Neil Dowling
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View article: A graph-theoretic approach to chaos and complexity in quantum systems
A graph-theoretic approach to chaos and complexity in quantum systems Open
There has recently been considerable interest in studying quantum systems via dynamical Lie algebras (DLAs) – Lie algebras generated by the terms which appear in the Hamiltonian of the system. However, there are some important properties t…
View article: Free Independence and Unitary Design from Random Matrix Product Unitaries
Free Independence and Unitary Design from Random Matrix Product Unitaries Open
Unitary randomness underpins both fundamental tasks in quantum information and the modern theory of quantum chaos. On one side, a central concept is that of approximate unitary designs: circuits that look random according to small moments …
View article: Diagnosing chaos with projected ensembles of process tensors
Diagnosing chaos with projected ensembles of process tensors Open
The process tensor provides a general representation of a quantum system evolving under repeated interventions and is fundamental for numerical simulations of local many-body dynamics. In this work, we introduce the projected process ensem…
View article: Bridging Entanglement and Magic Resources within Operator Space
Bridging Entanglement and Magic Resources within Operator Space Open
Local-operator entanglement (LOE) dictates the complexity of simulating Heisenberg evolution using tensor network methods, {and bears witness to many-body chaos for local dynamics}. We show that LOE is also sensitive to how non-Clifford a …
View article: Stabilizer Tensor Networks with Magic State Injection
Stabilizer Tensor Networks with Magic State Injection Open
This work augments the recently introduced Stabilizer Tensor Network (STN) protocol with magic state injection, reporting a new framework with significantly enhanced ability to simulate circuits with an extensive number of non-Clifford ope…
View article: Capturing Long-Range Memory Structures with Tree-Geometry Process Tensors
Capturing Long-Range Memory Structures with Tree-Geometry Process Tensors Open
We introduce a class of quantum non-Markovian processes—dubbed process trees—that exhibit polynomially decaying temporal correlations and memory distributed across timescales. This class of processes is described by a tensor network with t…
View article: Magic Resources of the Heisenberg Picture
Magic Resources of the Heisenberg Picture Open
We study a non-stabilizerness resource theory for operators, which is dual to that describing states. We identify that the stabilizer Rényi entropy analog in operator space is a good magic monotone satisfying the usual conditions while inh…
View article: Adversarial Robustness Guarantees for Quantum Classifiers
Adversarial Robustness Guarantees for Quantum Classifiers Open
Despite their ever more widespread deployment throughout society, machine learning algorithms remain critically vulnerable to being spoofed by subtle adversarial tampering with their input data. The prospect of near-term quantum computers …
View article: Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal-Entanglement Structure
Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal-Entanglement Structure Open
Chaotic systems are highly sensitive to a small perturbation and are ubiquitous throughout the biological sciences, the physical sciences, and even the social sciences. Taking this as the underlying principle, we construct an operational n…
View article: Capturing long-range memory structures with tree-geometry process tensors
Capturing long-range memory structures with tree-geometry process tensors Open
We introduce a class of quantum non-Markovian processes -- dubbed process trees -- that exhibit polynomially decaying temporal correlations and memory distributed across time scales. This class of processes is described by a tensor network…
View article: Equilibration of multitime quantum processes in finite time intervals
Equilibration of multitime quantum processes in finite time intervals Open
A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochasti…
View article: Relaxation of Multitime Statistics in Quantum Systems
Relaxation of Multitime Statistics in Quantum Systems Open
Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state quan…
View article: Scrambling is Necessary but Not Sufficient for Chaos
Scrambling is Necessary but Not Sufficient for Chaos Open
We show that out-of-time-order correlators (OTOCs) constitute a probe for Local-Operator Entanglement (LOE). There is strong evidence that a volumetric growth of LOE is a faithful dynamical indicator of quantum chaos, while OTOC decay corr…
View article: Report on 2112.01099v2
Report on 2112.01099v2 Open
Quantum stochastic processes are shown, within finite time intervals and for finite dimensional time-independent Hamiltonians, to be close to a corresponding stationary equilibrium process.This occurs for multitime observables that are coa…
View article: Report on 2112.01099v2
Report on 2112.01099v2 Open
Quantum stochastic processes are shown, within finite time intervals and for finite dimensional time-independent Hamiltonians, to be close to a corresponding stationary equilibrium process.This occurs for multitime observables that are coa…
View article: Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal Entanglement Structure
Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal Entanglement Structure Open
Chaotic systems are highly sensitive to a small perturbation, and are ubiquitous throughout biological sciences, physical sciences and even social sciences. Taking this as the underlying principle, we construct an operational notion for qu…
View article: Equilibration of Non-Markovian Quantum Processes in Finite Time Intervals.
Equilibration of Non-Markovian Quantum Processes in Finite Time Intervals. Open
Quantum stochastic processes are shown, within finite time intervals and for finite dimensional time-independent Hamiltonians, to be close to a corresponding stationary equilibrium process. This occurs for multitime observables that are co…
View article: Equilibration of Multitime Quantum Processes in Finite Time Intervals
Equilibration of Multitime Quantum Processes in Finite Time Intervals Open
A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochasti…
View article: Relaxation of Multitime Statistics in Quantum Systems
Relaxation of Multitime Statistics in Quantum Systems Open
Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state quan…
View article: Second law of thermodynamics for relativistic fluids formulated with relative entropy
Second law of thermodynamics for relativistic fluids formulated with relative entropy Open
The second law of thermodynamics is discussed and reformulated from a quantum\ninformation theoretic perspective for open quantum systems using relative\nentropy. Specifically, the relative entropy of a quantum state with respect to\nequil…