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This paper introduces a recursive algorithm that significantly reduces the compiled T and CX depth for controlled time-evolution circuits by grouping Pauli terms and removing ancilla control overhead. Benchmarking on structured spin Hamiltonians demonstrates substantial efficiency gains, such as an 85.2% reduction in T depth for a 24-spin Kagome system, which directly addresses gate count constraints in quantum algorithms. The approach offers a practical optimization for implementing fundamental building blocks like quantum eigenvalue transformation and Hamiltonian filtering on near-term hardware.
Efficient Quantum Circuit Construction of Controlled Time-Evolution for Arbitrary Pauli-Sum Hamiltonians
arXiv:2606.06070v1 Announce Type: new Abstract: Controlled time-evolution circuits select forward or backward Hamiltonian time evolution according to the state of an ancilla qubit. They are fundamental building blocks in quantum eigenvalue transformation of unitaries, Hamiltonian filtering, and related quantum algorithms. A direct realization adds ancilla control to the elementary gates of the time-evolution circuit and therefore increases the two-qubit gate count, compiled T depth and CX depth. We develop an efficient recursive algorithm that, for an arbitrary Pauli-sum Hamiltonian, partitions the input Pauli terms into groups and assigns to each group a sign-flip Pauli string that anti-commutes with the in-group terms, thereby removing ancilla control from the grouped time-evolution blocks. Numerical benchmarks on random Hamiltonians and structured spin Hamiltonians show reductions in compiled T depth and compiled CX depth. For a Kagome Hamiltonian with 24 spins under full connectivity, the proposed construction reduces the compiled T depth by 85.2% and the compiled CX depth by 68.9%, compared with a conventional implementation that decomposes the Hamiltonian into individual Pauli terms and implements the controlled time evolution of each term by directly adding the ancilla qubit to the corresponding Pauli-rotation circuit.
Abstract:Controlled time-evolution circuits select forward or backward Hamiltonian time evolution according to the state of an ancilla qubit. They are fundamental building blocks in quantum eigenvalue transformation of unitaries, Hamiltonian filtering, and related quantum algorithms. A direct realization adds ancilla control to the elementary gates of the time-evolution circuit and therefore increases the two-qubit gate count, compiled T depth and CX depth. We develop an efficient recursive algorithm that, for an arbitrary Pauli-sum Hamiltonian, partitions the input Pauli terms into groups and assigns to each group a sign-flip Pauli string that anti-commutes with the in-group terms, thereby removing ancilla control from the grouped time-evolution blocks. Numerical benchmarks on random Hamiltonians and structured spin Hamiltonians show reductions in compiled T depth and compiled CX depth. For a Kagome Hamiltonian with 24 spins under full connectivity, the proposed construction reduces the compiled T depth by 85.2% and the compiled CX depth by 68.9%, compared with a conventional implementation that decomposes the Hamiltonian into individual Pauli terms and implements the controlled time evolution of each term by directly adding the ancilla qubit to the corresponding Pauli-rotation circuit.
arXiv:2606.06070 [quant-ph]
(or arXiv:2606.06070v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.06070 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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