Abstract
The current generation of noisy intermediate scale quantum computers introduces new opportunities to study quantum many-body systems. In this paper, we show that quantum circuits can provide a dramatically more efficient representation than current classical numerics of the quantum states generated under non-equilibrium quantum dynamics. For quantum circuits, we perform both real- and imaginary-time evolution using an optimization algorithm that is feasible on near-term quantum computers. We benchmark the algorithms by finding the ground state and simulating a global quench of the transverse field Ising model with a longitudinal field on a classical computer. Furthermore, we implement (classically optimized) gates on a quantum processing unit and demonstrate that our algorithm effectively captures real time evolution.
Highlights
Ground states of strongly correlated systems and their quantum dynamics far from equilibrium present important problems in understanding quantum matter
We show that quantum circuits can provide a dramatically more efficient representation than current classical numerics of the quantum states generated under nonequilibrium quantum dynamics
The corresponding matrixproduct state (MPS) representation has an exponentially large bond dimension requiring O(2M ) parameters. We emphasize that this time evolution algorithm is different from the time-dependent variational principle (TDVP) algorithm simulating time evolution with a quantum circuit proposed in Refs. [13,14]
Summary
Ground states of strongly correlated systems and their quantum dynamics far from equilibrium present important problems in understanding quantum matter. (ii) The highly entangled and highcomplexity states occupy the majority of the full Hilbert space Such states are not physical because they can only be produced after an exponentially long time [18]. (iii) The remaining highly entangled and low-complexity states can be simulated efficiently on quantum but not classical devices. We refer to the latter partition of the Hilbert space as the “complexity window” [19]. For a given amount of entanglement, we see the quantum circuits requires exponentially fewer parameters than the matrix-product states, which agrees with the picture we describe While these states mark the limit of current classical numerical methods, quantum simulators and computers may allow us to study these physically interesting states in this complexity window. IV, by noting several future avenues of exploration using the techniques developed in this work
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