Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise amount of time, using a classical clock. A fully quantum mechanical description of such a device would include a quantum description of the clock whose state is generally disturbed because of the back-reaction on it. Such a description is needed if we wish to consider finite sized autonomous quantum machines requiring no external control. The extent of the back-reaction has implications on how small the device can be, on the length of time the device can run, and is required if we want to understand what a fully quantum mechanical treatment of an observer would look like. Here, we consider the implementation of a unitary by a finite sized device which we call the "Quasi-Ideal clock", and show that the back-reaction on it can be made exponentially small in the device's dimension with only a linear increase in energy. As a result, an autonomous quantum machine need only be of modest size and or energy. We are also able to solve a long-standing open problem by using a finite sized quantum clock to approximate the continuous evolution of an Idealised clock. The result has implications on the equivalence of different paradigms of quantum thermodynamics, some which allow external control and some which only allow autonomous thermal machines.
Time remains one of the least well understood concepts in physics, most notably in quantum mechanics. A central goal is to find the fundamental limits of measuring time. One of the main obstacles is the fact that time is not an observable and thus has to be measured indirectly. Here we explore these questions by introducing a model of time measurements that is complete and autonomous. Specifically, our autonomous quantum clock consists of a system out of thermal equilibrium --- a prerequisite for any system to function as a clock --- powered by minimal resources, namely two thermal baths at di…
There are many different types of time keeping devices. We use the phrase ticking clock to describe those which -- simply put -- "tick" at approximately regular intervals. Various important results have been derived for ticking clocks, and more are in the pipeline. It is thus important to understand the underlying models on which these results are founded. The aim of this paper is to introduce a new ticking clock model from axiomatic principles that overcomes concerns in the community about the physicality of the assumptions made in previous models. The ticking clock model in [arXiv:1806.00491…
According to thermodynamics, the inevitable increase of entropy allows the past to be distinguished from the future. From this perspective, any clock must incorporate an irreversible process that allows this flow of entropy to be tracked. In addition, an integral part of a clock is a clockwork, that is, a system whose purpose is to temporally concentrate the irreversible events that drive this entropic flow, thereby increasing the accuracy of the resulting clock ticks compared to counting purely random equilibration events. In this article, we formalise the task of autonomous temporal probabil…
We consider an isolated autonomous quantum machine, where an explicit quantum clock is responsible for performing all transformations on an arbitrary quantum system (the engine), via a time-independent Hamiltonian. In a general context, we show that this model can exactly implement any energy-conserving unitary on the engine, without degrading the clock. Furthermore, we show that when the engine includes a quantum work storage device we can approximately perform completely general unitaries on the remainder of the engine. This framework can be used in quantum thermodynamics to carry out arbitr…
We present some dynamic and entropic considerations about the evolution of a continuous time quantum walk implementing the clock of an autonomous machine. On a simple model, we study in quite explicit terms the Lindblad evolution of the clocked subsystem, relating the evolution of its entropy to the spreading of the wave packet of the clock. We explore possible ways of reducing the generation of entropy in the clocked subsystem, as it amounts to a deficit in the probability of finding the target state of the computation. We are thus lead to examine the benefits of abandoning some classical pre…
In this paper we pose two fundamental ideas on the motion of an elementary particle supporting the internal "spin motion" or $\textit{Zitterbewegung}$ and a particle as concentrated energy. First, the particle moves randomly in a limited area (in a quantum sized-volume) like random vibrating system where the particle will diffuse in a quantum-sized volume when it absorbs or emits the quantized amount of energy. The quantum sized-volume can move too and plays role similar to the carrier amplitude, while the vibrational motion of the fundamental particle with frequency and amplitude represents a…
This chapter presents autonomous quantum engines that generate work in the form of directed motion for a rotor. We first formulate a prototypical clock-driven model in a time-dependent framework and demonstrate how it can be translated into an autonomous engine with the introduction of a planar rotor degree of freedom. The rotor plays both the roles of internal engine clock and of work repository. Using the example of a single-qubit piston engine, the thermodynamic performance is then reviewed. We evaluate the extractable work in terms of ergotropy, the kinetic energy associated to net directe…
