Preprint arXiv:2511.16772 Submitted on 20 Nov 2025

As quantum simulators are scaled up to larger system sizes and lower noise rates, non-Markovian noise channels are expected to become dominant. While provably efficient protocols for Markovian models of quantum simulators, either closed system models (described by a Hamiltonian) or open system models (described by a Lindbladian), have been developed, it remains less well understood whether similar protocols for non-Markovian models exist. In this paper, we consider geometrically local lattice models with both quantum and classical non-Markovian noise and show that, under a Gaussian assumption on the noise, we can learn the noise with sample complexity scaling logarithmically with the system size. Our protocol requires preparing the simulator qubits initially in a product state, introducing a layer of single-qubit Clifford gates and measuring product observables.As quantum simulators are scaled up to larger system sizes and lower noise rates, non-Markovian noise channels are expected to become dominant. While provably efficient protocols for Markovian models of quantum simulators, either closed system models (described by a Hamiltonian) or open system models (described by a Lindbladian), have been developed, it remains less well understood whether similar protocols for non-Markovian models exist. In this paper, we consider geometrically local lattice models with both quantum and classical non-Markovian noise and show that, under a Gaussian assumption on the noise, we can learn the noise with sample complexity scaling logarithmically with the system size. Our protocol requires preparing the simulator qubits initially in a product state, introducing a layer of single-qubit Clifford gates and measuring product observables.

quant-pharXiv:2511.16772Nov 24, 20250 citations

Efficient learning of the structure and parameters of local Pauli noise channels

Cambyse Rouzé, Daniel Stilck França

The unavoidable presence of noise is a crucial roadblock for the development of large-scale quantum computers and the ability to characterize quantum noise reliably and efficiently with high precision is essential to scale quantum technologies further. Although estimating an arbitrary quantum channel requires exponential resources, it is expected that physically relevant noise has some underlying local structure, for instance that errors across different qubits have a conditional independence structure. Previous works showed how it is possible to estimate Pauli noise channels with an efficient number of samples in a way that is robust to state preparation and measurement errors, albeit departing from a known conditional independence structure. We present a novel approach for learning Pauli noise channels over n qubits that addresses this shortcoming. Unlike previous works that focused on learning coefficients with a known conditional independence structure, our method learns both the coefficients and the underlying structure. We achieve our results by leveraging a groundbreaking result by Bresler for efficiently learning Gibbs measures and obtain an optimal sample complexity of O(log(n)) to learn the unknown structure of the noise acting on n qubits. This information can then be leveraged to obtain a description of the channel that is close in diamond distance from O(poly(n)) samples. Furthermore, our method is efficient both in the number of samples and postprocessing without giving up on other desirable features such as SPAM-robustness, and only requires the implementation of single qubit Cliffords. In light of this, our novel approach enables the large-scale characterization of Pauli noise in quantum devices under minimal experimental requirements and assumptions.The unavoidable presence of noise is a crucial roadblock for the development of large-scale quantum computers and the ability to characterize quantum noise reliably and efficiently with high precision is essential to scale quantum technologies further. Although estimating an arbitrary quantum channel requires exponential resources, it is expected that physically relevant noise has some underlying local structure, for instance that errors across different qubits have a conditional independence structure. Previous works showed how it is possible to estimate Pauli noise channels with an efficient number of samples in a way that is robust to state preparation and measurement errors, albeit departing from a known conditional independence structure. We present a novel approach for learning Pauli noise channels over n qubits that addresses this shortcoming. Unlike previous works that focused on learning coefficients with a known conditional independence structure, our method learns both the coefficients and the underlying structure. We achieve our results by leveraging a groundbreaking result by Bresler for efficiently learning Gibbs measures and obtain an optimal sample complexity of O(log(n)) to learn the unknown structure of the noise acting on n qubits. This information can then be leveraged to obtain a description of the channel that is close in diamond distance from O(poly(n)) samples. Furthermore, our method is efficient both in the number of samples and postprocessing without giving up on other desirable features such as SPAM-robustness, and only requires the implementation of single qubit Cliffords. In light of this, our novel approach enables the large-scale characterization of Pauli noise in quantum devices under minimal experimental requirements and assumptions.

arXiv:2307.02959Jul 6, 20231 citation

A polynomial-time classical sampler for noisy quantum circuits from statistical mechanics

