Statistics of Work in Quantum Systems under Classical and Quantum Noise

We investigate the correspondence between classical noise and quantum environments. Although it is known that classical noise can be mapped to quantum environments for pure dephasing and infinite-temperature dissipation processes, we show how finite-temperature dissipation can be also described using classical noise by introducing auxiliary systems and conservation. Taking a two-level system as an example, we construct the so-called central spin model with its couplings fluctuating with the classical noise and then acquire its statistical-average dynamics which captures the dissipation beyond infinite temperature. By adjusting the number of auxiliary systems and their initial states, the noise-based model reproduces both Markovian and non-Markovian evolution. We also find that different quantities of the two-level system are governed by different model parameters, indicating that the constructed model is an effective simulator for specific observables rather than an equivalent form of a realistic open system. In addition, the model is also applicable to investigate topical mechanisms of open systems, e.g., negative temperatures and asymmetric equidistant quenches.We investigate the correspondence between classical noise and quantum environments. Although it is known that classical noise can be mapped to quantum environments for pure dephasing and infinite-temperature dissipation processes, we show how finite-temperature dissipation can be also described using classical noise by introducing auxiliary systems and conservation. Taking a two-level system as an example, we construct the so-called central spin model with its couplings fluctuating with the classical noise and then acquire its statistical-average dynamics which captures the dissipation beyond infinite temperature. By adjusting the number of auxiliary systems and their initial states, the noise-based model reproduces both Markovian and non-Markovian evolution. We also find that different quantities of the two-level system are governed by different model parameters, indicating that the constructed model is an effective simulator for specific observables rather than an equivalent form of a realistic open system. In addition, the model is also applicable to investigate topical mechanisms of open systems, e.g., negative temperatures and asymmetric equidistant quenches.

arXiv:2408.03543Physical Review ADec 26, 20243 citations

On the description of noise in quantum systems

Richard Bausch, Á. Stáhl

The European Physical Journal AFeb 1, 19679 citations

Work and work fluctuations in quantum systems

H. Schröder, Jens Teifel, G. Mahler

The European Physical Journal Special TopicsDec 1, 20079 citations

When can quantum decoherence be mimicked by classical noise?

Bing Gu, Ignacio Franco

Quantum decoherence arises due to uncontrollable entanglement between a system and its environment. However, the effects of decoherence are often thought of and modeled through a simpler picture in which the role of the environment is to introduce classical noise in the system's degrees of freedom. Here, we establish necessary conditions that the classical noise models need to satisfy to quantitatively model the decoherence. Specifically, for pure-dephasing processes, we identify well-defined statistical properties for the noise that are determined by the quantum many-point time correlation function of the environmental operators that enter into the system-bath interaction. In particular, for the exemplifying spin-boson problem with a Lorentz-Drude spectral density, we show that the high-temperature quantum decoherence is quantitatively mimicked by colored Gaussian noise. In turn, for dissipative environments, we show that classical noise models cannot describe decoherence effects due to relaxation through spontaneous emission of photons/phonons. These developments provide a rigorous platform to assess the validity of classical noise models of decoherence.Quantum decoherence arises due to uncontrollable entanglement between a system and its environment. However, the effects of decoherence are often thought of and modeled through a simpler picture in which the role of the environment is to introduce classical noise in the system's degrees of freedom. Here, we establish necessary conditions that the classical noise models need to satisfy to quantitatively model the decoherence. Specifically, for pure-dephasing processes, we identify well-defined statistical properties for the noise that are determined by the quantum many-point time correlation function of the environmental operators that enter into the system-bath interaction. In particular, for the exemplifying spin-boson problem with a Lorentz-Drude spectral density, we show that the high-temperature quantum decoherence is quantitatively mimicked by colored Gaussian noise. In turn, for dissipative environments, we show that classical noise models cannot describe decoherence effects due to relaxation through spontaneous emission of photons/phonons. These developments provide a rigorous platform to assess the validity of classical noise models of decoherence.

arXiv:1904.12977The Journal of Chemical PhysicsJul 3, 201941 citations

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

New trends in nonequilibrium statistical mechanics: classical and quantum systems

Bernardo Spagnolo, Alexander A. Dubkov, Davide Valenti

Abstract The main aim of this special issue is to report recent advances and new trends in nonequilibrium statistical mechanics of classical and quantum systems, from both theoretical and experimental points of view, within an interdisciplinary context. In particular, the nonlinear relaxation processes in the dynamics of out-of-equilibrium systems and the role of the metastability and environmental noise will be overviewed. Three main areas of nonequilibrium statistical mechanics will be covered: slow relaxation phenomena and dissipative dynamics; long-range interactions and classical systems; quantum systems. New trends such as quantum thermodynamics and novel types of quantum phase transitions occurring in nonequilibrium steady states and topological phase transitions will be also highlighted.Abstract The main aim of this special issue is to report recent advances and new trends in nonequilibrium statistical mechanics of classical and quantum systems, from both theoretical and experimental points of view, within an interdisciplinary context. In particular, the nonlinear relaxation processes in the dynamics of out-of-equilibrium systems and the role of the metastability and environmental noise will be overviewed. Three main areas of nonequilibrium statistical mechanics will be covered: slow relaxation phenomena and dissipative dynamics; long-range interactions and classical systems; quantum systems. New trends such as quantum thermodynamics and novel types of quantum phase transitions occurring in nonequilibrium steady states and topological phase transitions will be also highlighted.

Journal of Statistical Mechanics Theory and ExperimentSep 1, 20203 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.