arXiv subjects

Oscar Dahlsten

Publications and source records attributed to Oscar Dahlsten.

At least 37 records · Page 2Linked to original sources

arXiv2024

From reasonable postulates to generalised Hamiltonian systems

Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In both quantum and classical mechanics, Hamiltonian mechanics demands a precise relationship between time evolution and observable energy, albeit using slightly different terminology. We distil basic conditions satisfied in both quantum and classical mechanics, including canonical coordinate symmetries and inner product invariance. We express these conditions in the framework of generalised probabilistic theories, which includes generalizing the definition of energy eigenstates in terms of time-invariant properties of the Hamiltonian system. By postulating these conditions to hold, we derive a unified Hamiltonian system model. This unified framework describes quantum and classical mechanics in a consistent language, facilitating their comparison. We moreover discuss alternative theories: an equation of motion given by a mixture of commutation relations, an information-restricted version of quantum theory, and Spekken's toy theory. The findings give a deeper understanding of the Hamiltonian in quantum and classical theories and point to several potential research topics.

quant-ph↗

arXiv2024

Unification of energy concepts in generalised phase space theories

We consider how to describe Hamiltonian mechanics in generalised probabilistic theories with the states represented as quasi-probability distributions. We give general operational definitions of energy-related concepts. We define generalised energy eigenstates as the purest stationary states. Planck's constant plays two different roles in the framework: the phase space volume taken up by a pure state and a dynamical factor. The Hamiltonian is a linear combination of generalised energy eigenstates. This allows for a generalised Liouville time-evolution equation that applies to quantum and classical Hamiltonian mechanics and more. The approach enables a unification of quantum and classical energy concepts and a route to discussing energy in a wider set of theories.

quant-ph↗

arXiv2023

Quantum walks as thermalizations, with application to fullerene graphs

We consider to what extent quantum walks can constitute models of thermalization, analogously to how classical random walks can be models for classical thermalization. In a quantum walk over a graph, a walker moves in a superposition of node positions via a unitary time evolution. We show a quantum walk can be interpreted as an equilibration of a kind investigated in the literature on thermalization in unitarily evolving quantum systems. This connection implies that recent results concerning the equilibration of observables can be applied to analyse the node position statistics of quantum walks. We illustrate this in the case of a family of graphs known as fullerenes. We find that a bound from Short et al., implying that certain expectation values will at most times be close to their time-averaged value, applies tightly to the node position probabilities. Nevertheless, the node position statistics do not thermalize in the standard sense. In particular, quantum walks over fullerene graphs constitute a counter-example to the hypothesis that subsystems equilibrate to the Gibbs state. We also exploit the bridge created to show how quantum walks can be used to probe the universality of the eigenstate thermalisation hypothesis (ETH) relation. We find that whilst in C60 with a single walker, the ETH relation does not hold for node position projectors, it does hold for the average position, enforced by a symmetry of the Hamiltonian. The findings suggest a unified study of quantum walks and quantum self-thermalizations is natural and feasible.

quant-ph↗

arXiv2023

Bound on annealing performance from stochastic thermodynamics, with application to simulated annealing

Annealing is the process of gradually lowering the temperature of a system to guide it towards its lowest energy states. In an accompanying paper [Luo et al. Phys. Rev. E 108, L052105 (2023)], we derived a general bound on annealing performance by connecting annealing with stochastic thermodynamics tools, including a speed-limit on state transformation from entropy production. We here describe the derivation of the general bound in detail. In addition, we analyze the case of simulated annealing with Glauber dynamics in depth. We show how to bound the two case-specific quantities appearing in the bound, namely the activity, a measure of the number of microstate jumps, and the change in relative entropy between the state and the instantaneous thermal state, which is due to temperature variation. We exemplify the arguments by numerical simulations on the SK model of spin-glasses.

cond-mat.stat-mech↗

arXiv2023

General limit to thermodynamic annealing performance

Annealing has proven highly successful in finding minima in a cost landscape. Yet, depending on the landscape, systems often converge towards local minima rather than global ones. In this Letter, we analyse the conditions for which annealing is approximately successful in finite time. We connect annealing to stochastic thermodynamics to derive a general bound on the distance between the system state at the end of the annealing and the ground state of the landscape. This distance depends on the amount of state updates of the system and the accumulation of non-equilibrium energy, two protocol and energy landscape dependent quantities which we show are in a trade-off relation. We describe how to bound the two quantities both analytically and physically. This offers a general approach to assess the performance of annealing from accessible parameters, both for simulated and physical implementations.

