410 research outputs found
A Derivation of Moment Evolution Equations for Linear Open Quantum Systems
Given a linear open quantum system which is described by a Lindblad master
equation, we detail the calculation of the moment evolution equations from this
master equation. We stress that the moment evolution equations are well-known,
but their explicit derivation from the master equation cannot be found in the
literature to the best of our knowledge, and so we provide this derivation for
the interested reader
Dissipative stabilization of entangled cat states using a driven Bose-Hubbard dimer
We analyze a modified Bose-Hubbard model, where two cavities having on-site
Kerr interactions are subject to two-photon driving and correlated dissipation.
We derive an exact solution for the steady state of this interacting
driven-dissipative system, and use it show that the system permits the
preparation and stabilization of pure entangled non-Gaussian states, so-called
entangled cat states. Unlike previous proposals for dissipative stabilization
of such states, our approach requires only a linear coupling to a single
engineered reservoir (as opposed to nonlinear couplings to two or more
reservoirs). Our scheme is within the reach of state-of-the-art experiments in
circuit QED.Comment: 5 pages main text, 5 pages appendices, 6 figure
Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
We critically examine the internal consistency of a set of minimal
assumptions entering the theory of fault-tolerant quantum error correction for
Markovian noise. These assumptions are: fast gates, a constant supply of fresh
and cold ancillas, and a Markovian bath. We point out that these assumptions
may not be mutually consistent in light of rigorous formulations of the
Markovian approximation. Namely, Markovian dynamics requires either the
singular coupling limit (high temperature), or the weak coupling limit (weak
system-bath interaction). The former is incompatible with the assumption of a
constant and fresh supply of cold ancillas, while the latter is inconsistent
with fast gates. We discuss ways to resolve these inconsistencies. As part of
our discussion we derive, in the weak coupling limit, a new master equation for
a system subject to periodic driving.Comment: 19 pages. v2: Significantly expanded version. New title. Includes a
debate section in response to comments on the previous version, many of which
appeared here http://dabacon.org/pontiff/?p=959 and here
http://dabacon.org/pontiff/?p=1028. Contains a new derivation of the
Markovian master equation with periodic drivin
Colloquium: Quantum Batteries
Recent years have witnessed an explosion of interest in quantum devices for
the production, storage, and transfer of energy. In this Colloquium, we
concentrate on the field of quantum energy storage by reviewing recent
theoretical and experimental progress in quantum batteries. We first provide a
theoretical background discussing the advantages that quantum batteries offer
with respect to their classical analogues. We then review the existing quantum
many-body battery models and present a thorough discussion of important issues
related to their open nature. We finally conclude by discussing promising
experimental implementations, preliminary results available in the literature,
and perspectives.Comment: 36 pages, 12 figures, 311 references. Review and perspective article
on quantum batteries. Commissioned for Reviews of Modern Physics. Comments
and feedback are welcom
Interpolated Collision Model Formalism
The dynamics of open quantum systems (i.e., of quantum systems interacting
with an uncontrolled environment) forms the basis of numerous active areas of
research from quantum thermodynamics to quantum computing. One approach to
modeling open quantum systems is via a Collision Model. For instance, one could
model the environment as being composed of many small quantum systems
(ancillas) which interact with the target system sequentially, in a series of
"collisions". In this thesis I will discuss a novel method for constructing a
continuous-time master equation from the discrete-time dynamics given by any
such collision model. This new approach works for any interaction duration,
, by interpolating the dynamics between the time-points . I will contrast this with previous methods which only work in the
continuum limit (as ). Moreover, I will show that any
continuum-limit-based approach will always yield unitary dynamics unless it is
fine-tuned in some way. For instance, it is common to find non-unitary dynamics
in the continuum limit by taking an (I will argue unphysical) divergence in the
interaction strengths, , such that is constant as .Comment: 121 pages, 3 figures, Daniel Grimmer's PhD Thesis University of
Waterloo 202
Quantum Teleportation of Dynamics and Effective Interactions Between Remote Systems
Most protocols for Quantum Information Processing consist of a series of
quantum gates, which are applied sequentially. In contrast, interactions, for
example between matter and fields, as well as measurements such as homodyne
detection of light, are typically continuous in time. We show how the ability
to perform quantum operations continuously and deterministically can be
leveraged for inducing non-local dynamics between two separate parties. We
introduce a scheme for the engineering of an interaction between two remote
systems and present a protocol which induces a dynamics in one of the parties,
which is controlled by the other one. Both schemes apply to continuous variable
systems, run continuously in time and are based on real-time feedback
The SLH framework for modeling quantum input-output networks
Many emerging quantum technologies demand precise engineering and control
over networks consisting of quantum mechanical degrees of freedom connected by
