Pilot-Wave Simulator: Exact Classical Sampling from Ideal and Noisy Quantum Circuits up to Hundreds of Qubits

Gleb Kalachev; Pavel Mosharev; Zuoheng Zou; Pavel Panteleev; Man-Hong Yung

doi:10.22331/q-2026-07-23-2173

Pilot-Wave Simulator: Exact Classical Sampling from Ideal and Noisy Quantum Circuits up to Hundreds of Qubits

Gleb Kalachev¹, Pavel Mosharev², Zuoheng Zou³, Pavel Panteleev¹, and Man-Hong Yung⁴

¹Lomonosov Moscow State University, Moscow, 119991, Russia
²School of Physical Sciences, University of Science and Technology of China, Hefei, 230026, China
³School of Physics, Peking University, Beijing 100871, China
⁴Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China

Published:	2026-07-23, volume 10, page 2173
Editor:	Yuan Liu
Eprint:	arXiv:2510.24218v2
Doi:	https://doi.org/10.22331/q-2026-07-23-2173
Citation:	Quantum 10, 2173 (2026).

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Abstract

Quantum circuit simulators running on classical computers offer a vital platform for designing, testing, and optimizing quantum algorithms, driving innovation despite limited access to real quantum hardware. However, their scalability is inherently constrained by exponential memory and computational overhead, which restricts accurate simulation of large-scale quantum circuits and often results in approximate output distributions. Here, we propose an exact sampling algorithm that integrates tensor network contraction techniques with a Markov process, wherein a classical state evolves according to the local structure of the quantum circuit. As a demonstration, we target the challenge of generating samples from ideal and noisy QAOA circuits with up to 476 qubits, incorporating both depolarizing and amplitude damping noise models. These results enable further validation of several assumptions and conjectures at a scale previously out of reach, significantly expanding the scope of classical simulation in quantum algorithm research.

Popular summary

Simulating a quantum circuit on a classical computer usually requires tracking a quantum state whose size grows exponentially with the number of qubits. Yet many applications require only samples of the circuit’s measurement outcomes, rather than the complete quantum state.

Earlier work introduced a sequential, sometimes called gate-by-gate, sampling principle: a classical bit string is updated after each quantum gate using transition probabilities determined by a small number of quantum amplitudes. The bit string then follows exactly the same probability distribution as a measurement of the evolving quantum circuit. One can view this process as a pilot wave guiding the evolution of a classical configuration, while each update depends only on a small local fragment of that wave.

In this work, we turn this principle into an efficient simulator for large structured quantum circuits. Tensor-network contraction is used to calculate only the amplitudes required for each update. A block decomposition limits the number of possible transitions, while a large class of gates can be processed deterministically. We further show how common noise processes can be incorporated while keeping essentially the same tensor-network contraction complexity as for the ideal circuit. The method is particularly effective for shallow circuits with many qubits and sparse, structured interaction graphs.

We apply the resulting Pilot-Wave simulator to ideal and noisy QAOA circuits for Ising optimization problems on grid-like graphs. We reach up to 476 qubits for single-layer circuits and study deeper circuits on smaller systems. The generated samples provide numerical evidence that QAOA output distributions have a pseudo-Boltzmann low-energy profile, with lower effective temperature at greater circuit depth, while the probability of sampling the ground state decreases exponentially with system size. On grids of up to 256 qubits, our results also support a conjecture by Hastings: a simple classical local-update algorithm can perform comparably to shallow QAOA at the corresponding depth, while representative device noise shifts the comparison further in favor of the classical method.

These results expand the range of structured quantum circuits whose output statistics can be studied and benchmarked accurately using classical computers.

► BibTeX data

@article{Kalachev2026pilotwavesimulator,
  doi = {10.22331/q-2026-07-23-2173},
  url = {https://doi.org/10.22331/q-2026-07-23-2173},
  title = {Pilot-{W}ave {S}imulator: {E}xact {C}lassical {S}ampling from {I}deal and {N}oisy {Q}uantum {C}ircuits up to {H}undreds of {Q}ubits},
  author = {Kalachev, Gleb and Mosharev, Pavel and Zou, Zuoheng and Panteleev, Pavel and Yung, Man-Hong},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2173},
  month = jul,
  year = {2026}
}

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