cond-mat.stat-mech↗

arXiv2023

Thermodynamics of quantum switch information capacity activation

We address a new setting where the second law is under question: thermalizations in a quantum superposition of causal orders, enacted by the so-called quantum switch. This superposition has been shown to be associated with an increase in the communication capacity of the channels, yielding an apparent violation of the data-processing inequality and a possibility to separate hot from cold. We analyze the thermodynamics of this information capacity increasing process. We show how the information capacity increase is compatible with thermodynamics. We show that there may indeed be an information capacity increase for consecutive thermalizations obeying the first and second laws of thermodynamics if these are placed in an indefinite order and moreover that only a significantly bounded increase is possible. The increase comes at the cost of consuming a thermodynamic resource, the free energy of coherence associated with the switch.

quant-ph↗

arXiv2022

Inverse linear versus exponential scaling of work penalty in finite-time bit reset

Bit reset is a basic operation in irreversible computing. This costs work and dissipates energy in the computer, creating a limit on speeds and energy efficiency of future irreversible computers. It was recently shown in [Phys. Rev. Lett. 127, 190602 (2021)] that for a finite-time reset protocol, the additional work on top of the quasistatic protocol can always be minimized by considering a two-level system, and then be lower bounded through a thermodynamical speed limit. An important question is to understand under what protocol parameters, including bit reset error and maximum energy shift, this penalty decreases exponentially vs inverse linearly in the protocol time. Here we provide several analytical results to address this question, as well as numerical simulations of specific examples of protocols.

quant-ph↗

arXiv2021

Universal Bound on Energy Cost of Bit Reset in Finite Time

We consider how the energy cost of bit reset scales with the time duration of the protocol. Bit reset necessarily takes place in finite time, where there is an extra penalty on top of the quasistatic work cost derived by Landauer. This extra energy is dissipated as heat in the computer, inducing a fundamental limit on the speed of irreversible computers. We formulate a hardware-independent expression for this limit in the framework of stochastic processes. We derive a closed-form lower bound on the work penalty as a function of the time taken for the protocol and bit reset error. It holds for discrete as well as continuous systems, assuming only that the master equation respects detailed balance.

quant-ph↗

arXiv2021

Provable superior accuracy in machine learned quantum models

In modelling complex processes, the potential past data that influence future expectations are immense. Models that track all this data are not only computationally wasteful but also shed little light on what past data most influence the future. There is thus enormous interest in dimensional reduction-finding automated means to reduce the memory dimension of our models while minimizing its impact on its predictive accuracy. Here we construct dimensionally reduced quantum models by machine learning methods that can achieve greater accuracy than provably optimal classical counterparts. We demonstrate this advantage on present-day quantum computing hardware. Our algorithm works directly off classical time-series data and can thus be deployed in real-world settings. These techniques illustrate the immediate relevance of quantum technologies to time-series analysis and offer a rare instance where the resulting quantum advantage can be provably established.

quant-ph↗

arXiv2020

Quantum correlations in time

We investigate quantum correlations in time in different approaches. We assume that temporal correlations should be treated in an even-handed manner with spatial correlations. We compare the pseudo-density matrix formalism with several other approaches: indefinite causal structures, consistent histories, generalised quantum games, out-of-time-order correlations(OTOCs), and path integrals. We establish close relationships among these space-time approaches in non-relativistic quantum theory, resulting in a unified picture. With the exception of amplitude-weighted correlations in the path integral formalism, in a given experiment, temporal correlations in the different approaches are the same or operationally equivalent.

quant-ph↗

arXiv2020

Different instances of time as different quantum modes: quantum states across space-time for continuous variables

Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in general relativity space-time is taken as a combinator, curved around mass. Here we present a unified approach on both space and time in quantum theory, and build quantum states across spacetime instead of only on spatial slices. We no longer distinguish measurements on the same system at different times with measurements on different systems at one time and construct spacetime states upon these measurement statistics. As a first step towards non-relativistic quantum field theory, we consider how to approach this in the continuous-variable multi-mode regime. We propose six possible definitions for spacetime states in continuous variables, based on four different measurement processes: quadratures, displaced parity operators, position measurements and weak measurements. The basic idea is to treat different instances of time as different quantum modes. They are motivated by the pseudo-density matrix formulation among indefinite causal structures and the path integral formalism. We show that these definitions lead to desirable properties, and raise the differences and similarities between spatial and temporal correlations. An experimental proposal for tomography is presented, construing the operational meaning of the spacetime states.

