Quantum measurement is a fundamental cornerstone of experimental quantum computations. The main issues in current quantum measurement strategies are the high number of measurement rounds to determine a global optimal measurement output and the low success probability of finding a global optimal measurement output. Each measurement round requires preparing the quantum system and applying quantum operations and measurements with high-precision control in the physical layer. These issues result in extremely high-cost measurements with a low probability of success at the end of the measurement rounds. Here, we define a novel measurement for quantum computations called dense quantum measurement. The dense measurement strategy aims at fixing the main drawbacks of standard quantum measurements by achieving a significant reduction in the number of necessary measurement rounds and by radically improving the success probabilities of finding global optimal outputs. We provide application scenarios for quantum circuits with arbitrary unitary sequences, and prove that dense measurement theory provides an experimentally implementable solution for gate-model quantum computer architectures.
@cite_30: Preface Acknowledgement Nomenclature and notation Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its applications 6. Quantum search algorithms 7. Quantum computers: physical realisation Part III. Quantum Information: 8. Quantum noise, open quantum systems, and quantum operations 9. Distance measurement for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendix A. Notes on basic probability theory Appendix B. Group theory Appendix C. Approximating quantum gates: the Solvay-Kitaev theorem Appendix D. Number theory Appendix E. Public-key cryptography and the RSA cryptosystem Appendix F. Proof of Lieb's theorem References Index.
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@cite_33: Foreword to 2nd English edition.- Foreword to 2nd Russian edition.- Preface.- Chapters: I. Statistical Models.- II. Mathematics of Quantum Theory.- III. Symmetry Groups in Quantum Mechanics.- IV. Covariant Measurements and Optimality.- V. Gaussian States.- VI Unbiased Measurements.- Supplement - Statistical Structure of Quantum Theory and Hidden Variables.- References.
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@cite_65: The Quantum Challenge, Second Edition, is an engaging and thorough treatment of the extraordinary phenomena of quantum mechanics and of the enormous challenge they present to our conception of the physical world. Traditionally, the thrill of grappling with such issues is reserved for practicing scientists, while physical science, mathematics, and engineering students are often isolated from these inspiring questions. This book was written to remove this isolation.
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@cite_3: It is shown that it is possible to introduce determinism into quantum mechanics by tracing the probabilities in the Born rules back to pseudorandomness in the absolute phase constants of the wave functions. Each wave function is conceived to contain an individual phase factor exp(iα). In an ensemble of systems the phase constants α are taken to be pseudorandom numbers. A reduction process (collapse), independent of any measurement, is conceived to be a spatial contraction of two wavepackets when they meet and satisfy a certain criterion. The criterion depends on the phase constants of both wavepackets. The measurement apparatus fans out the incoming wavepacket into spatially separated eigenpackets of the observable and a reduction associates the point of contraction with an eigenvalue of the observable. The theory is nonlocal and contextual.
@cite_40: as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.
@cite_81: Preface 1. Quantum measurement theory 2. Useful concepts from information theory 3. Continuous measurement 4. Statistical mechanics, open systems, and measurement 5. Quantum feedback control 6. Metrology 7. Quantum mesoscopic systems I: circuits and measurements 8. Quantum mesoscopic systems II: measurement and control Appendices References Index.
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Quantum measurement has a fundamental role in quantum mechanics with several different theoretical interpretations @cite_11 @cite_84 @cite_46 @cite_81 @cite_40 @cite_65 @cite_51 @cite_3 @cite_62 @cite_74 @cite_33 @cite_41 @cite_30 . The measurement of a quantum system collapses of the quantum system into an eigenstate of the operator corresponding to the measurement. The measurement of a quantum system produces a measurement result, the expected values of measurement are associated with a particular probability distribution.