Time Evolution of Uniform Sequential Circuits

• URL: http://arxiv.org/abs/2210.03751v4
• Date: Mon, 21 Aug 2023 15:52:59 GMT
• Title: Time Evolution of Uniform Sequential Circuits
• Authors: Nikita Astrakhantsev, Sheng-Hsuan Lin, Frank Pollmann and Adam Smith
• Abstract summary: We present a hybrid quantum-classical scaling algorithm for time evolving a one-dimensional uniform system in the thermodynamic limit. We show numerically that this anatzs requires a number of parameters in the simulation time for a given accuracy. All steps of the hybrid optimization are designed with near-term digital quantum computers in mind.
• Score: 0.16385815610837165
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. In this work, we present a polynomially scaling hybrid quantum-classical algorithm for time evolving a one-dimensional uniform system in the thermodynamic limit. This algorithm uses a layered uniform sequential quantum circuit as a variational ansatz to represent infinite translation-invariant quantum states. We show numerically that this ansatz requires a number of parameters polynomial in the simulation time for a given accuracy. Furthermore, this favourable scaling of the ansatz is maintained during our variational evolution algorithm. All steps of the hybrid optimization are designed with near-term digital quantum computers in mind. After benchmarking the evolution algorithm on a classical computer, we demonstrate the measurement of observables of this uniform state using a finite number of qubits on a cloud-based quantum processing unit. With more efficient tensor contraction schemes, this algorithm may also offer improvements as a classical numerical algorithm.

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