Related papers: Sequent Calculus Representations for Quantum Circu…
Over a decade ago, it was demonstrated that quantum computing has the potential to revolutionize numerical linear algebra by enabling algorithms with complexity superior to what is classically achievable, e.g., the seminal HHL algorithm for…
Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed.…
A logical system derived from linear logic and called QMLL is introduced and shown able to capture all unitary quantum circuits. Conversely, any proof is shown to compute, through a concrete GoI interpretation, some quantum circuits. The…
One-way measurement based quantum computations (1WQC) may describe unitary transformations, via a composition of CPTP maps which are not all unitary themselves. This motivates the following decision problems: Is it possible to determine…
Quantum computing promises to exploit the laws of quantum mechanics for processing information in ways fundamentally different from today's classical computers, leading to unprecedented efficiency. One-way quantum computation, sometimes…
Quantum circuit compilation comprises many computationally hard reasoning tasks that nonetheless lie inside #$\mathbf{P}$ and its decision counterpart in $\mathbf{PP}$. The classical simulation of general quantum circuits is a core example.…
People are witnessing quantum computing revolutions nowadays. Progress in the number of qubits, coherence times and gate fidelities are happening. Although quantum error correction era has not arrived, the research and development of…
In this book chapter, we provide a tutorial introduction to one-way quantum computation and many of the techniques one can use to understand it. The techniques which are described include the stabilizer formalism and the logical Heisenberg…
This paper is a brief and informal presentation of cirquent calculus, a novel proof system for resource-conscious logics. As such, it is a refinement of sequent calculus with mechanisms that allow to explicitly account for the possibility…
We present a formulation of quantum circuits where the focus is set on whether a given circuit (made of unitary operators and projective measurements with definite outcomes) does reflect an actually realizable physical experiment. In order…
Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers. This naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to…
Classical simulation of quantum physics is a central approach to investigating physical phenomena. Quantum computers enhance computational capabilities beyond those of classical resources, but it remains unclear to what extent existing…
The proposed framework represents the first tool to compile a quantum circuit across photonic-connected distributed quantum processors. Its design follows a divide-and-conquer paradigm for circuit partitioning, transpilation, and assembly,…
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…
This paper describes an algorithmic system called SQT for the computer simulation of a wide class of quantum experiments on entangled particles. SQT maintains a hidden internal state for each particle and it provides an initialization…
Quantum computing promises to solve some important problems faster than conventional computations ever could. Currently available NISQ devices on which first practical applications are already executed demonstrate the potential -- with…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
A flagship application of quantum computers is the simulation of other quantum systems, including quantum field theories. In this article, we show how quantum computers can be employed to naturally calculate Feynman diagrams and their…
A systematic method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates…
This chapter is a short pedagogical introduction to the use of quantum logic for the simulation of complex quantum systems, including a simulation example on actual quantum hardware.