Related papers: Synthesizing Quantum Circuits for Simple Periodic …

We identify a sub-class of BQP that captures certain structural commonalities among many quantum algorithms including Shor's algorithms. This class does not contain all of BQP (e.g. Grover's algorithm does not fall into this class). Our…

This pedagogical review presents the proof of the Solovay-Kitaev theorem in the form of an efficient classical algorithm for compiling an arbitrary single-qubit gate into a sequence of gates from a fixed and finite set. The algorithm can be…

We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…

In order to realize a Quantum CPU some schemes for executing fundamental mathematical tasks are needed. In this paper we present some quantum circuits which, using elementary arithmetic operations, allow an approximated calculation of…

We consider the problem of the variational quantum circuit synthesis into a gate set consisting of the CNOT gate and arbitrary single-qubit (1q) gates with the primary target being the minimization of the CNOT count. First we note that…

A quantum processor (QuP) can be used to exploit quantum mechanics to find the prime factors of composite numbers[1]. Compiled versions of Shor's algorithm have been demonstrated on ensemble quantum systems[2] and photonic systems[3-5],…

The remarkable capability of quantum Fourier transformation (QFT) to extract the periodicity of a given periodic function has been exhibited by using nuclear magnetic resonance (NMR) techniques. Two separate sets of experiments were…

Given a quantum algorithm, it is highly nontrivial to devise an efficient sequence of physical gates implementing the algorithm on real hardware and incorporating topological quantum error correction. In this paper, we present a first step…

While advances in quantum hardware occur in modest steps, simulators running on classical computers provide a valuable test bed for the construction of quantum algorithms. Given a unitary matrix that performs certain operation, obtaining…

The simplest decomposition of a Toffoli gate acting on three qubits requires {\em five} 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to six. We show that the number of…

We consider quantum circuits composed of Clifford and T gates. In this context the T gate has a special status since it confers universal computation when added to the (classically simulable) Clifford gates. However it can be very expensive…

Tomography has reached its practical limits in characterization of new quantum devices, and there is a need for a new means of characterizing and validating new technological advances in this field. We propose a different verification…

Constructing general programmable circuits to be able to run any given unitary operator efficiently on a quantum processor is of fundamental importance. We present a new quantum circuit design technique resulting two general programmable…

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 decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as…

Multiplication over binary fields is a crucial operation in quantum algorithms designed to solve the discrete logarithm problem for elliptic curve defined over $GF(2^n)$. In this paper, we present an algorithm for constructing quantum…

We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…

Each year, the gap between theoretical proposals and experimental endeavours to create quantum computers gets smaller, driven by the promise of fundamentally faster algorithms and quantum simulations. This occurs by the combination of…

We study quantum period finding algorithms such as Simon and Shor (and its variants Eker{\aa}-H{\aa}stad and Mosca-Ekert). For a periodic function $f$ these algorithms produce -- via some quantum embedding of $f$ -- a quantum superposition…

There is a large body of work studying what forms of computational hardness are needed to realize classical cryptography. In particular, one-way functions and pseudorandom generators can be built from each other, and thus require equivalent…