Many-Body Time Evolution from a Correlation-Efficient Quantum Algorithm

Abstract

We introduce the correlation-efficient time-evolution (CETE) algorithm for simulating quantum many-body dynamics. CETE recasts each step of time evolution as a time-independent correlation problem: the ansatz begins from a mean-field single Slater determinant and is then correlated to capture the true time-evolved state. We derive this exact ansatz from a contraction of the time-dependent Schrödinger equation onto the space of two electrons. Unlike conventional evolution by sequential short-time propagators, which must both correlate and decorrelate the state as the degree of correlation fluctuates in time, CETE correlates only once. This substantially reduces circuit depth, extending accessible simulation times on near-term quantum devices. We demonstrate the approach by simulating the time evolution of the hydrogen molecule's electronic wavefunction, highlighting the potential for the CETE algorithm to simulate strongly correlated systems on near-term devices.

Figures (3)

• Figure 1: Measured diagonal 1-RDM $^1\hat{D}$ elements for H$_2$ obtained using the CETE ansatz and sequential evolution as a function of time. Pauli-sum tomography is performed at intervals of $0.9~\text{Ha}^{-1}$ using $10^4$ shots per Pauli string. All measurements are made on qubit 137 of ibm_fez. The solid line indicates a noiseless state-vector reference. At all time points $\langle {\hat{a}}^\dagger_0 {\hat{a}}^{}_0 \rangle = \langle a_2^\dagger {\hat{a}}^{}_2 \rangle$ and $\langle {\hat{a}}^\dagger_1 {\hat{a}}^{}_1 \rangle = \langle {\hat{a}}^\dagger_3 {\hat{a}}^{}_3 \rangle$.
• Figure 2: Measured energy values of H$_2$ obtained using the CETE ansatz $\boldsymbol{\circ}$ and sequential evolution $\boldsymbol{\times}$ as a function of time. Pauli-sum tomography is performed at intervals of $0.9~\text{Ha}^{-1}$ with $10^4$ shots per Pauli string. All measurements are made on qubit 137 of ibm_fez. The solid line indicates a noiseless state-vector reference.
• Figure 3: Depth of quantum circuits implementing the CETE ansatz $\boldsymbol{\circ}$ and sequential evolution $\boldsymbol{\times}$ as a function of time. Depths are evaluated at $0.9~\text{Ha}^{-1}$ intervals. The CETE ansatz for each time point is constructed using the noiseless AerSimulator.

Theorems & Definitions (2)

• Theorem
• proof