Shadow hamiltonian simulation
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1.
Google (United States)
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2.
California Institute of Technology
Abstract
Simulating quantum dynamics is one of the most important applications of quantum computers. Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity. Here, we present a different and novel approach to quantum simulation that uses a compressed quantum state that we call the "shadow state". The amplitudes of this shadow state are proportional to the time-dependent expectations of a specific set of operators of interest, and it evolves according to its own Schrödinger equation. This evolution can be simulated on a quantum computer efficiently under broad conditions. Applications of this approach to quantum simulation problems include simulating the dynamics of exponentially large systems of free fermions or free bosons, the latter example recovering a recent algorithm for simulating exponentially many classical harmonic oscillators. These simulations are hard for classical methods and also for traditional quantum approaches, as preparing the full states would require exponential resources. Shadow Hamiltonian simulation can also be extended to simulate expectations of more complex operators such as two-time correlators or Green's functions, and to study the evolution of operators themselves in the Heisenberg picture.
Copyright and License
© The Author(s) 2025.
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Acknowledgement
We thank Cristian Batista, Kipton Barros, David Gosset, Robert Huang, William Huggins, Stephen Jordan, Marika Kieferova, Nicholas Rubin, and Nathan Wiebe for discussions.
Contributions
R.D.S., R. King, R. Kothari, T.E.O., R.B. developed the theoretical formalism, contributed to the analysis of results, and to the writing of the manuscript.
Data Availability
No new data was generated or analyzed in this work; data availability is not applicable.
Supplemental Material
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Additional details
- Accepted
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2025-02-24
- Caltech groups
- Division of Engineering and Applied Science (EAS)
- Publication Status
- Published