materials. While the past few years have brought tremendous progress in efforts to build a perfect quantum computer, the current noisy intermediate-scale quantum (NISQ) technology is potentially decades away from being able to run Shor's and Lloyd's algorithms at practically relevant scales. The underlying reason is that NISQ computers possess of the order of hundreds of qubits as opposed to the millions required to fully correct for errors that arise from noisy gate operations. This severely limits the complexity of quantum algorithms compatible with NISQ hardware and exposes a critical need for further algorithmic advancement to achieve practical quantum advantage. In this project, the PIs develop algorithms tailored to NISQ quantum processing units (QPUs) that can address fundamental challenges in nonequilibrium physics. Specifically, the research team proposes new hybrid quantum-classical variational algorithms to simulate nonequilibrium dynamics and highly excited states in novel materials such as disordered quantum magnets. The algorithms will be implemented on QPUs from IBM and Rigetti and carefully benchmarked against existing state-of-the-art quantum and classical algorithms. In addition to finding opportunities for near-term quantum advantage, this project will provide new insights into fundamental questions of how systems of interacting particles relax to thermal equilibrium and how they respond to strong external fields. The educational component of this project addresses the national priorities of educating a quantum-enabled workforce and enhancing the participation and inclusion of traditionally underrepresented groups in STEM areas. Within this project, the PIs will educate and train one graduate student, one undergraduate student, and one postdoctoral scholar in applying quantum computing algorithms to challenging open scientific questions. The PIs will also design a hands-on outreach workshop on quantum computing and present it at "Go Further," a STEM career conference aimed at female middle- and high-school students. Finally, the PIs will create and maintain an online blog for the general public that highlights career options in quantum information science and informs readers about recent trends in quantum algorithms. Technical Summary This award is made on an EAGER proposal invited through the Quantum Algorithm Challenge Dear Colleague Letter. It supports research and education to develop and implement algorithms to run on quantum computers that currently exist or will exist in the near future. Noisy intermediate-scale quantum (NISQ) computing devices have computing capabilities that are beyond the reach of any classical supercomputer, as has recently been demonstrated by the Google team. Whether they also offer a practical quantum advantage for calculations of interest in physics, chemistry or materials science is an open question. Simulations of nonequilibrium dynamics and highly excited states in quantum many-body systems are a promising yet challenging target, since classical algorithms for such simulations suffer from the exponential complexity and highly entangled nature of generic excited states. The development of resource-efficient quantum algorithms for current NISQ hardware can unlock their potential to address important challenges in nonequilibrium many-body physics. Here, the PIs propose two novel variational quantum algorithms that are based on the variational quantum eigensolver (VQE) algorithm, which has been demonstrated on NISQ hardware. Instead of targeting ground states as in previous works, the PIs propose to use different cost functions to explore the manifold of highly excited and time-evolved quantum states. After careful benchmarking against known quantum and classical algorithms, both algorithms will be used to address fundamental open scientific questions in the fields of many-body localization, nonlinear response and nonequilibrium dynamics in strongly disordered and interacting quantum systems. The project will advance the capabilities of variational algorithms beyond exploring properties of low-energy states. Results of this research will provide insights into the properties of highly excited states in strongly disordered interacting spin chains, and address the existence of many-body localized phases and mobility emulsions, which violate the eigenstate thermalization hypothesis. The research team will also shed light on the correlation and entanglement properties of prethermal quantum states that emerge in post-quench dynamics and test the hypothesis that their temporal stability is related to a small energy variance, making them approximate eigenstates. Finally, by implementing efficient NISQ quantum algorithms for the computation of higher-order and out-of-time-ordered correlation functions, the PIs will determine whether these functions can disentangle effects of disorder and interactions on quasiparticle properties and explore the onset of quantum chaos in spin models. By addressing fundamental challenges in condensed matter physics, the research team will contribute to the open question of whether NISQ technology offers a practical quantum advantage. 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.