Tensor-based quantum phase difference estimation for large-scale demonstration

TL;DR

This paper introduces a tensor-based quantum phase difference estimation algorithm that enhances energy calculations in quantum systems, demonstrating significant improvements in noise reduction and scalability on real quantum hardware.

Contribution

The authors develop a novel tensor-network-based QPDE algorithm with noise reduction and demonstrate its application to large-scale quantum simulations on IBM devices.

Findings

Achieved energy gap calculations for 32-qubit Hubbard models.

Reduced depolarization noise exponentially.

Enabled molecular simulations up to 21 qubits.

Abstract

We develop an energy calculation algorithm leveraging quantum phase difference estimation (QPDE) scheme and a tensor-network-based unitary compression method in the preparation of superposition states and time-evolution gates. Alongside its efficient implementation, this algorithm reduces depolarization noise affections exponentially. We demonstrated energy gap calculations for one-dimensional Hubbard models on IBM superconducting devices using circuits up to 32-system (plus one-ancilla) qubits, a five-fold increase over previous QPE demonstrations, at the 7242 controlled-Z gate level of standard transpilation, utilizing a Q-CTRL error suppression module. Additionally, we propose a technique towards molecular executions using spatial orbital localization and index sorting, verified linear polyene simulations up to 21 qubits. Since QPDE can handle the same objectives as QPE, our algorithm represents a leap forward in quantum computing on real devices.