Potential of Quantum Finite Automata with Exact Acceptance

The potential of the exact quantum information processing is an interesting, important and intriguing issue. For examples, it has been believed that quantum tools can provide significant, that is larger than polynomial, advantages in the case of exact quantum computation only, or mainly, for problems with very special structures. We will show that this is not the case. In this paper the potential of quantum finite automata producing outcomes not only with a (high) probability, but with certainty (so called exactly) is explored in the context of their uses for solving promise problems and with respect to the size of automata. It is shown that for solving particular classes [Formula: see text] of promise problems, even those without some very special structure, that succinctness of the exact quantum finite automata under consideration, with respect to the number of (basis) states, can be very small (and constant) though it grows proportional to [Formula: see text] in the case deterministic finite automata (DFAs) of the same power are used. This is here demonstrated also for the case that the component languages of the promise problems solvable by DFAs are non-regular. The method used can be applied in finding more exact quantum finite automata or quantum algorithms for other promise problems.

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Introduction and Background

An Introduction to Quantum Computing ◽

10.1093/oso/9780198570004.003.0004 ◽

2006 ◽

Author(s):

Phillip Kaye ◽

Raymond Laflamme ◽

Michele Mosca

Keyword(s):

Information Processing ◽

Quantum Information ◽

Quantum Physics ◽

Quantum Information Processing ◽

Quantum Algorithms ◽

Physical Reality ◽

Quantum Computers ◽

Processing Task ◽

Computing Model ◽

Physical Task

A computer is a physical device that helps us process information by executing algorithms. An algorithm is a well-defined procedure, with finite description, for realizing an information-processing task. An information-processing task can always be translated into a physical task. When designing complex algorithms and protocols for various information-processing tasks, it is very helpful, perhaps essential, to work with some idealized computing model. However, when studying the true limitations of a computing device, especially for some practical reason, it is important not to forget the relationship between computing and physics. Real computing devices are embodied in a larger and often richer physical reality than is represented by the idealized computing model. Quantum information processing is the result of using the physical reality that quantum theory tells us about for the purposes of performing tasks that were previously thought impossible or infeasible. Devices that perform quantum information processing are known as quantum computers. In this book we examine how quantum computers can be used to solve certain problems more efficiently than can be done with classical computers, and also how this can be done reliably even when there is a possibility for errors to occur. In this first chapter we present some fundamental notions of computation theory and quantum physics that will form the basis for much of what follows. After this brief introduction, we will review the necessary tools from linear algebra in Chapter 2, and detail the framework of quantum mechanics, as relevant to our model of quantum computation, in Chapter 3. In the remainder of the book we examine quantum teleportation, quantum algorithms and quantum error correction in detail. We are often interested in the amount of resources used by a computer to solve a problem, and we refer to this as the complexity of the computation. An important resource for a computer is time. Another resource is space, which refers to the amount of memory used by the computer in performing the computation. We measure the amount of a resource used in a computation for solving a given problem as a function of the length of the input of an instance of that problem.

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Characterization and implementation of robust quantum information processing

10.23889/suthesis.56913 ◽

2020 ◽

Author(s):

◽

David Fernandez

Keyword(s):

Information Processing ◽

Quantum Information ◽

Quantum Information Processing ◽

Fault Tolerant ◽

Quantum Algorithms ◽

Practical Importance ◽

Quantum Systems ◽

Color Code ◽

Practical Applications ◽

Qubit Loss

Quantum information processing has practical applications like exponential speed ups in optimisation problems or the simulation of complex quantum systems. However, well controlled quantum systems realised experimentally to process the information are sensitive to noise. The progress in leading experimental platforms like superconducting qubits or trapped ions has al-lowed the realisation of high-fidelity quantum processors known as Noisy Intermediate-Scale Quantum (NISQ) devices with roughly 50 qubits. NISQ devices are meant to be large enough to show, despite their imperfections, an advantage over classical processors in some computational tasks and pro-vide a rich playground to prove principles for future quantum algorithms and protocols. However, quantum processors need to be scaled up to imple-ment quantum algorithms that are relevant for practical applications. For this purpose, Quantum Error Correction (QEC) codes, which encode the information in multi-partite quantum states that are generally highly en-tangled, become crucial to eliminate the errors introduced by noise sources like qubit loss. Here we introduce a protocol to correct qubit loss, i.e., the impossibility to access the information encoded in a qubit, in the color code, a leading candidate for fault-tolerant quantum computation. We show that the achieved tolerance of 46(1)% to qubit loss is related to a novel percola-tion problem on three coupled lattices. Our work shows the high robustness of the color under our protocol and has practical importance for implemen-tations of fault-tolerant QEC. In our second line of research we propose and analyse local entanglement witnesses as efficient and platform-agnostic detectors of the entanglement between qubit subsystems, providing a de-scription of the entanglement structure in, in principle, arbitrarily large quantum systems. Since entanglement is a genuinely quantum property used as a resource in most quantum algorithms, local witnesses, which can be implemented with current technology, are of interest for current and future quantum processors.

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PULSED ENDOR-BASED QUANTUM INFORMATION PROCESSING

International Journal of Quantum Information ◽

10.1142/s0219749905001377 ◽

2005 ◽

Vol 03 (supp01) ◽

pp. 197-204 ◽

Cited By ~ 17

Author(s):

ROBABEH RAHIMI ◽

KAZUNOBU SATO ◽

KOU FURUKAWA ◽

KAZUO TOYOTA ◽

DAISUKE SHIOMI ◽

...

Keyword(s):

Information Processing ◽

Quantum Information ◽

Electron Spin ◽

Nuclear Spin ◽

Quantum Information Processing ◽

Quantum Algorithms ◽

Double Resonance ◽

Electron Nuclear Double Resonance ◽

Preliminary Results ◽

Experimental Side

Pulsed Electron Nuclear DOuble Resonance (pulsed ENDOR) has been studied for realization of quantum algorithms, emphasizing the implementation of organic molecular entities with an electron spin and a nuclear spin for quantum information processing. The scheme has been examined in terms of quantum information processing. Particularly, superdense coding has been implemented from the experimental side and the preliminary results are represented as theoretical expectations.

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