quant-ph↗

arXiv2020

Entanglement swapping in black holes: restoring predictability

Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signalling, entanglement monogamy, and the equivalence principle. We here provide a quantum model for Hawking pair black hole evaporation within which these principles are all respected. The model does not involve exotic new physics, but rather uses quantum theory and general relativity. The black hole and radiation are in a joint superposition of different energy states at any stage of the evaporation process. In the particular branch where the black hole mass is 0, the radiation state is pure and one-to-one with the initial state forming the black hole. Thus there is no information loss upon full evaporation. The original Hawking's pair entanglement between infalling and outgoing particles gets transferred to outgoing particles via entanglement swapping, without violation of no-signalling or the entanglement's monogamy. The final state after the full black hole evaporation is pure, without loss of information, violation of monogamy, or the equivalence principle.

hep-th↗

arXiv2020

Unified Approach to Witness Nonentanglement-Breaking Quantum Channels

The ability of quantum devices to preserve or distribute entanglement is essential in employing quantum technologies. Such ability is described and guaranteed by the nonentanglement-breaking (nonEB) feature of participating quantum channels. For quantum information applications relying on entanglement, the certification of the nonEB feature is thus indispensable in designing, testing, and benchmarking quantum devices. Here, we develop a direct and operational approach for the certification of nonEB quantum channels. By utilizing the prepare-and-measure test, we derive a necessary and sufficient condition for witnessing nonEB channels, which is applicable in almost all experimental scenarios. The approach not only unifies and simplifies existing methods in the standard scenario and the measurement-device-independent scenario, but also goes further allowing for certifying the nonEB feature in the semi-device-independent scenario.

quant-ph↗

arXiv2019

Quantum advantage in training binary neural networks

The performance of a neural network for a given task is largely determined by the initial calibration of the network parameters. Yet, it has been shown that the calibration, also referred to as training, is generally NP-complete. This includes networks with binary weights, an important class of networks due to their practical hardware implementations. We therefore suggest an alternative approach to training binary neural networks. It utilizes a quantum superposition of weight configurations. We show that the quantum training guarantees with high probability convergence towards the globally optimal set of network parameters. This resolves two prominent issues of classical training: (1) the vanishing gradient problem and (2) common convergence to suboptimal network parameters. Moreover we achieve a provable polynomial---sometimes exponential---speedup over classical training for certain classes of tasks. We design an explicit training algorithm and implement it in numerical simulations.

quant-ph↗

arXiv2018

Learning Simon's quantum algorithm

We consider whether trainable quantum unitaries can be used to discover quantum speed-ups for classical problems. Using methods recently developed for training quantum neural nets, we consider Simon's problem, for which there is a known quantum algorithm which performs exponentially faster in the number of bits, relative to the best known classical algorithm. We give the problem to a randomly chosen but trainable unitary circuit, and find that the training recovers Simon's algorithm as hoped.

quant-ph↗

arXiv2018

On intelligent energy harvesting

We probe the potential for intelligent intervention to enhance the power output of energy harvesters. We investigate general principles and a case study: a bi-resonant piezo electric harvester. We consider intelligent interventions via pre-programmed reversible energy-conserving operations. We find that in important parameter regimes these can outperform diode-based intervention, which in contrast has a fundamental minimum power dissipation bound.

eess.SP↗

arXiv2018

A Firepoint at the Black Hole Singularity

In his original derivation, Hawking showed that a Schwarzschild black hole is unstable at quantum level and it evolves to a final thermal mixed state violating unitarity. There are some attempts to solve this information paradox based on a high energy surface located at the black hole event horizon: the firewall. In the wake of these proposals, we here propose the singularity itself as a "firepoint" capable to break the entanglement between the "int" and the "out" states created through the Hawking process. In this paper the singularity takes active part in the information paradox in two similar ways. In the first way, the singularity, coming in contact with the the "int" state, produces a pure state outside the horizon, but it violates causality allowing people inside the black hole to send signals to the outside. The second way consists of a map that breaks the entanglement between the interior and exterior of the black hole still using the singularity yet without violating causality. The monogamy theorem is not violated whether in the first where the "out" radiation state is rendered pure directly or in the second way where the Page idea is made possible again to solve the information loss problem.

hep-th↗

arXiv2017

Entropic equality for worst-case work at any protocol speed

We derive an equality for non-equilibrium statistical mechanics in finite-dimensional quantum systems. The equality concerns the worst-case work output of a time-dependent Hamiltonian protocol in the presence of a Markovian heat bath. It has has the form "worst-case work = penalty - optimum". The equality holds for all rates of changing the Hamiltonian and can be used to derive the optimum by setting the penalty to 0. The optimum term contains the max entropy of the initial state, rather than the von Neumann entropy, thus recovering recent results from single-shot statistical mechanics. Energy coherences can arise during the protocol but are assumed not to be present initially. We apply the equality to an electron box.

quant-ph↗