propagating electromagnetic fields, or quantum input-output networks. Here we
review recent progress in theory and experiment related to such quantum
input-output networks, with a focus on the SLH framework, a powerful modeling
framework for networked quantum systems that is naturally endowed with
properties such as modularity and hierarchy. We begin by explaining the
physical approximations required to represent any individual node of a network,
eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum
fields by an operator triple . Then we explain how these nodes can be
composed into a network with arbitrary connectivity, including coherent
feedback channels, using algebraic rules, and how to derive the dynamics of
network components and output fields. The second part of the review discusses
several extensions to the basic SLH framework that expand its modeling
capabilities, and the prospects for modeling integrated implementations of
quantum input-output networks. In addition to summarizing major results and
recent literature, we discuss the potential applications and limitations of the
SLH framework and quantum input-output networks, with the intention of
providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving
correction
Recommended from our members
Unconventional computing platforms and nature-inspired methods for solving hard optimisation problems
The search for novel hardware beyond the traditional von Neumann architecture has given rise to a modern area of unconventional computing requiring the efforts of mathematicians, physicists and engineers. Many analogue physical systems, including networks of nonlinear oscillators, lasers, condensates, and superconducting qubits, are proposed and realised to address challenging computational problems from various areas of social and physical sciences and technology. Understanding the underlying physical process by which the system finds the solutions to such problems often leads to new optimisation algorithms. This thesis focuses on studying gain-dissipative systems and nature-inspired algorithms that form a hybrid architecture that may soon rival classical hardware.
Chapter 1 lays the necessary foundation and explains various interdisciplinary terms that are used throughout the dissertation. In particular, connections between the optimisation problems and spin Hamiltonians are established, their computational complexity classes are explained, and the most prominent physical platforms for spin Hamiltonian implementation are reviewed.
Chapter 2 demonstrates a large variety of behaviours encapsulated in networks of polariton condensates, which are a vivid example of a gain-dissipative system we use throughout the thesis. We explain how the variations of experimentally tunable parameters allow the networks of polariton condensates to represent different oscillator models. We derive analytic expressions for the interactions between two spatially separated polariton condensates and show various synchronisation regimes for periodic chains of condensates. An odd number of condensates at the vertices of a regular polygon leads to a spontaneous formation of a giant multiply-quantised vortex at the centre of a polygon. Numerical simulations of all studied configurations of polariton condensates are performed with a mean-field approach with some theoretically proposed physical phenomena supported by the relevant experiments.
Chapter 3 examines the potential of polariton graphs to find the low-energy minima of the spin Hamiltonians. By associating a spin with a condensate phase, the minima of the XY model are achieved for simple configurations of spatially-interacting polariton condensates. We argue that such implementation of gain-dissipative simulators limits their applicability to the classes of easily solvable problems since the parameters of a particular Hamiltonian depend on the node occupancies that are not known a priori. To overcome this difficulty, we propose to adjust pumping intensities and coupling strengths dynamically. We further theoretically suggest how the discrete Ising and -state planar Potts models with or without external fields can be simulated using gain-dissipative platforms. The underlying operational principle originates from a combination of resonant and non-resonant pumping. Spatial anisotropy of pump and dissipation profiles enables an effective control of the sign and intensity of the coupling strength between any two neighbouring sites, which we demonstrate with a two dimensional square lattice of polariton condensates. For an accurate minimisation of discrete and continuous spin Hamiltonians, we propose a fully controllable polaritonic XY-Ising machine based on a network of geometrically isolated polariton condensates.
In Chapter 4, we look at classical computing rivals and study nature-inspired methods for optimising spin Hamiltonians. Based on the operational principles of gain-dissipative machines, we develop a novel class of gain-dissipative algorithms for the optimisation of discrete and continuous problems and show its performance in comparison with traditional optimisation techniques. Besides looking at traditional heuristic methods for Ising minimisation, such as the Hopfield-Tank neural networks and parallel tempering, we consider a recent physics-inspired algorithm, namely chaotic amplitude control, and exact commercial solver, Gurobi. For a proper evaluation of physical simulators, we further discuss the importance of detecting easy instances of hard combinatorial optimisation problems. The Ising model for certain interaction matrices, that are commonly used for evaluating the performance of unconventional computing machines and assumed to be exponentially hard, is shown to be solvable in polynomial time including the Mobius ladder graphs and Mattis spin glasses.
