Related papers: A Complete Equational Theory for Quantum Circuits
For quantum computer circuits, it is proposed that they have, besides the presently used compact graphs, an expanded system of subgraphs, in line with the quantum mechanics superposition axiom. The representation of each process by these…
We show that quantum computation circuits with coherent states as the logical qubits can be constructed using very simple linear networks, conditional measurements and coherent superposition resource states.
This paper addresses quantum circuit mapping for Noisy Intermediate-Scale Quantum (NISQ) computers. Since NISQ computers constraint two-qubit operations on limited couplings, an input circuit must be transformed into an equivalent output…
The design of efficient quantum circuits is an important issue in quantum computing. It is in general a formidable task to find a highly optimized quantum circuit for a given unitary matrix. We propose a quantum circuit design method that…
Using the techniques of optomechanics, a high-$Q$ mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of…
No quantum circuit can turn a completely unknown unitary gate into its coherently controlled version. Yet, coherent control of unknown gates has been realised in experiments, making use of a different type of initial resources. Here, we…
In order to realize a Quantum CPU some schemes for executing fundamental mathematical tasks are needed. In this paper we present some quantum circuits which, using elementary arithmetic operations, allow an approximated calculation of…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
This paper presents a highly efficient decomposition scheme and its associated Mathematica notebook for the analysis of complicated quantum circuits comprised of single/multiple qubit and qudit quantum gates. In particular, this scheme…
From a geometric approach, we derive the minimum number of applications needed for an arbitrary Controlled-Unitary gate to construct a universal quantum circuit. A new analytic construction procedure is presented and shown to be either…
In this paper we identify full list of Elementary Cellular Automata rules which can be simulated using a quantum circuit (there are 22 such rules). For every such rule we present quantum circuit implementing it with $O(N)$ gates.
We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly…
The intriguing appeal of circuits lies in their modularity and ease of fabrication. Based on a toolbox of simple building blocks, circuits present a powerful framework for achieving new functionality by combining circuit elements into…
Suppose that a quantum circuit with K elementary gates is known for a unitary matrix U, and assume that U^m is a scalar matrix for some positive integer m. We show that a function of U can be realized on a quantum computer with at most…
We construct quantum circuits for solving one-dimensional Schr\"odinger equations. Simulations of three typical examples, i.e., harmonic oscillator, square-well and Coulomb potential, show that reasonable results can be obtained with eight…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
The applications of geometric control theory methods on Lie groups and homogeneous spaces to the theory of quantum computations are investigated. These methods are shown to be very useful for the problem of constructing an universal set of…
This paper addresses the problem of designing universal quantum circuits to transform $k$ uses of a $d$-dimensional unitary input-operation into a unitary output-operation in a probabilistic heralded manner. Three classes of protocols are…
Fully convolutional networks are robust in performing semantic segmentation, with many applications from signal processing to computer vision. From the fundamental principles of variational quantum algorithms, we propose a feasible pure…
Quantum computing holds the potential to revolutionize various fields by efficiently tackling complex problems. At its core are quantum circuits, sequences of quantum gates manipulating quantum states. The selection of the right quantum…