arXiv:2501.06619 · Physical Review Letters

Classical Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics

William M. Watkins, Gregory Quiroz

Published Aug 11, 2025• 0 citations

Abstract

In quantum dynamics, symmetries are vital for identifying and assessing conserved quantities that govern the evolution of a quantum system. When promoted to the open quantum system setting, dynamical symmetries can be negatively altered by system-environment interactions, thus, complicating their analysis. Previous work on noisy symmetric quantum dynamics has focused on the Markovian setting, despite the ubiquity of non-Markovian noise in a number of widely used quantum technologies. In this Letter, we develop a framework for quantifying the impact of non-Markovian noise on symmetric quantum evolution via root space decompositions and the filter function formalism. We demonstrate analytically that symmetry-preserving noise maintains the symmetric subspace, while nonsymmetric noise leads to highly specific leakage errors that are block diagonal in the symmetry representation. We support our findings with numerical studies of a transverse-field Ising model and a quantum error detecting code subject to spatiotemporally correlated multiaxis noise. Our results are broadly applicable, providing new analytic insights into the control and characterization of open quantum system dynamics.

DOI: 10.1103/t78h-c9s3

Related papers

Filter-function formalism and software package to compute quantum processes of gate sequences for classical non-Markovian noise

Tobias Hangleiter, Pascal Cerfontaine, Hendrik Bluhm

Correlated, non-Markovian noise is present in many solid-state systems employed as hosts for quantum information technologies, significantly complicating the realistic theoretical description of these systems. In this regime, the effects of noise on sequences of quantum gates cannot be described by concatenating isolated quantum operations if the environmental correlation times are on the scale of the typical gate durations. The filter-function formalism has been successful in characterizing the decay of coherence under the influence of such classical, non-Markovian environments, and here we show it can be applied to describe unital evolution within the quantum operations formalism. We find exact results for the quantum process and a simple composition rule for a sequence of operations. This enables the detailed study of effects of noise correlations on algorithms and periodically driven systems. Moreover, we point out the method's suitability for numerical applications and present the open-source Python software package filter_functions. Amongst other things, it facilitates computing the noise-averaged transfer matrix representation of a unital quantum operation in the presence of universal classical noise for arbitrary control sequences. We apply the presented methods to selected examples.

arXiv:2103.02403Physical Review ResearchOct 18, 202117 citations

Markovian evolution of quantum coherence under symmetric dynamics

Matteo Lostaglio, Kamil Korzekwa, Antony Milne

Both conservation laws and practical restrictions impose symmetry constraints on the dynamics of open quantum systems. In the case of time-translation symmetry, which arises naturally in many physically relevant scenarios, the quantum coherence between energy eigenstates becomes a valuable resource for quantum information processing. In this work, we identify the minimum amount of decoherence compatible with this symmetry for a given population dynamics. This yields a generalization to higher-dimensional systems of the relation ${T}_{2}\ensuremath{\le}2{T}_{1}$ for qubit decoherence and relaxation times. It also enables us to witness and assess the role of non-Markovianity as a resource for coherence preservation and transfer. Moreover, we discuss the relationship between ergodicity and the ability of Markovian dynamics to indefinitely sustain a superposition of different energy states. Finally, we establish a formal connection between the resource-theoretic and the master equation approaches to thermodynamics, with the former being a non-Markovian generalization of the latter. Our work thus brings the abstract study of quantum coherence as a resource towards the realm of actual physical applications.

arXiv:1703.01826Physical Review ASep 11, 201740 citations

Quantum search in a non-Markovian environment

Sheikh Parvez Mandal

This MS thesis explores the effects and origins of a 'noise with memory' in the dynamics of an open quantum system. The system considered here is a multi-qubit register performing the Grover's quantum search algorithm. We show that a Markovian-correlated noise can enhance the efficiency of the algorithm over a time correlation-less noise. We also analytically find the set of necessary and sufficient conditions for the algorithm's success probability to remain invariant with respect to the number of noisy sites in the register and point out that these conditions hold irrespective of the presence of time-correlations in the noise. We then investigate the origins of the type of noise considered. In this regard, a 'collisional model' is constructed that exactly reproduces the noisy evolution of the open system. Non-Markovianity in the system's evolution is then assessed using two well-known measures and they are shown to be non-coincident. Our model is then slightly modified to accommodate an elementary thermal bath. There we show that increasing the bath's temperature increases information drainage from the system.

