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Any unitary transformation of quantum computational networks is explicitly decomposed, in an exact and unified form, into a sequence of a limited number of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal unitary…
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…
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…
Contemporary quantum computers encode and process quantum information in binary qubits (d = 2). However, many architectures include higher energy levels that are left as unused computational resources. We demonstrate a superconducting…
Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to…
Quantum algorithms require a universal set of gates that can be implemented in a physical system. For these, an optimal decomposition into a sequence of available operations is desired. Here, we present a method to find such sequences for a…
A quantum compiling algorithm is an algorithm for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). Suppose $U_{in}$ is an $\nb$-bit unstructured unitary matrix (a unitary matrix with no…
NISQ devices have inherent limitations in terms of connectivity and hardware noise. The synthesis of CNOT circuits considers the physical constraints and transforms quantum algorithms into low-level quantum circuits that can execute on…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
Quantum algorithm design usually assumes access to a perfect quantum computer with ideal properties like full connectivity, noise-freedom and arbitrarily long coherence time. In Noisy Intermediate-Scale Quantum (NISQ) devices, however, the…
Crosstalk and several sources of operational interference are invisible when qubit or a gate is calibrated or benchmarked in isolation. These are unlocked during the execution of full quantum circuit applying entangling gates to several…
The native gate set is fundamental to the performance of quantum devices, as it governs the accuracy of basic quantum operations and dictates the complexity of implementing quantum algorithms. Traditional approaches to extending gate sets…
The most general structure (in matrix form) of a single-qubit gate is presented. Subsequently, used that to obtain a set of conditions for testing (a) whether a given 2-qubit gate is genuinely a 2-qubit gate, i.e., not decomposable into two…
We propose how to realize a three-step controlled-phase gate of one superconducting qubit simultaneously controlling n qubits selected from N qubits in a cavity (1<n<N). The operation time of this gate is independent of the number n of…
We investigate the counterparts of random walk in universal quantum computing and their implementation using standard quantum circuits. Quantum walk have been recently well investigated for traversing graphs with certain oracles. We focus…
Quantum circuit synthesis is the task of decomposing a given quantum operator into a sequence of elementary quantum gates. Since the finite target gate set cannot exactly implement any given operator, approximation is often necessary. Model…
A scalable and programmable quantum computer holds the potential to solve computationally intensive tasks that classical computers cannot accomplish within a reasonable time frame, achieving quantum advantage. However, the vulnerability of…
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…
A CNOT circuit is the key gadget for entangling qubits in quantum computing systems. However, the qubit connectivity of noisy intermediate-scale quantum (NISQ) devices is constrained by their {limited connectivity architecture}. To improve…
Executing quantum algorithms on a quantum computer requires compilation to representations that conform to all restrictions imposed by the device. Due to devices' limited coherence times and gate fidelities, the compilation process has to…