Abstract
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 multi-scale entanglement renormalization ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than $10^4$ parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for the 1D/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.
Highlights
Advances in digital quantum computing have led to renewed interest in quantum circuit (QC) representations of many-body states
We benchmark the performance of the quantum circuit MPS” (QMPS), QMERA, and global QC Ansatz versus the dense matrix product state (MPS) (DMRG) and dense multiscale entanglement renormalization Ansatz (MERA) for the 1D Heisenberg and Fermi-Hubbard models with L 1⁄4 32 (2D results are discussed in a later section)
We studied the variational power of quantum circuit tensor networks, and in particular, quantum circuit matrix product states and the quantum circuit multiscale entanglement renormalization Ansatz, for representing the ground states of quantum many-particle problems
Summary
Advances in digital quantum computing have led to renewed interest in quantum circuit (QC) representations of many-body states. Our focus is on establishing the variational power of quantum tensor networks to capture quantum many-body ground states. This is an application where traditional dense tensor networks do well, and is in some sense the hardest test for quantum circuit tensor networks to pass. With careful optimization strategies, quantum circuit tensor networks are very expressive, and in some cases even more expressive than classical dense tensor networks This suggests a regime where a quantum advantage in the sense of expressiveness may be observed in physical ground-state simulations. We finish with a discussion of our findings in the context of computational quantum advantage
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