arXiv:2303.14121Mar 23, 20230 citations

Open quantum systems and quantum information dynamics

́Angel Rivas

In the first part of this thesis we extensively review the general theory of open quantum systems. We introduce new approaches to describe, in a hopefully more transparent way, some aspects which are usually misleading in a broad range of the literature. In addition, we revise new concepts and methods developed in recent years that complement the general theory mainly developed in the 1970s. In the second part, we focus our attention on the so-called Markovian processes which have been described in the previous part. We study the validity of typical equations used in simple systems such as harmonic oscillators, and propose and check different strategies to describe Markovian dynamics in more complicated interacting systems. Finally we propose a counter-intuitive situation where some level of noise can be actually useful for information tasks. In the third and last part, we approach the problem of the non-Markovian description of open quantum systems. To quantify how non-Markovian an open quantum system is we introduce a computable measure and apply it to some relevant situations. We also propose a way of probing the complexity of an environment by visualizing properties of a pair of qubits embedded in it. In addition, we develop a technique based on orthogonal polynomial theory to transform a wide range of environments into simple chains of particles which can be efficiently simulated with numerical techniques.

Jan 1, 20111 citation

Noise Filtering in Quantum Information

Todd J. Green

We present novel techniques for modelling and mitigating the effects of time-dependent noise created by interactions between a quantum system and its environment, and by errors in applied controls. Our scope encompasses quantum storage and nontrivial QIP tasks in both single- and multi-qubit systems, with a particular focus on control operations applied to trapped-ion qubits. The work begins with the introduction of a computationally efficient approach to characterizing the impact of time-dependent noise in single-qubit systems, in terms of the spectral characteristics of the noise and a set of generalized control filter functions. In conjunction with brute-force numerical simulation, we show that this novel analytical technique can used to model the evolution of a noisy single-qubit system subject to an arbitrary piecewise-constant control sequence, and to accurately predict the effects of experimentally engineered noise in single-qubit trapped ion systems. We also obtain a number of new and important results that extend the range of utility of state-preserving dynamical decoupling control sequences. These device-independent results provide a means to create a practically useful high-fidelity, long-time quantum memory in both single- and multi-qubit systems. We go on to explain how, given the freedom to arbitrarily and quasi-instantaneously change the phase of the interaction between a system of qubits and a finite collection of oscillators, frequency-specific phase modulation protocols can be implemented that decouple the qubits from targeted oscillator modes at pre-determined times. This technique can be used to generate fast, high-fidelity multi-qubit entangling operations in, for example, ion trap QIP devices.

Oct 14, 20160 citations

Noise-Assisted Quantum Entanglement: Memory-Enhanced Coherence in Stochastic Jaynes-Cummings Dynamics

Fang Wang, Quanzhen Ding, Jun Jing +1 more

We investigate qubit entanglement dynamics in a two-qubit cavity system with stochastically fluctuating coupling strength, comparing white noise (Markovian) and Ornstein-Uhlenbeck noise (non-Markovian) processes. We analytically solve the system dynamics for both Fock and coherent cavity states and systematically characterize how initial qubit configurations affect entanglement generation and preservation. Our results reveal distinct dynamical regimes: in the Fock-state cavity, initial states in the single-excitation subspace generate robust qubit entanglement in decoherence-free subspaces, while initially entangled states in the double-excitation subspace exhibit inevitable decay without protective symmetries. For coherent cavities, we identify a critical photon-number threshold in the intermediate coherent-state amplitude regime where dynamics transition from low-frequency to high-frequency entanglement oscillations, while universal entanglement loss occurs at large amplitudes. Remarkable resilience against entanglement sudden death emerges under strong non-Markovian noise with long correlation times, where repeated revivals occur. These findings establish cavity photon statistics and environmental memory time as key control parameters for engineering qubit entanglement dynamics in qubit-cavity systems, revealing how system-environment correlations govern quantum information preservation.

quant-pharXiv:2610.31947Oct 26, 20260 citations