Redefining Lexicographical Ordering: Optimizing Pauli String Decompositions for Quantum Compiling

TL;DR

This paper introduces a new algorithm for Pauli string decomposition in quantum circuit compilation that reduces gate count and accounts for qubit connectivity, improving efficiency without increasing Trotter error.

Contribution

The paper presents a novel synthesis algorithm for trotterized operators that minimizes gates and considers hardware connectivity, outperforming existing methods.

Findings

Significant gate reduction compared to previous methods.

No additional CNOT gates needed for target hardware.

Trotter error remains comparable to baseline methods.

Abstract

In quantum computing, the efficient optimization of Pauli string decompositions is a crucial aspect for the compilation of quantum circuits for many applications, such as chemistry simulations and quantum machine learning. In this paper, we propose a novel algorithm for the synthesis of trotterized time-evolution operators that results in circuits with significantly fewer gates than previous solutions. Our synthesis procedure takes the qubit connectivity of a target quantum computer into account. As a result, the generated quantum circuit does not require routing, and no additional CNOT gates are needed to run the resulting circuit on a target device. We compare our algorithm against Paulihedral and TKET, and show a significant improvement for randomized circuits and different molecular ansatzes. We also investigate the Trotter error introduced by our ordering of the terms in the Hamiltonian versus default ordering and the ordering from the baseline methods and conclude that our method on average does not increase the Trotter error.