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Controlled unitary gates are a basic element in many quantum algorithms. Converting a general unitary $U$ with a known decomposition into its controlled version, controlled-$U$, can introduce a large overhead in terms of the depth of the…

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…

In this work we investigate that whether one can construct single and two qubit gates for arbitrary quantum states from the principle of no signalling. We considered the problem for Pauli gates, Hadamard gate, C-Not gate.

We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed…

We experimentally demonstrate an optical controlled-NOT (CNOT) gate with arbitrary single inputs based on a 4-photon 6-qubit cluster state entangled both in polarization and spatial modes. We first generate the 6-qubit state, and then by…

We analyze the operation of quantum gates for neutral atoms with qubits that are delocalized in space, i.e., the computational basis states are defined by the presence of a neutral atom in the ground state of one out of two trapping…

Effective spin-spin interactions between N+1 qubits enable the determination of the eigenvalue of an arbitrary Pauli product of dimension N with a constant, small number of multi-qubit gates that is independent of N and encodes the…

We propose a quantum circuit composed of $cNOT$ gates and four single-qubit gates to generate a $W$ state of three qubits. This circuit was then enhanced by integrating two-qubit gates to create a $W$ state of four and five qubits. After a…

We present the theoretical basis for and experimental verification of arbitrary single-qubit state generation, using the polarization of photons generated via spontaneous parametric downconversion. Our precision measurement and state…

The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits. Recall that a…

We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate…

In recent years, quantum state engineering and quantum information processing using microwave fields and photons have received increasing attention. In addition, multiqubit gates play an important role in quantum information processing. In…

Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…

We propose a new way of implementing several elementary quantum gates for qubits in the coherent state basis. The operations are probabilistic and employ single photon subtractions as the driving force. Our schemes for single-qubit phase…

We show how to construct a multi-qubit control gate on a quantum register of an arbitrary size N. This gate performs a single-qubit operation on a specific qubit conditioned by the state of other N-1 qubits. We provide an algorithm how to…

We discuss techniques for producing, manipulating and measureing qubits encoded optically as vacuum and single photon states. We show that a universal set of non-deterministic gates can be constructed using linear optics and photon…

Any single-qubit unitary operation or quantum gate can be considered a rotation. Typical experimental implementations of single-qubit gates involve two or three fixed rotation axes, and up to three rotation steps. Here we show that, if the…

The phase estimation algorithm is so named because it allows the estimation of the eigenvalues associated with an operator. However it has been proposed that the algorithm can also be used to generate eigenstates. Here we extend this…

A novel mechanism is proposed for single and double qubit state manipulations in quantum computation with four-fold degenerate energy levels. The principle is based on starting with a four fold degeneracy, lifting it stepwise adiabatically…

In circuit-based quantum computing, the available gate set typically consists of single-qubit gates acting on each individual qubit and at least one entangling gate between pairs of qubits. In certain physical architectures, however, some…