arXiv subjects

Felix A. Pollock

Publications and source records attributed to Felix A. Pollock.

At least 19 recordsLinked to original sources

arXiv2025

What can unitary sequences tell us about multi-time physics?

Multi-time quantum processes are endowed with the same richness as multipartite states, including temporal entanglement and exotic causal structures. However, experimentally probing these rich phenomena leans heavily on fast and clean mid-circuit measurements, which are rarely available. We show here how surprisingly accessible these phenomena are in nascent quantum processors even when faced with substantially limited control. We work within the limitation where only unitary control is allowed, followed by a terminating measurement. Within this setting, we first develop a witness for genuine multi-time entanglement, and then methods to bound (from top and bottom) multi-time entanglement, non-Markovianity, purity, entropy, and other correlative measures. Our tools are designed to be implemented on quantum information processors, which we proceed to demonstrate. Finally, we discuss the limitations of these methods by testing them across random multi-time processes. Conceptually, this broadens our understanding of the extent to which temporal correlations may be determined with only deterministic control. Our techniques are pertinent to generic quantum stochastic dynamical processes, with a scope ranging across condensed matter physics, quantum biology, and in-depth diagnostics of NISQ-era quantum devices.

quant-ph↗

arXiv2023

Signatures of quantum chaos in an out-of-time-order tensor

Motivated by the famous ink-drop experiment, where ink droplets are used to determine the chaoticity of a fluid, we propose an experimentally implementable method for measuring the scrambling capacity of quantum processes. Here, a system of interest interacts with a small quantum probe whose dynamical properties identify the chaoticity of the system. Specifically, we propose a fully quantum version of the out-of-time-order correlator (OTOC) - which we term the out-of-time-order matrix (OTOM) - whose correlations offer clear information theoretic meanings about the chaoticity of a process. We illustrate the utility of the OTOM as a signature of chaos using random unitary processes as well as in the quantum kicked rotor, where the chaoticity is tuneable.

quant-ph↗

arXiv2023

Relaxation of Multitime Statistics in Quantum Systems

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 quantum statistical mechanics, which focus on single time statistics, to show the equilibration of isolated quantum processes. Namely, we show that most multitime observables for sufficiently large times cannot distinguish a nonequilibrium process from an equilibrium one, unless the system is probed for an extremely large number of times or the observable is particularly fine-grained. A corollary of our results is that the size of non-Markovianity and other multitime characteristics of a nonequilibrium process also equilibrate.

quant-ph↗

arXiv2023

Equilibration of Multitime Quantum Processes in Finite Time Intervals

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 stochastic processes, we prove that under loose assumptions, quantum processes equilibrate within finite time intervals. Sufficient conditions for this to occur are that multitime observables are coarse grained in both space and time, and that the initial state overlaps with many different energy eigenstates. These results help bridge the gap between (unitary) quantum and (non-unitary) statistical physics, i.e., when all multitime properties and correlations are well approximated by stationary quantities, which includes non-Markovianity and temporal entanglement. We discuss implications of this result for the emergence of classical stochastic processes from multitime measurements of an underlying genuinely quantum system.

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arXiv2022

Non-Markovian Quantum Process Tomography

Characterisation protocols have so far played a central role in the development of noisy intermediate-scale quantum (NISQ) computers capable of impressive quantum feats. This trajectory is expected to continue in building the next generation of devices: ones that can surpass classical computers for particular tasks -- but progress in characterisation must keep up with the complexities of intricate device noise. A missing piece in the zoo of characterisation procedures is tomography which can completely describe non-Markovian dynamics over a given time frame. Here, we formally introduce a generalisation of quantum process tomography, which we call process tensor tomography. We detail the experimental requirements, construct the necessary post-processing algorithms for maximum-likelihood estimation, outline the best-practice aspects for accurate results, and make the procedure efficient for low-memory processes. The characterisation is a pathway to diagnostics and informed control of correlated noise. As an example application of the hardware-agnostic technique, we show how its predictive control can be used to substantially improve multi-time circuit fidelities on superconducting quantum devices. Our methods could form the core for carefully developed software that may help hardware consistently pass the fault-tolerant noise threshold.