The inexorable miniaturisation of technologies, the relentless drive to improve efficiency and the enticing prospect of boosting performance through quantum effects are all compelling reasons to investigate microscopic machines. Thermal absorption machines are a particularly interesting class of device that operate autonomously and use only heat flows to perform a useful task. In the quantum regime, this provides a natural setting in which to quantify the thermodynamic cost of various operations such as cooling, timekeeping or entanglement generation. This article presents a pedagogical introd…
Finite-size clocks in quantum field theory and the twin paradox
University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（佩雷尔曼理论物理研究所）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；KTH Royal Institute of Technology and Stockholm University（瑞典皇家理工学院与斯德哥尔摩大学）
Building scalable quantum systems that demonstrate genuine performance enhancement based on entanglement is a major scientific goal for fields including computing, networking, simulations, and metrology. The tremendous challenge arises from the fragility of entanglement in increasingly larger sized quantum systems. Optical atomic clocks utilizing a large number of atoms have pushed the frontier of measurement science, building on precise engineering of quantum states and control of atomic interactions. However, today's state-of-the-art optical atomic clocks are limited by the quantum projectio…
University of York（约克大学）；York Center for Quantum Technologies, University of York（约克大学量子技术中心）；University of Malta（马耳他大学）；Technische Universität Wien（维也纳工业大学）
Quantum error correction provides a fertile context for exploring the interplay of feedback control, microscopic physics and noncommutative probability. In this paper we deepen our understanding of this nexus through high-level analysis of a class of quantum memory models that we have previously proposed, which implement continuous-time versions of well-known stabilizer codes in autonomous nanophotonic circuits that require no external clocking or control. We show that the presence of the gauge subsystem in the nine-qubit Bacon-Shor code allows for an optimized layout of the corresponding nano…
Quantum error correction (QEC) is fundamental for quantum information processing but entails a substantial overhead of classically-controlled quantum operations, which can be architecturally cumbersome to accommodate. Here we discuss a novel approach to designing elementary QEC memory cells, in which all control operations are performed autonomously by an embedded optical feedback loop. Our approach is natural for nanophotonic implementations in which each qubit can be coupled to its own optical resonator, and our design for a memory cell based on the quantum bit-flip or phase-flip code requir…
All clocks, in some form or another, use the evolution of nature towards higher entropy states to quantify the passage of time. Due to the statistical nature of the second law and corresponding entropy flows, fluctuations fundamentally limit the performance of any clock. This suggests a deep relation between the increase in entropy and the quality of clock ticks. Indeed, minimal models for autonomous clocks in the quantum realm revealed that a linear relation can be derived, where for a limited regime every bit of entropy linearly increases the accuracy of quantum clocks. But can such a linear…
There are both practical and foundational motivations to consider the thermodynamics of quantum systems at small scales. Here we address the issue of autonomous quantum thermal machines that are tailored to achieve some specific thermodynamic primitive, such as work extraction in the presence of a thermal environment, while having minimal or no control from the macroscopic regime. Beyond experimental implementations, this provides an arena in which to address certain foundational aspects such as the role of coherence in thermodynamics, the use of clock degrees of freedom and the simulation of …
We show that every finite-dimensional quantum system with Markovian (i.e., GKLS-generated) time evolution has an autonomous unitary dilation which can be dynamically decoupled. Since there is also always an autonomous unitary dilation which cannot be dynamically decoupled, this highlights the role of dilations in the control of quantum noise. We construct our dilation via a time-dependent version of Stinespring in combination with Howland's clock Hamiltonian and certain point-localised states, which may be regarded as a C*-algebraic analogue of improper bra-ket position eigenstates and which a…
The resource theory of quantum thermodynamics has been a very successful theory and has generated much follow-up work in the community. It requires energy-preserving unitary operations to be implemented over a system, bath, and catalyst as part of its paradigm. So far, such unitary operations have been considered a "free" resource in the theory. However, this is only an idealization of a necessarily inexact process. Here, we include an additional auxiliary control system which can autonomously implement the unitary by turning an interaction "on or off". However, the control system will inevita…
Giving a universal upper bound on the power output of heat engines is a long-standing open problem. We tackle this problem for generic quantum machines in self-contained formulation by carefully including the switching process of the interaction. In this way, we show a fundamental upper bound on the power associated with the energy-time uncertainty principle. As a result, the energy fluctuation of the external controller is verified as a necessary resource for producing the power. This bound implies a trade-off between the power and `noise' for work extraction, which yields an estimation on th…
