Related papers: Quantum Logic and Quantum Computation
We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert state space of rotational states of a rigid body. These codes, which protect against both drift in the body's…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…
We describe an approach for characterizing the process of quantum gates using quantum process tomography, by first modeling them in an extended Hilbert space, which includes non-qubit degrees of freedom. To prevent unphysical processes from…
Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
Invariance under translation is exploited to efficiently simulate one-dimensional quantum lattice systems in the limit of an infinite lattice. Both the computation of the ground state and the simulation of time evolution are considered.
The last two decades have seen an explosive growth in the theory and practice of both quantum computing and machine learning. Modern machine learning systems process huge volumes of data and demand massive computational power. As silicon…
In quantum logic, i.e., within the structure of the Hilbert lattice imposed on all closed linear subspaces of a Hilbert space, the assignment of truth values to quantum propositions (i.e., experimentally verifiable propositions relating to…
While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers. In this work, we introduce the Quantum Laplace Transform (QLT),…
We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not…
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…
Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters),…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
The cluster state model for quantum computation [Phys. Rev. Lett. 86, 5188] outlines a scheme that allows one to use measurement on a large set of entangled quantum systems in what is known as a cluster state to undertake quantum…
The purpose of this paper is to explore the applications of quantum computing to energy systems optimization problems and discuss some of the challenges faced by quantum computers with techniques to overcome them. The basic concepts…
Finite frame quantization is a discrete version of the coherent state quantization. In the case of a quantum system with finite-dimensional Hilbert space, the finite frame quantization allows us to associate a linear operator to each…
Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced,…
A `register' in quantum information processing -- is composition of k quantum systems, `qudits'. The dimensions of Hilbert spaces for one qudit and whole quantum register are d and d^k respectively, but we should have possibility to prepare…
We describe a quantum computer based upon the coherent manipulation of two-level atoms between discrete one-dimensional momentum states. Combinations of short laser pulses with kinetic energy dependent free phase evolution can perform the…
Due to the existence of incompatible observables, the propositional calculus of a quantum system does not form a Boolean algebra but an orthomodular lattice. Such lattice can be realised as a lattice of subspaces on a real, complex or…