Related papers: Symbolic Quantum State Representation and its Simu…
In our previous work [1] we described quantized computation using Horn clauses and based the semantics, dubbed as entanglement semantics as a generalization of denotational and distribution semantics, and founded it on quantum probability…
In the present paper we continue our study of non-commutative operator graphs in infinite-dimensional spaces. We consider examples of the non-commutative operator graphs generated by resolutions of identity corresponding to the…
In this paper a generalization of Weyl quantization which maps a dynamical operator in a function space to a dynamical superoperator in an operator space is suggested. Quantization of dynamical operator, which cannot be represented as…
In this paper we present a simple algorithm for representation of statistical data of any origin by complex probability amplitudes. Numerical simulation with Mathematica-6 is performed. The Bloch's sphere is used for visualization of…
We introduce coherent-state propagation, a computational framework for simulating bosonic systems. We focus on bosonic circuits composed of displaced linear optics augmented by Kerr nonlinearities, a universal model of bosonic quantum…
Non-commutativity is ubiquitous in mathematical modeling of reality and in many cases same algebraic structures are implemented in different situations. Here we consider the canonical commutation relation of quantum theory and discuss a…
Quantum simulation provides quantum systems under study with analogous controllable quantum systems and has wide applications from condensed-matter physics to high energy physics and to cosmology. The quantum system of a homogeneous and…
In a series of papers we have argued that the 'basic' physical procedure of minimal coupling giving the quantum description of a Hamiltonian system interacting with a magnetic field, can be given a very satisfactory mathematical formulation…
The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed.…
Numerical modeling of radio-frequency waves in plasma with sufficiently high spatial and temporal resolution remains challenging even with modern computers. However, such simulations can be sped up using quantum computers in the future.…
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…
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…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done by a projective representation of double-phase space, and we…
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
A growing cohort of experimental linear photonic networks implementing Gaussian boson sampling (GBS) have now claimed quantum advantage. However, many open questions remain on how to effectively verify these experimental results, as…
The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of…
Non commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non commutative configuration space. Taking this as departure point, we formulate a coherent state approach…
The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in $\hbar$. Its semiclassical expansion…
A non--commutative analogue of the classical differential forms is constructed on the phase--space of an arbitrary quantum system. The non--commutative forms are universal and are related to the quantum mechanical dynamics in the same way…