Related papers: The Controlled-U and Unitary Transformation in Two…
We will present a few new generalizations of the multi-controlled X (MCX) gate that uses the quantum Fourier transform (QFT). Firstly, we will optimize QFT-MCX and prove that it is equivalent to a stair MCX gates array. This stair-wise…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
Universal quantum entangling gates are a crucial building block in the large-scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the…
We consider the unitary and the anti--unitary operator realizations of two important genuine quantum gates that transform elements of the computational basis of into superpositions: the square root of the identity and the square root of the…
In this paper, we design and experimentally implement various robust quantum unitary transformations (gates) acting on $d$-dimensional vectors (qudits) by tuning a single control parameter using optimal control theory. The quantum state is…
Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only…
Gate-based quantum computation has been extensively investigated using quantum circuits based on qubits. In many cases, such qubits are actually made out of multilevel systems but with only two states being used for computational purpose.…
We construct a generalized controlled phased gate entangler for a multi-qubit state based on the geometrical structure of quantum systems. We also investigate relation between the generalized controlled phase construction of a quantum gate…
We introduce unitary-gate randomized benchmarking (URB) for qudit gates by extending single-and multi-qubit URB to single- and multi-qudit gates. Specifically, we develop a qudit URB procedure that exploits unitary 2-designs. Furthermore,…
In this paper we provide an explicit parameterization of arbitrary unitary transformation acting on n qubits, in terms of one and two qubit quantum gates. The construction is based on successive Cartan decompositions of the semi-simple Lie…
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.…
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…
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…
Quantum circuit model is the most popular paradigm for implementing complex quantum computation. Based on Cartan decomposition, we show that $2(N-1)$ generalized controlled-$X$ (GCX) gates, $6$ single-qubit rotations about the $y$- and…
We show, within the circuit model, how any quantum computation can be efficiently performed using states with only real amplitudes (a result known within the Quantum Turing Machine model). This allows us to identify a 2-qubit (in fact…
We design composite controlled-phase gates, which compensate errors in the phase of a single gate. The errors can be of various nature, such as relative, absolute or both. We present composite sequences which are robust to relative errors…
Optimal control can be used to significantly improve multi-qubit gates in quantum information processing hardware architectures based on superconducting circuit quantum electrodynamics. We apply this approach not only to dispersive gates of…
We construct a Universal Quantum Entanglement Concentration Gate (QEC-Gate). Special times operations of QEC-Gate can transform a pure 2-level bipartite entangled state to nearly maximum entanglement. The transformation can attain any…
Gate-based quantum computers typically encode and process information in two-dimensional units called qubits. Using $d$-dimensional qudits instead may offer intrinsic advantages, including more efficient circuit synthesis, problem-tailored…
The universal quantum computer is a device capable of simulating any physical system and represents a major goal for the field of quantum information science. Algorithms performed on such a device are predicted to offer significant gains…