scholarly journals Can small quantum systems learn

2017 ◽  
Vol 17 (7&8) ◽  
pp. 568-594
Author(s):  
Nathan Wiebe ◽  
Christopher Grandade
Keyword(s):  
Quantum Mechanics ◽  
Fault Tolerance ◽  
Bayesian Inference ◽  
Quantum System ◽  
Lower Bounds ◽  
State Vector ◽  
Quantum Systems ◽  
Posterior Distributions ◽  
Quantum Devices ◽  
Small Quantum

We examine the question of whether quantum mechanics places limitations on the ability of small quantum devices to learn. We specifically examine the question in the context of Bayesian inference, wherein the prior and posterior distributions are encoded in the quantum state vector. We conclude based on lower bounds from Grover’s search that an efficient blackbox method for updating the distribution is impossible. We then address this by providing a new adaptive form of approximate quantum Bayesian inference that is polynomially faster than its classical anolog and tractable if the quantum system is augmented with classical memory or if the low–order moments of the distribution are protected through redundant preparation. This work suggests that there may be a connection between fault tolerance and the capacity of a quantum system to learn from its surroundings.

Loss and Dissipation: The RLC Circuit

2021 ◽  
pp. 230-246
Author(s):  
Duncan G. Steel
Keyword(s):  
Quantum Mechanics ◽  
Energy Loss ◽  
Quantum System ◽  
Equations Of Motion ◽  
Quantum Systems ◽  
Quantum Vacuum ◽  
Classical Systems ◽  
Rlc Circuit ◽  
Quantum Behavior ◽  
Continuum Of States

The effects of energy loss or dissipation is well-known and understood in classical systems. It is the source of heat in LCR circuits and in the application of brakes in a vehicle or why a struck bell does not ring indefinitely. Understanding quantum behavior begins with understanding the Hamiltonian for the problem. Classically, loss arises from a coupling of the Hamiltonian for an isolated quantum system to a continuum of states. We look at such a Hamiltonian and develop the equations of motion following the rules of quantum mechanics and find that even in a quantum system, this coupling leads to loss and non-conservation of probability in the otherwise isolated quantum system. This is the Weisskopf–Wigner formalism that is then used to understand the quantum LCR circuit. The same formalism is used in Chapter 15 for the decay of isolated quantum systems by coupling to the quantum vacuum and the resulting emission of a photon.

MEASUREMENT, IRREVERSIBILITY AND DECOHERENCE IN QUANTUM MECHANICS

1994 ◽  
Vol 09 (22) ◽  
pp. 3913-3924
Author(s):  
BELAL E. BAAQUIE
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum System ◽  
Quantum Measurement ◽  
State Vector ◽  
Space Time ◽  
Measuring Apparatus ◽  
Rigged Hilbert Space ◽  
Friedrichs Model ◽  
Time Irreversibility

We review Prigogine's model of quantum measurement. The measuring apparatus is considered to be an unstable quantum system with its state vector belonging to a rigged Hilbert space. Time irreversibility arises due to the dissipative nature of the measuring apparatus (an unstable quantum system) which induces decoherence in the system being measured. Friedrichs' model is used to concretely illustrate these ideas.

scholarly journals Más allá de la presuposición newtoniana: propiedades genuinamente disposicionales en la mecánica cuántica

1990 ◽  
Vol 22 (66) ◽  
pp. 25-37
Author(s):  
Sergio Martínez
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Physical System ◽  
Modern Science ◽  
Quantum Systems ◽  
Theoretical Modeling ◽  
Different Types ◽  
Modern Physics ◽  
Dispositional Properties

A central metaphysical thesis of modern science has been the idea that the structure of a physical system can be explained in terms of the properties of its constitutive subsystems. I call this presupposition the Newtonian merological presupposition. After some brief introductory remarks on the role of this presupposition in the methodology of modern physics, and after mentioning some recent challenges to it, I focus my attention on quantum systems. Quantum mechanics is the only highly confirmed theory in which the Newtonian merological presupposition is denied. I argue that the presence of a non-Newtonian (holistic) merological structure is the result of the existence of two different types of properties, and in particular of the existence of genuinely dispositional properties. Genuinely dispositional properties are properties of a system which are not reducible to occurrent properties of the subsystems. This distinction between two different types of properties can be made precise in a lattice theoretical modeling of the possible properties and states attributable to a quantum system. I conclude by giving an example of the sort of genuinely dispositional properties that are constitutive of quantum systems.

scholarly journals Thermalization of small quantum systems: From the zeroth law of thermodynamics

2021 ◽  
Author(s):  
Jiaozi Wang ◽  
Wen-Ge Wang ◽  
Jiao Wang
Keyword(s):  
Quantum System ◽  
Chaotic Systems ◽  
Environmental Temperature ◽  
Quantum Systems ◽  
Necessary Condition ◽  
Environmental System ◽  
Small System ◽  
Composite Systems ◽  
Small Quantum

Abstract Thermalization of isolated quantum systems has been studied intensively in recent years and significant progresses have been achieved. Here, we study thermalization of small quantum systems that interact with large chaotic environments under the consideration of Schrödinger evolution of composite systems, from the perspective of the zeroth law of thermodynamics. Namely, we consider a small quantum system that is brought into contact with a large environmental system; after they have relaxed, they are separated and their temperatures are studied. Our question is under what conditions the small system may have a detectable temperature that is identical with the environmental temperature. This should be a necessary condition for the small quantum system to be thermalized and to have a well-defined temperature. By using a two-level probe quantum system that plays the role of a thermometer, we find that the zeroth law is applicable to quantum chaotic systems, but not to integrable systems.

