Variational Power of Quantum Circuit Tensor Networks
We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multiscale entanglement renormalization Ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than 104 parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for the 1D and 2D Heisenberg and 1D Fermi-Hubbard models. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of advantage in quantum expressiveness in the representation of physical ground states.
- Research Organization:
- Emory Univ., Atlanta, GA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC); Simons Foundation; National Science Foundation (NSF); Amazon Web Services, Inc.
- Grant/Contract Number:
- SC0019374; 2040549
- OSTI ID:
- 1854378
- Alternate ID(s):
- OSTI ID: 1980361
- Journal Information:
- Physical Review. X, Journal Name: Physical Review. X Vol. 12 Journal Issue: 1; ISSN 2160-3308
- Publisher:
- American Physical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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