Jon Nelson, Joel Rajakumar, Chao Yin +2 more

Developing classical simulation algorithms for noisy quantum circuits is essential to delineating the limits of quantum advantage. Existing classical sampling approaches for general circuits require circuit depths to grow logarithmically with system size, so that noise drives the global output state close to a trivial state. Here we show that local accumulation of noise at a depth independent of system size is already sufficient. Specifically, we prove that any geometrically local circuit composed of unital operations and interspersed with single-qubit depolarizing noise of strength $p$ after $Θ(p^{-1} \log p^{-1})$ depth can be approximately sampled from a polynomial-time classical computer. This generalizes existing results that impose anticoncentration assumptions or non-universal gate sets in order to obtain a classical sampler at such shallow depths. Our proof maps the output state of the circuit to a polymer model in statistical mechanics, and combines a convergent cluster expansion with hypercontractivity of the depolarizing channel.Developing classical simulation algorithms for noisy quantum circuits is essential to delineating the limits of quantum advantage. Existing classical sampling approaches for general circuits require circuit depths to grow logarithmically with system size, so that noise drives the global output state close to a trivial state. Here we show that local accumulation of noise at a depth independent of system size is already sufficient. Specifically, we prove that any geometrically local circuit composed of unital operations and interspersed with single-qubit depolarizing noise of strength $p$ after $Θ(p^{-1} \log p^{-1})$ depth can be approximately sampled from a polynomial-time classical computer. This generalizes existing results that impose anticoncentration assumptions or non-universal gate sets in order to obtain a classical sampler at such shallow depths. Our proof maps the output state of the circuit to a polymer model in statistical mechanics, and combines a convergent cluster expansion with hypercontractivity of the depolarizing channel.

quant-pharXiv:2610.00548Oct 2, 20260 citations

Characterizing Arbitrary Lindbladian Dynamics with a Few Pauli Measurements

Taiqi Zhou, Weiyuan Gong

Quantum devices are open systems whose dynamics interleave coherent evolution with dissipation, and benchmarking, error mitigation, and error correction all rest on a faithful model of both. Existing characterization protocols either assume prior knowledge of the interaction and noise structure, or demand ancillas, entangled probes, or mid-circuit control, or capture only the Pauli-diagonal part of the noise. Here, we present a protocol that reconstructs an arbitrary sparse Markovian generator, including every Hamiltonian together with the jump operator coefficients, using only product Pauli state preparation, single uninterrupted forward evolutions, and product Pauli measurements. Given a sparsity budget $M_0$ and a strength bound $Γ$ of the Lindbladian, every coefficient is learned to precision $ε$ from $\widetilde{O}(Γ^2M_0^2/ε^4)$ experiments and $\widetilde{O}(ΓM_0^2/ε^2)$ total evolution time, with both supports identified from data without locality assumptions. The protocol runs at a logarithmic number of positive evolution times on a hardware clock lattice and is provably robust to calibrated state-preparation and measurement errors.Quantum devices are open systems whose dynamics interleave coherent evolution with dissipation, and benchmarking, error mitigation, and error correction all rest on a faithful model of both. Existing characterization protocols either assume prior knowledge of the interaction and noise structure, or demand ancillas, entangled probes, or mid-circuit control, or capture only the Pauli-diagonal part of the noise. Here, we present a protocol that reconstructs an arbitrary sparse Markovian generator, including every Hamiltonian together with the jump operator coefficients, using only product Pauli state preparation, single uninterrupted forward evolutions, and product Pauli measurements. Given a sparsity budget $M_0$ and a strength bound $Γ$ of the Lindbladian, every coefficient is learned to precision $ε$ from $\widetilde{O}(Γ^2M_0^2/ε^4)$ experiments and $\widetilde{O}(ΓM_0^2/ε^2)$ total evolution time, with both supports identified from data without locality assumptions. The protocol runs at a logarithmic number of positive evolution times on a hardware clock lattice and is provably robust to calibrated state-preparation and measurement errors.