quant-ph↗

arXiv2022

Reduced Dynamics of Full Counting Statistics

We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they can be difficult to formulate for observables spanning the system and its environment, such as those characterizing transport properties. A large variety of mixed system--environment observables, as well as their statistical properties, can be evaluated by considering counting fields. Given a numerical method able to simulate the field-modified dynamics over the memory timescale, we show that the long-lived full counting statistics can be efficiently obtained from the reduced dynamics. We demonstrate the utility of the technique by computing the long-time current in the nonequilibrium Anderson impurity model from short-time Monte Carlo simulations.

quant-ph↗

arXiv2022

Eliminating radiative losses in long-range exciton transport

We demonstrate that it is possible to effectively eliminate radiative losses during excitonic energy transport in systems with an intrinsic energy gradient. By considering chain-like systems of repeating `unit' cells which can each consist of multiple sites, we show that tuning a single system parameter (the intra-unit-cell coupling) leads to efficient and highly robust transport over relatively long distances. This remarkable transport performance is shown to originate from a partitioning of the system's eigenstates into energetically-separated bright and dark subspaces, allowing long range transport to proceed efficiently through a `dark chain' of eigenstates. Finally, we discuss the effects of intrinsic dipole moments, which are of particular relevance to molecular architectures, and demonstrate that appropriately-aligned dipoles can lead to additional protection against other (non-radiative) loss processes. Our dimensionless open quantum systems model is designed to be broadly applicable to a range of experimental platforms.

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arXiv2021

Non-Markovian Memory Strength Bounds Quantum Process Recoverability

Generic non-Markovian quantum processes have infinitely long memory, implying an exact description that grows exponentially in complexity with observation time. Here, we present a finite memory ansatz that approximates (or recovers) the true process with errors bounded by the strength of the non-Markovian memory. The introduced memory strength is an operational quantity and depends on the way the process is probed. Remarkably, the recovery error is bounded by the smallest memory strength over all possible probing methods. This allows for an unambiguous and efficient description of non-Markovian phenomena, enabling compression and recovery techniques pivotal to near-term technologies. We highlight the implications of our results by analyzing an exactly solvable model to show that memory truncation is possible even in a highly non-Markovian regime.

quant-ph↗

arXiv2021

Extracting Quantum Dynamical Resources: Consumption of Non-Markovianity for Noise Reduction

Noise is possibly the most formidable challenge for quantum technologies. As such, a great deal of effort is dedicated to developing methods for noise reduction. One remarkable achievement in this direction is dynamical decoupling; it details a clear set of instructions for counteracting the effects of quantum noise. Yet, the domain of its applicability remains limited to devices where exercising fast control is possible. In practical terms, this is highly limiting and there is a growing need for better noise reduction tools. Here we take a significant step in this direction, by identifying the crucial ingredients required for noise suppression and the development of methods that far outperform traditional dynamical decoupling techniques. Using resource theoretic methods, we show that the key resource responsible for the efficacy of dynamical decoupling, and related protocols, is non-Markovianity (or temporal correlations). Using this insight, we then propose two methods to identify optimal pulse sequences for noise reduction. With an explicit example, we show that our methods enable a more optimal exploitation of temporal correlations, and extend the timescales at which noise suppression is viable by at least two orders of magnitude. Importantly, the corresponding tools are built on operational grounds and are easily implemented in the current generation of quantum devices.

quant-ph↗

arXiv2021

Principles underlying efficient exciton transport unveiled by information-geometric analysis

Adapting techniques from the field of information geometry, we show that open quantum system models of Frenkel exciton transport, a prevalent process in photosynthetic networks, belong to a class of mathematical models known as 'sloppy'. Performing a Fisher-information-based multi-parameter sensitivity analysis to investigate the full dynamical evolution of the system and reveal this sloppiness, we establish which features of a transport network lie at the heart of efficient performance. We find that fine tuning the excitation energies in the network is generally far more important than optimizing the network geometry and that these conclusions hold for different measures of efficiency and when model parameters are subject to disorder within parameter regimes typical of molecular complexes involved in photosynthesis. Our approach and insights are equally applicable to other physical implementations of quantum transport.

