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We adopt a method of the quantum gate teleportation for converting circuit-based quantum computation primitives into fusion networks. By using the presented scheme for the CNOT gate we construct translation of the circuit for the foliated…

We have recently constructed compact, CNOT-efficient, quantum circuits for fermionic and qubit excitations of arbitrary many-body rank [I. Magoulas and F.A. Evangelista, J. Chem. Theory Comput. 19, 822 (2023)]. Here, we present…

For certain {\it specific} (or {\it"magic"}) Lamb-Dicke (LD) parameters, Monroe {\it et al} showed [Phys. Rev. {\bf A 55}, R2489 (1997)] that a two-qubit quantum operation, between the external and internal degrees of freedom of a single…

Controlled operations are fundamental building blocks of quantum algorithms. Decomposing $n$-control-NOT gates ($C^n(X)$) into arbitrary single-qubit and CNOT gates, is a crucial but non-trivial task. This study introduces $C^n(X)$ circuits…

The design and architecture of a quantum instruction set are paramount to the performance of a quantum computer. This work introduces a gate scheme for qubits with $XX+YY$ coupling that directly and efficiently realizes any two-qubit gate…

One of the main advantages of an optical approach to quantum computing is the fact that optical fibers can be used to connect the logic and memory devices to form useful circuits, in analogy with the wires of a conventional computer. Here…

Single qubit rotation gate and the controlled-NOT (CNOT) gate constitute a complete set of gates for universal quantum computation. In general the CNOT gate are only for two nearby qubits. For two qubits which are remote from each other, we…

One of the main problems that optical quantum computing has to overcome is the efficient construction of two-photon gates. Theoretically these gates can be realized using Kerr-nonlinearities, but the techniques involved are experimentally…

A controlled-NOT logic gate based on conditional spectroscopy has been demonstrated recently for a pair of superconducting flux qubits [Plantenberg et al., Nature 447, 836 (2007)]. Here we study the fidelity of this type of gate applied to…

We consider the decomposition of arbitrary isometries into a sequence of single-qubit and Controlled-NOT (C-NOT) gates. In many experimental architectures, the C-NOT gate is relatively 'expensive' and hence we aim to keep the number of…

We review quantum information processing with cold neutral particles, that is, atoms or polar molecules. First, we analyze the best suited degrees of freedom of these particles for storing quantum information, and then we discuss both…

CNOT circuits are a common building block of general quantum circuits. The problem of synthesizing and optimizing such circuits has received a lot of attention in the quantum computing literature. This problem is especially challenging for…

Characterizing the noise in the set of gate operations that form the building blocks of a quantum computational device is a necessity for assessing the quality of the device. Here, we introduce randomized linear gate set tomography, an…

An essential element of classical computation is the "if-then" construct, that accepts a control bit and an arbitrary gate, and provides conditional execution of the gate depending on the value of the controlling bit. On the other hand,…

We present an economical dynamical control scheme to perform quantum computation on a one dimensional optical lattice, where each atom encodes one qubit. The model is based on atom tunneling transitions between neighboring sites of the…

We present the first NMR implementation of a scheme for selective and efficient quantum process tomography without ancilla. We generalize this scheme such that it can be implemented efficiently using only a set of measurements involving…

Linear optics is a promising candidate to enable the construction of quantum computers. A number of quantum protocols gates based on linear optics have been demonstrated. However, it is well-known that these gates are non-deterministic and…

The quantum Fourier transform (QFT) is a crucial subroutine in many quantum algorithms. In this paper, we study the exact lower bound problem of CNOT gate complexity for fault-tolerant QFT. First, we consider approximating the ancilla-free…

Scalable and fault-tolerant quantum computation will require error correction. This will demand constant measurement of many-qubit observables, implemented using a vast number of CNOT gates. Indeed, practically all operations performed by a…

Linear-Optical Passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the…