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This article defines and proves basic properties of the standard quantum circuit model of computation. The model is developed abstractly in close analogy with (classical) deterministic and probabilistic circuits, without recourse to any…
Classical simulation is important because it sets a benchmark for quantum computer performance. Classical simulation is currently the only way to exercise larger numbers of qubits. To achieve larger simulations, sparse matrix processing is…
We introduce a new graphical framework for designing quantum error correction codes based on classical principles. A key feature of this graphical language, over previous approaches, is that it is closely related to that of factor graphs or…
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations…
The emergence of quantum computing proposes a revolutionary paradigm that can radically transform numerous scientific and industrial application domains. The ability of quantum computers to scale computations exponentially imply better…
Quantum computing has the potential to provide exponential performance benefits in processing over classical computing. It utilizes quantum mechanics phenomena (such as superposition, entanglement, and interference) to solve a computational…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the…
Classical representations of quantum states and operations as vectors and matrices are plagued by an exponential growth in memory and runtime requirements for increasing system sizes. Based on their use in classical computing, an…
Quantum computation has received great attention in recent years for its possible application to difficult problem in classical calculation. Despite the experimental problems of implementing quantum devices, theoretical physicists have…
Quantum Computing is a new paradigm that enables several advances which are impossible using classical technology. With the rise of quantum computers, the software is also invited to change so that it can better fit this new computation…
Although computational complexity is a fundamental aspect of program behavior, it is often at odds with common type theoretic principles such as function extensionality, which identifies all functions with the same $\textit{input-output}$…
We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem…
Split-execution computing leverages the capabilities of multiple computational models to solve problems, but splitting program execution across different computational models incurs costs associated with the translation between domains. We…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
A common scenario in distributed computing involves a client who asks a server to perform a computation on a remote computer. An important problem is to determine the minimum amount of communication needed to specify the desired…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…
Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways,…
The Quantum Internet is envisioned as the final stage of the quantum revolution, opening fundamentally new communications and computing capabilities, including the distributed quantum computing. But the Quantum Internet is governed by the…