Classical simulation of a quantum circuit with noisy magic inputs

• URL: http://arxiv.org/abs/2601.10111v2
• Date: Mon, 19 Jan 2026 05:59:35 GMT
• Title: Classical simulation of a quantum circuit with noisy magic inputs
• Authors: Jiwon Heo, Sojeong Park, Changhun Oh,
• Abstract summary: We characterize how noise on magic resources changes the classical simulability of quantum circuits.<n>We adopt a resource-centric noise model in which only the injected magic components are noisy, while the baseline states, operations, and measurements belong to an efficiently simulable family.
• Score: 0.6287298138084187
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Magic states are essential for universal quantum computation and are widely viewed as a key source of quantum advantage, yet in realistic devices they are inevitably noisy. In this work, we characterize how noise on injected magic resources changes the classical simulability of quantum circuits and when it induces a transition from classically intractable behavior to efficient classical simulation. We adopt a resource-centric noise model in which only the injected magic components are noisy, while the baseline states, operations, and measurements belong to an efficiently simulable family. Within this setting, we develop an approximate classical sampling algorithm with controlled error and prove explicit noise-dependent conditions under which the algorithm runs in polynomial time. Our framework applies to both qubit circuits with Clifford baselines and fermionic circuits with matchgate baselines, covering representative noise channels such as dephasing and particle loss. We complement the analysis with numerical estimates of the simulation cost, providing concrete thresholds and runtime scaling across practically relevant parameter regimes.

Related papers

• When quantum resources backfire: Non-gaussianity and symplectic coherence in noisy bosonic circuits [1.0874100424278175]
  We introduce the $textitdisplacement propagation$ algorithm for simulating noisy bosonic circuits.<n>We identify several computational phase transitions, revealing regimes where even modest noise levels render bosonic circuits efficiently classically simulable.<n>In particular, our analysis reveals a surprising phenomenon: computational resources usually associated with bosonic quantum advantage, namely non-Gaussianity and symplectic coherence, can make the system easier to classically simulate in presence of noise.
  arXiv  Detail & Related papers  (2025-10-08T17:25:47Z)
• Classically Sampling Noisy Quantum Circuits in Quasi-Polynomial Time under Approximate Markovianity [0.616870773176256]
  We present a classical algorithm that runs in $nrmpolylog(n)$ time for simulating quantum circuits under local depolarizing noise.<n>Our results significantly extend the boundary of classical simulability and suggest that noise generically enforces approximate Markovianity and classical simulability.
  arXiv  Detail & Related papers  (2025-10-07T18:00:03Z)
• Provably Robust Training of Quantum Circuit Classifiers Against Parameter Noise [49.97673761305336]
  Noise remains a major obstacle to achieving reliable quantum algorithms.<n>We present a provably noise-resilient training theory and algorithm to enhance the robustness of parameterized quantum circuit classifiers.
  arXiv  Detail & Related papers  (2025-05-24T02:51:34Z)
• Correlating noise floor with magic and entanglement in Pauli product states [37.69303106863453]
  We show the ability to recover resources specific to quantum computing from noisy states generated by Pauli product formulas.<n>The fidelity of purified states represents the noise floor of a given computation.<n>We experimentally validate these findings by collecting classical shadow data for a range of small circuits.
  arXiv  Detail & Related papers  (2025-05-07T19:24:00Z)
• A polynomial-time classical algorithm for noisy quantum circuits [1.2708457954150887]
  We provide a-time classical algorithm for noisy quantum circuits. Our approach is based upon the intuition that noise exponentially damps non-local correlations. For constant noise rates, any quantum circuit for which error mitigation is efficient on most input states, is also classically simulable on most input states.
  arXiv  Detail & Related papers  (2024-07-17T17:48:39Z)
• Scalable noisy quantum circuits for biased-noise qubits [37.69303106863453]
  We consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. For realistic noise models, phase-flip will not be negligible, but in the Pauli-Twirling approximation, we show that our benchmark could check the correctness of circuits containing up to $106$ gates.
  arXiv  Detail & Related papers  (2023-05-03T11:27:50Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Efficient classical simulation and benchmarking of quantum processes in the Weyl basis [0.0]
  We develop a randomized benchmarking algorithm which uses Weyl unitaries to efficiently identify and learn a mixture of error models. We apply our methods to ansatz circuits that appear in the Variational Quantum Eigensolver.
  arXiv  Detail & Related papers  (2020-08-27T16:46:12Z)
• Efficient classical simulation of random shallow 2D quantum circuits [104.50546079040298]
  Random quantum circuits are commonly viewed as hard to simulate classically. We show that approximate simulation of typical instances is almost as hard as exact simulation. We also conjecture that sufficiently shallow random circuits are efficiently simulable more generally.
  arXiv  Detail & Related papers  (2019-12-31T19:00:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.