quant-ph↗

arXiv2021

Memory in quantum dot blinking

The photoluminescence intermittency (blinking) of quantum dots is interesting because it is an easily-measured quantum process whose transition statistics cannot be explained by Fermi's Golden Rule. Commonly, the transition statistics are power-law distributed, implying that quantum dots possess at least trivial memories. By investigating the temporal correlations in the blinking data, we demonstrate with high statistical confidence that quantum dot blinking data has non-trivial memory, which we define to be statistical complexity greater than one. We show that this memory cannot be discovered using the transition distribution. We show by simulation that this memory does not arise from standard data manipulations. Finally, we conclude that at least three physical mechanisms can explain the measured non-trivial memory: 1) Storage of state information in the chemical structure of a quantum dot; 2) The existence of more than two intensity levels in a quantum dot; and 3) The overlap in the intensity distributions of the quantum dot states, which arises from fundamental photon statistics.

cond-mat.mes-hall↗

arXiv2021

Genuine Multipartite Entanglement in Time

While spatial quantum correlations have been studied in great detail, much less is known about the genuine quantum correlations that can be exhibited by temporal processes. Employing the quantum comb formalism, processes in time can be mapped onto quantum states, with the crucial difference that temporal correlations have to satisfy causal ordering, while their spatial counterpart is not constrained in the same way. Here, we exploit this equivalence and use the tools of multipartite entanglement theory to provide a comprehensive picture of the structure of correlations that (causally ordered) temporal quantum processes can display. First, focusing on the case of a process that is probed at two points in time -- which can equivalently be described by a tripartite quantum state -- we provide necessary as well as sufficient conditions for the presence of bipartite entanglement in different splittings. Next, we connect these scenarios to the previously studied concepts of quantum memory, entanglement breaking superchannels, and quantum steering, thus providing both a physical interpretation for entanglement in temporal quantum processes, and a determination of the resources required for its creation. Additionally, we construct explicit examples of W-type and GHZ-type genuinely multipartite entangled two-time processes and prove that genuine multipartite entanglement in temporal processes can be an emergent phenomenon. Finally, we show that genuinely entangled processes across multiple times exist for any number of probing times.

quant-ph↗

arXiv2021

Markovianization with approximate unitary designs

Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the environment forgetful. Here we prove that there are physical non-Markovian processes that with high probability look highly Markovian for all orders of correlations; we call this phenomenon Markovianization. Formally, we show that when a quantum process has dynamics given by an approximate unitary design, a large deviation bound on the size of non-Markovian memory is implied. We exemplify our result employing an efficient construction of an approximate unitary circuit design using two-qubit interactions only, showing how seemingly simple systems can speedily become forgetful. Conversely, since the process is closed, it should be possible to detect the underlying non-Markovian effects. However, for these processes, observing non-Markovian signatures would require highly entangling resources and hence be a difficult task.

quant-ph↗

arXiv2021

Quantum chicken-egg dilemmas: Delayed-choice causal order and the reality of causal non-separability

Recent frameworks describing quantum mechanics in the absence of a global causal order admit the existence of causally indefinite processes, where it is impossible to ascribe causal order for events A and B. These frameworks even allow for processes that violate the so-called causal inequalities, which are analogous to Bell's inequalities. However, the physicality of these exotic processes is, in the general case, still under debate, bringing into question their foundational relevance. While it is known that causally indefinite processes can be probabilistically realised by means of a quantum circuit, along with an additional conditioning event C, concrete insights into the ontological meaning of such implementation schemes have heretofore been limited. Here, we show that causally indefinite processes can be realised with schemes where C serves only as a classical flag heralding which causally indefinite process was realised. We then show that there are processes where any pure conditioning measurement of C leads to a causally indefinite process for A and B, thus establishing causal indefiniteness as a basis-independent quantity. Finally, we demonstrate that quantum mechanics allows for phenomena where C can deterministically decide whether A comes before B or vice versa, without signalling to either. This is akin to Wheeler's famous delayed-choice experiment establishing definite causal order in quantum mechanics as instrument-\textit{dependent} property.

