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Fast-forwarding quantum evolution

Gu, Shouzhen and Somma, Rolando D. and Şahinoğlu, Burak (2021) Fast-forwarding quantum evolution. Quantum, 5 . Art. No. 577. ISSN 2521-327X. doi:10.22331/q-2021-11-15-577.

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We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that considers the model of quantum computation, the Hamiltonians that induce the evolution, and the properties of the initial states. Our definition accounts for any asymptotic complexity improvement of the general case and we use it to demonstrate fast-forwarding in several quantum systems. In particular, we show that some local spin systems whose Hamiltonians can be taken into block diagonal form using an efficient quantum circuit, such as those that are permutation-invariant, can be exponentially fast-forwarded. We also show that certain classes of positive semidefinite local spin systems, also known as frustration-free, can be polynomially fast-forwarded, provided the initial state is supported on a subspace of sufficiently low energies. Last, we show that all quadratic fermionic systems and number-conserving quadratic bosonic systems can be exponentially fast-forwarded in a model where quantum gates are exponentials of specific fermionic or bosonic operators, respectively. Our results extend the classes of physical Hamiltonians that were previously known to be fast-forwarded, while not necessarily requiring methods that diagonalize the Hamiltonians efficiently. We further develop a connection between fast-forwarding and precise energy measurements that also accounts for polynomial improvements.

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Additional Information:© 2021. This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. Published: 2021-11-15. We acknowledge support from the U.S. Department of Energy, Office of Science, High-Energy Physics and Office of Advanced Scientific Computing Research, under the Accelerated Research in Quantum Computing (ARQC) program. This material is also based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center. Los Alamos National Laboratory is managed by Triad National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under Contract No. 89233218CNA000001.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Department of Energy (DOE)89233218CNA000001
Record Number:CaltechAUTHORS:20211222-638987300
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112645
Deposited By: Tony Diaz
Deposited On:22 Dec 2021 21:45
Last Modified:22 Dec 2021 21:45

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