Half the Interference, Most of the Answer: Approximate Quantum Simulation via Path-Sum Pruning

• URL: http://arxiv.org/abs/2606.01922v1
• Date: Mon, 01 Jun 2026 08:57:44 GMT
• Title: Half the Interference, Most of the Answer: Approximate Quantum Simulation via Path-Sum Pruning
• Abstract summary: We introduce statistical interference sampling, a framework that makes this second bottleneck explicit.<n>On benchmark circuits for Deutsch-Jozsa, Grover search, Simon's problem, and small Shor period-finding instances, we find that nearly 50% of endpoint interference reactions can be omitted.
• Score: 0.15554111333620432
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Classical simulation of quantum circuits is expensive for two distinct reasons. The obvious one is state-space size: an n-qubit system requires exponentially many amplitudes. The less obvious one is interference: useful output distributions emerge only after many computational histories have been coherently combined at common endpoints, and this aggregation step is itself a substantial source of cost. We introduce statistical interference sampling, a framework that makes this second bottleneck explicit by treating endpoint interference as a separately schedulable computation. Using the Chemical Abstract Machine (ChAM) as our model, weighted path contributions evolve as concurrent molecular species, and interference reactions combine contributions that share a common output state. A threshold rule terminates the process once an endpoint accumulates sufficient amplitude, discarding the remaining reactions. The method does not improve worst-case complexity and is not intended as a general-purpose simulator. Its purpose is to ask a more targeted question: how much of the interference calculation can be skipped while still recovering a useful output distribution? On benchmark circuits for Deutsch-Jozsa, Grover search, Simon's problem, and small Shor period-finding instances, we find that nearly 50% of endpoint interference reactions can be omitted while maintaining over 90% output accuracy for most algorithms tested. These results suggest that interference arithmetic is a structured resource that admits meaningful approximation, and that exposing it explicitly opens new opportunities for pruning strategies across path-sum, Pauli-path, and tensor-network simulation methods.

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