quant-pharXiv:2607.23044Jul 28, 20260 citations

Preprint arXiv:2509.02268 Submitted on 2 Sep 2025

X. Yu, H. Li, J. Cirac +1 more

Many-body systems arising in condensed matter physics and quantum optics inevitably couple to the environment and need to be modelled as open quantum systems.While near-optimal algorithms have been developed for simulating many-body quantum dynamics, algorithms for their open system counterparts remain less well investigated.We address the problem of simulating geometrically local many-body open quantum systems interacting with a stationary Gaussian environment.Under a smoothness assumption on the system-environment interaction, we develop near-optimal algorithms that, for a model with N spins and evolution time t, attain a simulation error δ in the system-state with O(N t(N t/δ) o( 1)) gates, O(t(N t/δ) o( 1)) parallelized circuit depth and Õ(N (N t/δ) o( 1)) ancillas.We additionally show that, if only simulating local observables is of interest, then the circuit depth of the digital algorithm can be chosen to be independent of the system size N .This provides theoretical evidence for the utility of these algorithms for simulating physically relevant models, where typically local observables are of interest, on pre-fault tolerant devices.Finally, for the limiting case of Markovian dynamics with commuting jump operators, we propose two algorithms based on sampling a Wiener process and on a locally dilated Hamiltonian construction, respectively.These algorithms reduce the asymptotic gate complexity on N compared to currently available algorithms in terms of the required number of geometrically local gates.Many-body systems arising in condensed matter physics and quantum optics inevitably couple to the environment and need to be modelled as open quantum systems.While near-optimal algorithms have been developed for simulating many-body quantum dynamics, algorithms for their open system counterparts remain less well investigated.We address the problem of simulating geometrically local many-body open quantum systems interacting with a stationary Gaussian environment.Under a smoothness assumption on the system-environment interaction, we develop near-optimal algorithms that, for a model with N spins and evolution time t, attain a simulation error δ in the system-state with O(N t(N t/δ) o( 1)) gates, O(t(N t/δ) o( 1)) parallelized circuit depth and Õ(N (N t/δ) o( 1)) ancillas.We additionally show that, if only simulating local observables is of interest, then the circuit depth of the digital algorithm can be chosen to be independent of the system size N .This provides theoretical evidence for the utility of these algorithms for simulating physically relevant models, where typically local observables are of interest, on pre-fault tolerant devices.Finally, for the limiting case of Markovian dynamics with commuting jump operators, we propose two algorithms based on sampling a Wiener process and on a locally dilated Hamiltonian construction, respectively.These algorithms reduce the asymptotic gate complexity on N compared to currently available algorithms in terms of the required number of geometrically local gates.

Sep 2, 20250 citations

Ansatz-Free Learning of Lindbladian Dynamics In Situ

Petr Ivashkov, Nikita Romanov, Weiyuan Gong +3 more

Characterizing the dynamics of open quantum systems at the level of microscopic interactions and error mechanisms is essential for calibrating quantum hardware, designing robust simulation protocols, and developing tailored error-correction methods. Under Markovian noise/dissipation, a natural characterization approach is to identify the full Lindbladian generator that gives rise to both coherent (Hamiltonian) and dissipative dynamics. Prior protocols for learning Lindbladians from dynamical data assumed pre-specified interaction structure, which can be restrictive when the relevant noise channels or control imperfections are not known in advance. In this paper, we present a sample-efficient protocol for learning sparse Lindbladians without assuming any a priori structure. Our protocol is ancilla-free, uses only product-state preparations and Pauli-basis measurements, admits provably stable coefficient reconstruction, and achieves near-optimal time resolution, making it compatible with near-term experimental capabilities. Together, this provides a systematic route to scalable characterization of open-system quantum dynamics, especially in settings where the error mechanisms of interest are unknown.Characterizing the dynamics of open quantum systems at the level of microscopic interactions and error mechanisms is essential for calibrating quantum hardware, designing robust simulation protocols, and developing tailored error-correction methods. Under Markovian noise/dissipation, a natural characterization approach is to identify the full Lindbladian generator that gives rise to both coherent (Hamiltonian) and dissipative dynamics. Prior protocols for learning Lindbladians from dynamical data assumed pre-specified interaction structure, which can be restrictive when the relevant noise channels or control imperfections are not known in advance. In this paper, we present a sample-efficient protocol for learning sparse Lindbladians without assuming any a priori structure. Our protocol is ancilla-free, uses only product-state preparations and Pauli-basis measurements, admits provably stable coefficient reconstruction, and achieves near-optimal time resolution, making it compatible with near-term experimental capabilities. Together, this provides a systematic route to scalable characterization of open-system quantum dynamics, especially in settings where the error mechanisms of interest are unknown.

quant-pharXiv:2603.05492Mar 6, 20260 citations

p

after

Θ(p^{-1} \log p^{-1})

depth can be approximately sampled from a polynomial-time classical computer. This generalizes existing results that impose anticoncentration assumptions or non-universal gate sets in order to obtain a classical sampler at such shallow depths. Our proof maps the output state of the circuit to a polymer model in statistical mechanics, and combines a convergent cluster expansion with hypercontractivity of the depolarizing channel.

M_0

and a strength bound

Γ

of the Lindbladian, every coefficient is learned to precision

ε

from

\widetilde{O}(Γ^2M_0^2/ε^4)

experiments and

\widetilde{O}(ΓM_0^2/ε^2)

total evolution time, with both supports identified from data without locality assumptions. The protocol runs at a logarithmic number of positive evolution times on a hardware clock lattice and is provably robust to calibrated state-preparation and measurement errors.