Low $T$-count preparation of nuclear eigenstates with tensor networks

TL;DR

This paper introduces a classical-quantum hybrid method using tensor networks and variational circuits to efficiently prepare nuclear eigenstates with low T-count, facilitating early fault-tolerant quantum computing.

Contribution

It demonstrates a novel approach combining DMRG and circuit synthesis to achieve low T-count state preparation for large nuclear systems.

Findings

Achieved low T-count circuits (~20,000 T gates) for nuclear eigenstates on up to 76 qubits.

High-fidelity state preparation suggests feasibility on early fault-tolerant quantum computers.

Utilized specialized U3 synthesis techniques to optimize circuit complexity.

Abstract

We present an efficient protocol leveraging classical computation to support Initial State Preparation for strongly correlated fermionic systems, a critical bottleneck for fault-tolerant quantum simulation. Focusing on nuclear shell model eigenstates, we first demonstrate that the Density Matrix Renormalization Group algorithm can efficiently approximate target states as Matrix Product States, capitalizing on the favourable entanglement structure of these fermionic systems. These high-fidelity approximations are then leveraged as a classical resource in a variational circuit optimization scheme to compile shallow quantum circuits. We establish concrete resource estimates by decomposing the resulting circuits into the industry-standard Clifford$+T$ gateset, exploring the benefits of specialized $U3$ synthesis techniques. For all nuclear systems tested, on up to 76 qubit Hamiltonians, we consistently find low $T$-count circuits preparing the nuclear eigenstates to high fidelity with $\sim 2\times 10^4$ total $T$ gates. This low number gives confidence these eigenstates can be prepared on early fault-tolerant quantum computers. Our work establishes a viable path toward practical ground state preparation for nuclear structure and other fermionic applications.