Related papers: Decomposition of unitary matrix into quantum gates
Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are…
Parametrized quantum optical circuits are a class of quantum circuits in which the carriers of quantum information are photons and the gates are optical transformations. Classically optimizing these circuits is challenging due to the…
Quantum computing is a promising approach of computation that is based on equations from Quantum Mechanics. A simulator for quantum algorithms must be capable of performing heavy mathematical matrix transforms. The design of the simulator…
Based on the column pivoted QR decomposition, we propose some randomized algorithms including pass-efficient ones for the generalized CUR decompositions of matrix pair and matrix triplet. Detailed error analyses of these algorithms are…
Quantum-circuit optimization is essential for any practical realization of quantum computation, in order to beat decoherence. We present a scheme for implementing the final stage in the compilation of quantum circuits, i.e., for finding the…
We study efficient generations of random diagonal-unitary matrices, an ensemble of unitary matrices diagonal in a given basis with randomly distributed phases for their eigenvalues. Despite the simple algebraic structure, they cannot be…
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…
Since the final quantum state in the Grover search algorithm is the normalized marked quantum state from the Gram-Schmidt process, Abrams and Lloyd [1] has shown that we can generate this vector by using a non-unitary gate. Following their…
Quantum computing is an emerging technology that has the potential to revolutionize fields such as cryptography, machine learning, optimization, and quantum simulation. However, a major challenge in the realization of quantum algorithms on…
Quantum circuits of a general quantum gate acting on multiple $d$-level quantum systems play a prominent role in multi-valued quantum computation. We first propose a new recursive Cartan decomposition of semi-simple unitary Lie group…
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 show how to express the information contained in a Quantum Bayesian (QB) net as a product of unitary matrices. If each of these unitary matrices is expressed as a sequence of elementary operations (operations such as controlled-nots and…
This paper presents a highly efficient decomposition scheme and its associated Mathematica notebook for the analysis of complicated quantum circuits comprised of single/multiple qubit and qudit quantum gates. In particular, this scheme…
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…
Quantum circuit synthesis describes the process of converting arbitrary unitary operations into a gate sequence of a fixed universal gate set, usually defined by the operations native to a given hardware platform. Most current synthesis…
We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as…
We study a sequence of quantum gates in finite-dimensional Hilbert spaces given by the normalized eigenvectors of the unitary operators. The corresponding sequence of the Hamilton operators is also given. From the Hamilton operators we…
Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized…
We provide a new algorithm that translates a unitary matrix into a quantum circuit according to the G=KAK theorem in Lie group theory. With our algorithm, any matrix decomposition corresponding to type-AIII KAK decompositions can be derived…
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…