Moments of quantum channel ensembles
- URL: http://arxiv.org/abs/2511.12700v1
- Date: Sun, 16 Nov 2025 17:36:43 GMT
- Title: Moments of quantum channel ensembles
- Authors: Matthew Duschenes, Diego García-Martín, Zoë Holmes, M. Cerezo,
- Abstract summary: We develop a theoretical framework to compute moment operators for ensembles of quantum channels.<n>By deriving hierarchies between ensembles, we define useful concepts such as that of channel $t$-designs.<n>We perform theoretical and numerical studies which show that different types of noise can decrease the norm of the moment operators.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Moments of ensembles of unitaries play a central role in quantum information theory as they capture the statistical properties of dynamics of systems with some form of randomness. Indeed, concepts such as approximate $t$-designs arise when comparing how close an associated moment operator of a given unitary ensemble is to that of another, reference ensemble. Despite the importance of moment operators, their properties have not been as explored for quantum channels. In this work we develop a theoretical framework to compute moment operators for ensembles of quantum channels, for all moment orders $t$, with a special focus on determining ensembles that can be used as points of reference. By deriving hierarchies between ensembles, via inequalities of their moment operator norms, we give them operational meaning, and define useful concepts such as that of channel $t$-designs. Finally, we perform theoretical and numerical studies which show that different types of noise can decrease the norm of the moment operators (e.g., depolarizing noise), as well as increase it (e.g., amplitude damping), and generalize noise-induced concentration phenomena to channel-design-induced phenomena. Along the way, we find a block-orthogonal basis for permutations, which greatly simplifies our analyses, and may be of independent interest.
Related papers
- Quantumness via Discrete Structures [0.0]
This thesis charts the role of discrete structures in assessing quantumness.<n>I present work on contextuality that extensively relies on (undirected) graphs and hypergraphs as the discrete structures of interest.<n>I present work on causality, where the discrete structures of interest are directed graphs.
arXiv Detail & Related papers (2025-12-10T20:34:21Z) - Network theory classification of quantum matter based on wave function snapshots [0.0025655761752240496]
We develop a theoretical framework to link quantum phases of matter to their snapshots, based on a combination of data complexity and network theory analyses.<n>Our framework is of immediate experimental relevance, and can be further extended both in terms of more advanced network mathematics.
arXiv Detail & Related papers (2025-12-01T19:00:04Z) - Correlated Noise Estimation with Quantum Sensor Networks [18.51122677780099]
We develop a theoretical framework to determine the limits of correlated (weak) noise estimation with quantum sensor networks.<n>We identify a sensing protocol, reminiscent of a many-body echo sequence, that achieves the fundamental limits of measurement sensitivity for a broad class of problems.
arXiv Detail & Related papers (2024-12-23T19:00:06Z) - Random-matrix models of monitored quantum circuits [0.0]
We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits.
For projective measurements, we derive various properties of the statistical ensemble of Kraus operators.
We expect that the statistical properties of Kraus operators will serve as a model for the entangling phase of monitored quantum systems.
arXiv Detail & Related papers (2023-12-14T18:46:53Z) - Engineering Transport via Collisional Noise: a Toolbox for Biology
Systems [44.99833362998488]
We study a generalised XXZ model in the presence of collision noise, which allows to describe environments beyond the standard Markovian formulation.
Results constitute an example of the essential building blocks for the understanding of quantum transport in noisy and warm disordered environments.
arXiv Detail & Related papers (2023-11-15T12:55:28Z) - A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits [37.84307089310829]
Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit.
Despite their promise, the trainability of these algorithms is hindered by barren plateaus.
We present a general Lie algebra that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits.
arXiv Detail & Related papers (2023-09-17T18:14:10Z) - Scrambling and quantum chaos indicators from long-time properties of
operator distributions [0.0]
Scrambling is a key concept in the analysis of nonequilibrium properties of quantum many-body systems.
We study the structure of the expansion coefficients treated as a coarse-grained probability distribution in the space of operators.
We show that the long-time properties of the operator distribution display common features across these cases.
arXiv Detail & Related papers (2022-11-29T02:06:30Z) - Noisy Quantum Kernel Machines [58.09028887465797]
An emerging class of quantum learning machines is that based on the paradigm of quantum kernels.
We study how dissipation and decoherence affect their performance.
We show that decoherence and dissipation can be seen as an implicit regularization for the quantum kernel machines.
arXiv Detail & Related papers (2022-04-26T09:52:02Z) - Experimental violations of Leggett-Garg's inequalities on a quantum
computer [77.34726150561087]
We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems.
Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
arXiv Detail & Related papers (2021-09-06T14:35:15Z) - Out-of-time-order correlations and the fine structure of eigenstate
thermalisation [58.720142291102135]
Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation.
We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH)
We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
arXiv Detail & Related papers (2021-03-01T17:51:46Z) - Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor.
We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
arXiv Detail & Related papers (2021-01-21T22:18:49Z) - Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy.
We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy.
In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
arXiv Detail & Related papers (2020-07-31T19:23:26Z) - Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range.
For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z)
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.