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Quantum Information and Measurement (QIM)

Dense Measurements for Quantum Computations

László Gyöngyösi, Sándor Imre

Published Jan 1, 2019• 0 citations
Publisher

Abstract

Quantum measurement is a fundamental cornerstone of experimental quantum computations. We define a novel measurement for quantum computations called dense quantum measurement. The dense measurement aims at fixing the main drawbacks of standard quantum measurements.
DOI
10.1364/qim.2019.f5a.38

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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.
Quantum measurement is a cornerstone of quantum mechanics, yet the inherent probabilistic nature of the outcome often challenges intuitive interpretations. Traditional approaches treat quantum measurement as a classical process, limiting the possibilities for fundamentally different measurement outcomes. This paper proposes a novel framework for defining and utilizing non-Euclidean metric spaces within quantum measurement, aiming to unlock previously unexplored avenues of quantum phenomena. This framework allows for the exploration of fundamentally different measurement outcomes, potentially revealing new aspects of quantum reality.
Measurement is a fundamental operation in quantum computing and has many important use cases in quantum algorithms. This article provides a comprehensive overview of the basic measurement operations in quantum computing and represents a selected set of their applications in quantum algorithms. Our goal is to provide one of the first algorithmic overviews of measurement processes in quantum computing. From the quantum information-theoretical perspective, measurements are either a method to access the result of a quantum computation or a technique to modify a quantum state. We also identify measurement-based methods to solve quantum computational challenges, such as error mitigation and circuit cutting. We discuss three main categories of measurements: performing measurements in static quantum circuits, modifying the quantum state in dynamic quantum circuits via measurements, and addressing challenges in quantum computing with measurements. Based on the reviewed topics, the measurement operations are frequently not at the center of the quantum algorithm design. However, the most novel and error-prone quantum algorithms will likely require sophisticated measurement schemes. Thus, the central message of this article is to broaden the view of measurement operations and highlight their importance at every level of quantum algorithm design.
New prospects in several emerging technologies such as quantum computation and certain aspects of low-power design motivated an intensive consideration of the design of reversible circuits. Since most of the existing synthesis approaches usually generate circuits of high costs, post-synthesis optimization is frequently applied. Here, the reduction of control line connections is a major focus as they are a main reason for high quantum costs in the respective reversible circuits. Previous approaches aimed for exploiting so-called common control lines for this purpose. However, while these solutions indeed lead to substantial improvements in the costs, they inherit some drawbacks and restrictions. In this work, we propose an alternative approach for the reduction of common control lines in reversible circuits, which (1) is based in the concepts of previously proposed solutions, but (2) combines them in a new fashion. This enables us to achieve the same or even better improvements, while - at the same time - overcome their drawbacks. Experimental evaluations confirm these benefits, i.e. significant improvements compared to the previous methods can often be achieved without the need to deal with their drawbacks.
Measurement-based quantum computation (MBQC) has emerged as a new approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model that takes unitary operations as fundamental. Among measurement-based quantum computation methods the recently introduced one-way quantum computer stands out as basic and fundamental. The key idea is to start from an entangled state and then use measurements and one-qubit unitaries, which may be dependent on the outcomes of measurements, to guide the computation. The main point is that one never has to perform unitaries on more than one qubit at a time after the initial preparation of an entangled state. The “programs” that one writes in this model are traditionally called “patterns.” In this chapter, we develop a rigorous mathematical model underlying measurement-based quantum computation. We give syntax, operational semantics, denotational semantics, and an algebra of programs derived from the denotational semantics. We also present a rewrite theory and prove a general standardization theorem that allows all programs to be put in a semantically equivalent standard form. Standardization has far-reaching consequences: a new physical architecture based on performing all the entanglement in the beginning, parallelization by exposing the dependency structure of measurements, and expressiveness theorems. We use our general measurement calculus not just to formalize the one-way model but also several other measurement-based models, e.g., Teleportation, Phase, and Pauli models, and present compositional embeddings of them into and from the one-way model.
Quantum measurement problem is a long-standing problem at the heart of the foundations of modern physics and nascent technology, such as quantum technology. The last forty years brought a renowned interest in this problem with an emphasis on the new foundations of quantum theory and unpredicted formulation of some new quantum disciplines, such as the open quantum systems theory and the quantum information and computation science. A state of the art of the problem of measurement is shortly presented, including a brief historical view, with a review of the authors' original contributions.