Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
By Mario Motta, Chong Sun, A. T. Tan, M. O’Rourke, Erika Ye, A. Minnich, Fernando G. S. L. Brandão, Garnet Kin-Lic Chan. Nature Physics, 2019
819 citations recorded by the source corpus.
The accurate computation of Hamiltonian ground, excited and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. In this regard, existing techniques based on phase estimation or variational algorithms display potential disadvantages; phase estimation requires deep circuits with ancillae, that are hard to execute reliably without error correction, while variational algorithms, while flexible with respect to circuit depth, entail additional high-dimensional classical optimization. Here, we introduce the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogues of classical algorithms for finding ground and excited states. Compared with their classical counterparts, they require exponentially less space and time per iteration, and can be implemented without deep circuits and ancillae, or high-dimensional optimization. We furthermore discuss quantum imaginary time evolution as a subroutine to generate Gibbs averages through an analogue of minimally entangled typical thermal states. Finally, we demonstrate the potential of these algorithms via an implementation using exact classical emulation as well as through prototype circuits on the Rigetti quantum virtual machine and Aspen-1 quantum processing unit. The quantum imaginary time evolution and Lanczos algorithms offer a resource-efficient way to compute ground or excited states of target Hamiltonians on quantum computers. This offers promise for quantum simulation on near-term noisy devices.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/007cba6f122d786583c32c0ba56b78e97a7edc1b
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Quantum simulation of fundamental particles and forces (2023, background): “…techniques include adiabatically approaching states of a target theory from those of a simpler theory [147], adiabaticity-violating processes such as quenched dynamics, imaginary-time evolution [148–151], and variational procedures that may incorporate global entangling operators [152–154].”
- Challenges and opportunities in quantum optimization (2023, neutral): “A heuristic based on time evolution is quantum imaginary time evolution (QITE) 68,69 .”