aiqbench analysis
This research advances exact quantum circuit simulation by optimizing sum-of-powers calculations through rank-width decomposition and stabilizer-rank techniques. The proposed dynamic programming approach offers a complementary solution to existing treewidth-based methods, particularly excelling on structured circuit families where traditional baselines become computationally prohibitive. By managing non-Clifford phases efficiently, this work provides new theoretical bounds and practical tools for simulating complex quantum algorithms without exponential overhead.
Quadratic Sums-of-Powers for Fixed-Parameter Tractable Quantum-Circuit Simulation
arXiv:2605.29944v2 Announce Type: replace Abstract: Strongly simulating a quantum circuit, that is, computing an output amplitude, can be done by summing the circuit's Feynman paths: a weighted count over assignments to Boolean path variables. The circuit's gates induce correlations among these variables, forming a graph whose structure controls several exact simulation routes. This sum-of-powers (SOP) viewpoint underlies recent simulators built on binary decision diagrams and weighted model counting. For a quadratic SOP with $n$ variables, even modulus $r$, and a rank-decomposition of its variable graph of width $k$, our dynamic program (DP) computes an amplitude using only $O(4^kpoly(n))$ arithmetic operations. For Clifford$+T$ circuits, the amplitude is given by an SOP with modulus $8$. Rank-width never exceeds linear rank-width, which governs some decision-diagram approaches, and is at most one greater than the Markov--Shi contraction complexity of the circuit tensor network. Moreover, there are non-Clifford families of bounded rank-width where both competing parameters diverge. We also present a stabilizer-rank optimization, exploiting that the DP tables are stabilizer-type Gauss sums. Each subtree runs at the width price of its cut-ranks or at a magic price that discharges the non-Clifford phases below it. The resulting best total cost never exceeds $O(4^kpoly(n))$, yet is polynomial on mixed families where the pure rank-width and pure $T$-count guarantees are both exponential. Clifford amplitudes take polynomial time on any graph, the exact-amplitude consequence of Gottesman--Knill. A prototype evaluation on standard circuit benchmarks finds treewidth bucket elimination the strongest baseline, with the new rank-width DP complementary: it wins on structured families where treewidth blows up.
Abstract:Strongly simulating a quantum circuit, that is, computing an output amplitude, can be done by summing the circuit's Feynman paths: a weighted count over assignments to Boolean path variables. The circuit's gates induce correlations among these variables, forming a graph whose structure controls several exact simulation routes. This sum-of-powers (SOP) viewpoint underlies recent simulators built on binary decision diagrams and weighted model counting. For a quadratic SOP with $n$ variables, even modulus $r$, and a rank-decomposition of its variable graph of width $k$, our dynamic program (DP) computes an amplitude using only $O(4^kpoly(n))$ arithmetic operations. For Clifford$+T$ circuits, the amplitude is given by an SOP with modulus $8$. Rank-width never exceeds linear rank-width, which governs some decision-diagram approaches, and is at most one greater than the Markov--Shi contraction complexity of the circuit tensor network. Moreover, there are non-Clifford families of bounded rank-width where both competing parameters diverge. We also present a stabilizer-rank optimization, exploiting that the DP tables are stabilizer-type Gauss sums. Each subtree runs at the width price of its cut-ranks or at a magic price that discharges the non-Clifford phases below it. The resulting best total cost never exceeds $O(4^kpoly(n))$, yet is polynomial on mixed families where the pure rank-width and pure $T$-count guarantees are both exponential. Clifford amplitudes take polynomial time on any graph, the exact-amplitude consequence of Gottesman--Knill. A prototype evaluation on standard circuit benchmarks finds treewidth bucket elimination the strongest baseline, with the new rank-width DP complementary: it wins on structured families where treewidth blows up.
Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS); Logic in Computer Science (cs.LO)
arXiv:2605.29944 [quant-ph]
(or arXiv:2605.29944v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2605.29944 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 353 words
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