Abstract
We propose a neural-network variational quantum algorithm to simulate the time evolution of quantum many-body systems. Based on a modified restricted Boltzmann machine (RBM) wavefunction ansatz, the proposed algorithm can be efficiently implemented in near-term quantum computers with low measurement cost. Using a qubit recycling strategy, only one ancilla qubit is required to represent all the hidden spins in an RBM architecture. The variational algorithm is extended to open quantum systems by employing a stochastic Schrodinger equation approach. Numerical simulations of spin-lattice models demonstrate that our algorithm is capable of capturing the dynamics of closed and open quantum many-body systems with high accuracy without suffering from the vanishing gradient (or 'barren plateau') issue for the considered system sizes.
Highlights
Accurate and efficient simulation of quantum many-body dynamics remains one of the most challenging problems in physics, despite nearly a century of progress
We study the dynamics of a transverse-field Ising (TFI) model induced by quantum quench
We compare the results from the unitary-coupled RBM (uRBM) algorithm with results from exact diagonalization by studying the evolution of transverse spin polarization σ1x and its correlation σ1xσ2x
Summary
Accurate and efficient simulation of quantum many-body dynamics remains one of the most challenging problems in physics, despite nearly a century of progress. Renewed interest has been sparked in this field due to recent experiments with Rydberg atoms [1,2], which suggest the existence of scar states which do not thermalize This has led to new studies of fragmented Hilbert spaces for such constrained models [3,4,5] along with further studies on fractons, which are restricted excitations which can disperse only in certain directions [6,7]. One of the most powerful numerical tools at the disposal of condensed matter theorists is quantum Monte Carlo, which has performed remarkably well for equilibrium physics of numerous systems [11,12] This has made the applicability of this technique important to study real time dynamics. The proposed method is benchmarked against canonical spin-lattice models and performs well for dynamics of both closed and open systems
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