quant-ph↗

arXiv2021

Resource theories of multi-time processes: A window into quantum non-Markovianity

We investigate the conditions under which an uncontrollable background processes may be harnessed by an agent to perform a task that would otherwise be impossible within their operational framework. This situation can be understood from the perspective of resource theory: rather than harnessing 'useful' quantum states to perform tasks, we propose a resource theory of quantum processes across multiple points in time. Uncontrollable background processes fulfil the role of resources, and a new set of objects called superprocesses, corresponding to operationally implementable control of the system undergoing the process, constitute the transformations between them. After formally introducing a framework for deriving resource theories of multi-time processes, we present a hierarchy of examples induced by restricting quantum or classical communication within the superprocess - corresponding to a client-server scenario. The resulting nine resource theories have different notions of quantum or classical memory as the determinant of their utility. Furthermore, one of these theories has a strict correspondence between non-useful processes and those that are Markovian and, therefore, could be said to be a true 'quantum resource theory of non-Markovianity'.

quant-ph↗

arXiv2021

A Technical Critique of Some Parts of the Free Energy Principle

We summarize the original formulation of the free energy principle, and highlight some technical issues. We discuss how these issues affect related results involving generalised coordinates and, where appropriate, mention consequences for and reveal, up to now unacknowledged, differences to newer formulations of the free energy principle. In particular, we reveal that various definitions of the "Markov blanket" proposed in different works are not equivalent. We show that crucial steps in the free energy argument which involve rewriting the equations of motion of systems with Markov blankets, are not generally correct without additional (previously unstated) assumptions. We prove by counterexample that the original free energy lemma, when taken at face value, is wrong. We show further that this free energy lemma, when it does hold, implies equality of variational density and ergodic conditional density. The interpretation in terms of Bayesian inference hinges on this point, and we hence conclude that it is not sufficiently justified. Additionally, we highlight that the variational densities presented in newer formulations of the free energy principle and lemma are parameterised by different variables than in older works, leading to a substantially different interpretation of the theory. Note that we only highlight some specific problems in the discussed publications. These problems do not rule out conclusively that the general ideas behind the free energy principle are worth pursuing.

q-bio.NC↗

arXiv2020

Demonstration of non-Markovian process characterisation and control on a quantum processor

In the scale-up of quantum computers, the framework underpinning fault-tolerance generally relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated (Markovian). However, as physical devices progress well into the complex multi-qubit regime, attention is turning to understanding the appearance and mitigation of correlated -- or non-Markovian -- noise, which poses a serious challenge to the progression of quantum technology. This error type has previously remained elusive to characterisation techniques. Here, we develop a framework for characterising non-Markovian dynamics in quantum systems and experimentally test it on multi-qubit superconducting quantum devices. Where noisy processes cannot be accounted for using standard Markovian techniques, our reconstruction predicts the behaviour of the devices with an infidelity of $10^{-3}$. Our results show this characterisation technique leads to superior quantum control and extension of coherence time by effective decoupling from the non-Markovian environment. This framework, validated by our results, is applicable to any controlled quantum device and offers a significant step towards optimal device operation and noise reduction.

quant-ph↗

arXiv2020

A discrete memory-kernel for multi-time correlations in non-Markovian quantum processes

Efficient simulations of the dynamics of open systems is of wide importance for quantum science and tech-nology. Here, we introduce a generalization of the transfer-tensor, or discrete-time memory kernel, formalism to multi-time measurement scenarios. The transfer-tensor method sets out to compute the state of an open few-body quantum system at long times, given that only short-time system trajectories are available. Here, we showthat the transfer-tensor method can be extended to processes which include multiple interrogations (e.g. measurements) of the open system dynamics as it evolves, allowing us to propagate high order short-time correlation functions to later times, without further recourse to the underlying system-environment evolution. Our approach exploits the process-tensor description of open quantum processes to represent and propagate the dynamics in terms of an object from which any multi-time correlation can be extracted. As an illustration of the utility of the method, we study the build-up of system-environment correlations in the paradigmatic spin-boson model, and compute steady-state emission spectra, taking fully into account system-environment correlations present in the steady state.

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