Related papers: Single-qubit unitary gates by graph scattering
A primary objective of quantum computation is to efficiently simulate quantum physics. Scientifically and technologically important quantum Hamiltonians include those with spin-$s$, vibrational, photonic, and other bosonic degrees of…
The quantum circuit model is the most commonly used model for implementing quantum computers and quantum neural networks whose essential tasks are to realize certain unitary operations. The circuit model usually implements a desired unitary…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total…
An algorithm is proposed to convert arbitrary unitary matrix to a sequence of $X$ gates and fully controlled $R_y, R_z$ and $R_1$ gates. This algorithm is used to generate Q# implementation for arbitrary unitary matrix. Some optimizations…
Future quantum devices often rely on favourable scaling with respect to the system components. To achieve desirable scaling, it is therefore crucial to implement unitary transformations in an efficient manner. We develop an upper bound for…
We show how the spin independent scattering between two identical flying qubits can be used to implement an entangling quantum gate between them. We consider one dimensional models with a delta interaction in which the qubits undergoing the…
Successfully implementing a quantum algorithm involves maintaining a low logical error rate by ensuring the validity of the quantum fault-tolerance theorem. The required number of physical qubits arranged in an array depends on the chosen…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
We investigate the propagation of a massless scalar field on a star graph, modeling the junction of $n$ quantum wires. The vertex of the graph is represented by a point-like impurity (defect), characterized by a one-body scattering matrix.…
In quantum circuits, qubits and the quantum gates acting on them have traditionally been analysed using matrix algebra and Dirac notation. While powerful, these can be unintuitive for conceptual understanding and rapid problem solving. In…
We describe in detail the application of four qubit cluster states, built on the simultaneous entanglement of two photons in the degrees of freedom of polarization and linear momentum, for the realization of a complete set of basic one-way…
In a quantum ring connected with two external leads the spin properties of an incoming electron are modified by the spin-orbit interaction resulting in a transformation of the qubit state carried by the spin. The ring acts as a one qubit…
Although the quality of quantum bits (qubits) and quantum gates has been steadily improving, the available quantity of qubits has increased quite slowly. To address this important issue in quantum computing, we have demonstrated arbitrary…
This work deals with the average scattering entropy of quantum graphs. We explore this concept in several distinct scenarios that involve periodic, aperiodic and random distribution of vertices of distinct degrees. In particular, we compare…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain…
Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are…
Quantum walks have frequently envisioned the behavior of a quantum state traversing a classically defined, generally finite, graph structure. While this approach has already generated significant results, it imposes a strong assumption: all…
Spin qubits are very valuable and scalable candidates in the area of quantum computation and simulation applications. In the last decades, they have been deeply investigated from a theoretical point of view and realized on the scale of few…
We present two techniques that can greatly reduce the number of gates required to realize an energy measurement, with application to ground state preparation in quantum simulations. The first technique realizes that to prepare the ground…