scholarly journals A new epoch of quantum manipulation

2013 ◽  
Vol 1 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Yongjian Han ◽  
Zhen Wang ◽  
Guang-Can Guo
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Nobel Prize ◽  
Quantum Computer ◽  
Classical Mechanics ◽  
Quantum Systems ◽  
Microscopic Particle ◽  
Nobel Prize In Physics ◽  
Classical Particles

Abstract The behavior of individual microscopic particles, such as an atom (or a photon), predicted using quantum mechanics, is dramatically different from the behavior of classical particles, such as a planet, determined using classical mechanics. How can the counter-intuitive behavior of the microscopic particle be verified and manipulated experimentally? David Wineland and Serge Haroche, who were awarded the Nobel Prize in physics in 2012, developed a set of methods to isolate the ions and photons from their environment to create a genuine quantum system. Furthermore, they also developed methods to measure and manipulate these quantum systems, which open a path not only to explore the fundamental principles of quantum mechanics, but also to develop a much faster computer: a quantum computer.

scholarly journals Tangible reduction in learning sample complexity with large classical samples and small quantum system

2021 ◽  
Vol 20 (8) ◽  
Author(s):  
Wooyeong Song ◽  
Marcin Wieśniak ◽  
Nana Liu ◽  
Marcin Pawłowski ◽  
Jinhyoung Lee ◽  
...  
Keyword(s):  
Quantum System ◽  
Learning Sample ◽  
Sample Complexity ◽  
Small Quantum

scholarly journals Fundamental limitations on distillation of quantum channel resources

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Bartosz Regula ◽  
Ryuji Takagi
Keyword(s):  
Lower Bounds ◽  
Quantum Channel ◽  
Quantum Communication ◽  
Fault Tolerant ◽  
State Of The Art ◽  
Quantum Systems ◽  
Noisy Channels ◽  
General Transformation ◽  
Fundamental Limitations ◽  
Strong Converse

AbstractQuantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols. Focusing on the class of distillation tasks — which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels — we develop fundamental restrictions on the error incurred in such transformations, and comprehensive lower bounds for the overhead of any distillation protocol. In the asymptotic setting, our results yield broadly applicable bounds for rates of distillation. We demonstrate our results through applications to fault-tolerant quantum computation, where we obtain state-of-the-art lower bounds for the overhead cost of magic state distillation, as well as to quantum communication, where we recover a number of strong converse bounds for quantum channel capacity.

scholarly journals Simulating molecules on a cloud-based 5-qubit IBM-Q universal quantum computer

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
S. Leontica ◽  
F. Tennie ◽  
T. Farrow
Keyword(s):  
Quantum System ◽  
Energy Transport ◽  
Quantum Computer ◽  
Complex Molecule ◽  
Dissipative System ◽  
Quantum Simulation ◽  
Quantum Systems ◽  
Molecular Structures ◽  
Unitary Evolution ◽  
Universal Quantum

AbstractSimulating the behaviour of complex quantum systems is impossible on classical supercomputers due to the exponential scaling of the number of quantum states with the number of particles in the simulated system. Quantum computers aim to break through this limit by using one quantum system to simulate another quantum system. Although in their infancy, they are a promising tool for applied fields seeking to simulate quantum interactions in complex atomic and molecular structures. Here, we show an efficient technique for transpiling the unitary evolution of quantum systems into the language of universal quantum computation using the IBM quantum computer and show that it is a viable tool for compiling near-term quantum simulation algorithms. We develop code that decomposes arbitrary 3-qubit gates and implement it in a quantum simulation first for a linear ordered chain to highlight the generality of the approach, and second, for a complex molecule. We choose the Fenna-Matthews-Olsen (FMO) photosynthetic protein because it has a well characterised Hamiltonian and presents a complex dissipative system coupled to a noisy environment that helps to improve the efficiency of energy transport. The method can be implemented in a broad range of molecular and other simulation settings.

scholarly journals The measure problem in no-collapse (many worlds) quantum mechanics

2017 ◽  
Vol 26 (03) ◽  
pp. 1730008 ◽  
Author(s):  
Stephen D. H. Hsu
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Probability Measure ◽  
Ab Initio ◽  
Subjective Probability ◽  
State Vector ◽  
A Priori ◽  
Born Rule ◽  
Many Worlds ◽  
Measure Problem

We explain the measure problem (cf. origin of the Born probability rule) in no-collapse quantum mechanics. Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold — these branches exhibit highly improbable behaviors, including possibly the breakdown of decoherence or even the absence of an emergent semi-classical reality. Derivations of the Born rule which originate in decision theory or subjective probability (i.e. the reasoning of individual observers) do not resolve this problem, because they are circular: they assume, a priori, that the observer occupies a non-maverick branch. An ab initio probability measure is sometimes assumed to explain why we do not occupy a maverick branch. This measure is constrained by, e.g. Gleason’s theorem or envariance to be the usual Hilbert measure. However, this ab initio measure ultimately governs the allocation of a self or a consciousness to a particular branch of the wave function, and hence invokes primitives which lie beyond the Everett wave function and beyond what we usually think of as physics. The significance of this leap has been largely overlooked, but requires serious scrutiny.

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