In Chapter 5 we discuss possible future applications of unconventional computing platforms including emulation of search algorithms such as PageRank, realisation of a proof-of-work protocol for blockchain technology, and reservoir computing
Exploring new routes to decoherence-free quantum computing; and quantum thermodynamics for fermions
This thesis has two parts; the first part is a contribution to the research field of quantum measurement in quantum optics while the second part focuses on quantum thermodynamics for fermionic systems.
The aim of the research on quantum optics is to detect and subsequently characterize quantum states of light. Specifically, we focus on characterizing 1) entanglement between a two-level atom and superposition of coherent states (known as Bell cat state) 2) quantum superposition of coherent states (Schr\"odinger cat states). The photon is the particle of light which carries quantum information; it is usually lost (destroyed) while being detected. Many physical implementations of quantum logic gate aim to encode quantum information processing into large registers of entangled qubits. However for these larger much distinguishable states, creating and preserving entanglement becomes difficult due to rapid onset of decoherence. Encoding quantum information on Schrodinger's cat states take advantage of a cavity resonators much larger Hilbert space, as compared with that of a two-level system. This architecture allows redundant qubit encodings that can simplify the operations needed to initialize, manipulate and measure the encoded information. For such a system to be viable as a quantum computing platform, efficient measurement of such encoded qubit observables must be possible.
The concept of quantum non demolition measurement was introduced to evade the problem of decoherence. Researchers now know through quantum theory that it is indeed possible to count photons in a given state of light without destroying them. This nondestructive measurement scheme is coined in the term ``quantum non-demolition measurement". We can extend the ideas of quantum nondemolition measurement scheme to detect a system made up of two or more quantum states (not necessarily states of light) that are combined based on the superposition principle. An example is the Schr\"odinger's cat state which is a superposition of two coherent states of light of equal amplitudes but opposite phase. At this point, one is not only interested in counting photons, but in understanding the nature of the superposition, the possible problems and the different physical properties that follow. Ways to detect the Schr\"odinger cat states and subsequently a Bell cat state (Schr\"odinger cat entangled with a qubit) without significantly perturbing them are discussed. The method analyzed is the mode-invisibility measurement scheme earlier proposed to detect single Fock states and coherent states of light. The method gives a new insight to the known properties of Schr\"odinger cat states and contributes to our understanding of the quantum-classical boundary problem.
The second part of the thesis falls in the research field of quantum thermodynamics and open quantum systems. Most problems in quantum thermodynamics have been explored in bosonic systems with little or less done in fermionic systems. Therefore the aim of this part of the thesis is to explore related quantum thermodynamical problems in fermionic systems. I begin by considering the problem of work extraction from noninteracting fermionic systems. For work to be extracted from the state of a quantum system, a unitary operation on the state must act to reduce the average energy of the system. Passive states are those states whose energy cannot be reduced through unitary transformation, that is work cannot be extracted via unitary transformations given only a single copy of the system. It follows that some passive states may have extractable work if several copies of the system is processed. Passive states for which no work can be extracted, no matter the number of available copies, are called completely passive states. An example is the thermal Gibbs state. Here, the limit for which multiple copies of passive states in fermionic systems can be activated for work extraction is studied. It was observed for n > 3 fermionic modes at the same frequency, the product state of n thermal states with different temperatures is not passive. This in principle implies that the construction of a heat engine in fermionic systems need access to three thermal baths at different temperature. This is unlike the bosonic system, where access to only two thermal baths are required.
On the other hand, while the product state of three thermal states of three fermionic modes at the same frequency but different temperatures is not passive, the unitary transformation required to extract work from the state is difficult to realize. A set of operations that are easier to realize are Gaussian unitaries which are generated by Hamiltonian that are at most quadratic in the system's operators. One may consider extracting work via the restricted class of Gaussian unitaries. Hence fermionic Gaussian passive states for which energy cannot be extracted using only Gaussian operations are characterized.
The last problem I investigate is that of understanding the dynamics of an open Markovian non-interacting fermionic system. I introduce a classification scheme for the generators of open fermionic Gaussian dynamics and simultaneously partition the dynamics along the following four lines: 1) unitary vs. non-unitary, 2) active vs. passive, 3) state-dependent vs. state-independent, and 4) single-mode vs. multi-mode. Unlike in the bosonic case where only eleven of these sixteen types of dynamics turn out to be possible, one observe only nine types of dynamics in the fermionic setting. Using this partition I discuss the consequences of imposing complete positivity on fermionic Gaussian dynamics. In particular, I show that completely positive dynamics must be either unitary (and so can be implemented without a quantized environment) or active (and so must involve particle exchange with an environment)
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