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This research introduces a rigorous Hamiltonian-level certificate to validate the accuracy of distributed quantum simulations before gate decomposition, directly addressing efficiency bottlenecks in circuit cutting. By quantifying cross-module residuals and linking them to entanglement properties, the work provides essential tools for scaling quantum computations across smaller devices without sacrificing fidelity. The demonstrated block-factorised simulation up to 20 qubits highlights practical pathways for leveraging modular architectures in near-term quantum hardware.
A Hamiltonian-Level Certificate for Network-Free Distributed Quantum Simulation:Exact Tensor-Separability Criterion and Approximate Residual Bounds
arXiv:1901.04629v2 Announce Type: replace Abstract: Circuit cutting allows quantum circuits to be evaluated on smaller devices at the cost of additional sampling and classical reconstruction. For Hamiltonian-simulation circuits, the target unitary $\exp[it\mathbf H]$ connects this decomposition problem to the structure of the generator. We develop a Hamiltonian-level certificate that assesses exact separability and the accuracy of independent module evolution before a gate decomposition is chosen. For a time-independent Hamiltonian and a fixed module partition, the Hilbert--Schmidt projection onto sums of module-local terms isolates a cross-module residual $H_{ns}$. Its vanishing is necessary and sufficient for product evolution at all times; for Pauli-list inputs, this condition is checked in one pass over the combined coefficients. When $H_{ns}\ne0$, the projected evolution has operator-norm error at most $|t| ||H_{ns}||_{op}$. Across a bipartition, an explicit first-order algebraic correction has the same operator-Schmidt rank as $H_{ns}$ and leaves a second-order residual. The same Hamiltonian residual connects this approximation to short-time entanglement, determining the leading state-space and operator-space entangling powers and, through its Schmidt spectrum, the leading Choi tripartite-information terms. Numerical experiments test these relations and demonstrate block-factorised simulation up to $20$ qubits.
Abstract:Circuit cutting allows quantum circuits to be evaluated on smaller devices at the cost of additional sampling and classical reconstruction. For Hamiltonian-simulation circuits, the target unitary $\exp[it\mathbf H]$ connects this decomposition problem to the structure of the generator. We develop a Hamiltonian-level certificate that assesses exact separability and the accuracy of independent module evolution before a gate decomposition is chosen. For a time-independent Hamiltonian and a fixed module partition, the Hilbert--Schmidt projection onto sums of module-local terms isolates a cross-module residual $H_{ns}$. Its vanishing is necessary and sufficient for product evolution at all times; for Pauli-list inputs, this condition is checked in one pass over the combined coefficients. When $H_{ns}\ne0$, the projected evolution has operator-norm error at most $|t| ||H_{ns}||_{op}$. Across a bipartition, an explicit first-order algebraic correction has the same operator-Schmidt rank as $H_{ns}$ and leaves a second-order residual. The same Hamiltonian residual connects this approximation to short-time entanglement, determining the leading state-space and operator-space entangling powers and, through its Schmidt spectrum, the leading Choi tripartite-information terms. Numerical experiments test these relations and demonstrate block-factorised simulation up to $20$ qubits.
Quantum Physics (quant-ph); Distributed, Parallel, and Cluster Computing (cs.DC)
arXiv:1901.04629 [quant-ph]
(or arXiv:1901.04629v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.1901.04629 Focus to learn more arXiv-issued DOI via DataCite
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