Related papers: Quaternionic Computing
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
In a quantum computer, creating superpositions of quantum bits (qubits) in different states can lead to a speed-up over classical computers [1], but quantum mechanics also allows for the superposition of quantum circuits [2]. In fact, it…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more…
Within the general context of the architecture in quantum computer design, this paper aims is to provide a general strategy to obtain a block-matrix representation of quantum gates applied to qubits placed in arbitrary positions over an…
Probabilistic graphical models such as Bayesian networks are widely used to model stochastic systems to perform various types of analysis such as probabilistic prediction, risk analysis, and system health monitoring, which can become…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
We develop a unitary dependence theory to characterize the behaviors of quantum circuits and states in terms of how quantum gates manipulate qubits and determine their measurement probabilities. A qubit has dependence on a 1-qubit unitary…
A universal set of gates for (classical or quantum) computation is a set of gates that can be used to approximate any other operation. It is well known that a universal set for classical computation augmented with the Hadamard gate results…
We consider a unitary transformation which maps any given state of an $n$-qubit quantum register into another one. This transformation has applications in the initialization of a quantum computer, and also in some quantum algorithms.…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is…
Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the…
Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schr\"odinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately…
We describe an architecture based on a processing 'core' where multiple qubits interact perpetually, and a separate 'store' where qubits exist in isolation. Computation consists of single qubit operations, swaps between the store and the…
The "Power of One Qubit" refers to a computational model that has access to only one pure bit of quantum information, along with n qubits in the totally mixed state. This model, though not as powerful as a pure-state quantum computer, is…
A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field…
Models for quantum computation with circuit connections subject to the quantum superposition principle have been recently proposed. There, a control quantum system can coherently determine the order in which a target quantum system…
Let G(A,B) denote the 2-qubit gate which acts as the 1-qubit SU(2) gates A and B in the even and odd parity subspaces respectively, of two qubits. Using a Clifford algebra formalism we show that arbitrary uniform families of circuits of…