Related papers: QuAlg -- A symbolic algebra package for quantum in…
Using a quantumlike description for light propagation in nonhomogeneous optical fibers, quantum information processing can be implemented by optical means. Quantum-like bits (qulbits) are associated to light modes in the optical fiber and…
In this paper, we propose a novel quantum multiple access technique based on optical coherent states. The information of several coherent state optical qubits is combined into a single qudit, which is the superposition of almost orthogonal…
We introduce a proof language for Intuitionistic Multiplicative Additive Linear Logic (IMALL), extended with a modality B to capture mixed-state quantum computation. The language supports algebraic constructs such as linear combinations,…
We give an axiomatic formulation of quantum structures like semilogics and quasilogics which generalize the boolean semirings of events and fuzzy logics. The notions of distributions, states, representations observables and semiobservables…
Some ideas about phenomenological applications of quantum algebras to physics are reviewed. We examine in particular some applications of the algebras $U_ q (su_2)$ and $U_{qp}({\rm u}_2)$ to various dynamical systems and to atomic and…
Q# is a standalone domain-specific programming language from Microsoft for writing and running quantum programs. Like most industrial languages, it was designed without a formal specification, which can naturally lead to ambiguity in its…
This paper describes a novel approach to emulate a universal quantum computer with a wholly classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any…
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
Quantum process tomography (QPT) is a fundamental tool for fully characterizing quantum systems. It relies on querying a set of quantum states as input to the quantum process. Previous QPT methods typically employ a straightforward strategy…
We introduce an open source software package UniversalQCompiler written in Mathematica that allows the decomposition of arbitrary quantum operations into a sequence of single-qubit rotations (with arbitrary rotation angles) and…
For a finite dimensional semisimple Lie algebra ${\frak{g}}$ and a root $q$ of unity in a field $k,$ we associate to these data a double quiver $\bar{\cal{Q}}.$ It is shown that a restricted version of the quantized enveloping algebras…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
We define QSE, a symbolic execution framework for quantum programs by integrating symbolic variables into quantum states and the outcomes of quantum measurements. The soundness of QSE is established through a theorem that ensures the…
As we enter a new era of quantum technology, it is increasingly important to develop methods to aid in the accurate preparation of quantum states for a variety of materials, matter, and devices. Computational techniques can be used to…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
A new method is developed to derive an algebraic equations for the geometric measure of entanglement of three qubit pure states. The equations are derived explicitly and solved in cases of most interest. These equations allow oneself to…
It is proposed to map the quantum information qubit not to individual spin 1/2 states, but to the collective spin states being eigenfunctions of the Hamiltonian including spin-spin interactions, which may be not small. Such an approach…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
The process algebra has been used successfully to provide a novel formulation of quantum mechanics in which non-relativistic quantum mechanics (NRQM) emerges as an effective theory asymptotically. The process algebra is applied here to the…