Related papers: Engineering Functional Quantum Algorithms
We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits -- a unitary transformation with 4^n degrees of freedom. For synthesizing the gate sequence, a method based on the…
Quantum circuits which perform integer arithmetic could potentially outperform their classical counterparts. In this paper, a quantum circuit is considered which performs a specific computational pattern on classically represented integers…
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…
We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x \oplus y)$) is universal in the sense that all unitary operations on arbitrarily many…
The design of efficient quantum circuits is an important issue in quantum computing. It is in general a formidable task to find a highly optimized quantum circuit for a given unitary matrix. We propose a quantum circuit design method that…
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…
Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
To build a general-purpose quantum computer, it is crucial for the quantum devices to implement classical boolean logic. A straightforward realization of quantum boolean logic is to use auxiliary qubits as intermediate storage. This…
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…
We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis…
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…
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 discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
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…
A quantum circuit is generalized to a nonunitary one whose constituents are nonunitary gates operated by quantum measurement. It is shown that a specific type of one-qubit nonunitary gates, the controlled-NOT gate, as well as all one-qubit…
We prove that for any $n$-qubit unitary transformation $U$ and for any $r = 2^{o(n / \log n)}$, there exists a quantum circuit to implement $U^{\otimes r}$ with at most $O(4^n)$ gates. This asymptotically equals the number of gates needed…
In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over $Z_q$, which is considered the most ``quantum'' part of Shor's algorithm, can in fact be simulated efficiently by classical computers.…