Related papers: Computing Shor's algorithmic steps with classical …
We describe an implementation of Shor's quantum algorithm to factor n-bit integers using only 2n+2 qubits. In contrast to previous space-optimized implementations, ours features a purely Toffoli based modular multiplication circuit. The…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
The coherent interaction between a laser-driven single trapped atom and an optical high-finesse resonator allows to produce entangled multi-photon light pulses on demand. The mechanism is based on the mechanical effect of light. The degree…
Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm this peculiar problem can be solved in…
An efficient quantum modular exponentiation method is indispensible for Shor's factoring algorithm. But we find that all descriptions presented by Shor, Nielsen and Chuang, Markov and Saeedi, et al., are flawed. We also remark that some…
The Feynman path integral formalism has inspired the development of memory-efficient and parallelizable classical algorithms for simulating quantum computers. We adapt this approach for the calculation of probability amplitudes of…
Shor's algorithm is one of the most promising applications of quantum computers. However, since $\sim 10^6$ physical qubits are believed to be required for established approaches, the algorithm will need to be distributed across many…
We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grover's algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on…
Efficient realization of quantum algorithms is among main challenges on the way towards practical quantum computing. Various libraries and frameworks for quantum software engineering have been developed. Here we present a software package…
Many areas of science and engineering encounter data defined on spherical manifolds. Modelling and analysis of spherical data often necessitates spherical harmonic transforms, at high degrees, and increasingly requires efficient computation…
We experimentally demonstrate polarization entanglement for squeezed vacuum pulses containing more than 10^5 photons. We also study photon-number entanglement by calculating the Schmidt number and measuring its operational counterpart.…
The spatial correlation with classical lights, which has some similar aspects as that with entangled lights, is an interesting and fundamentally important topic. But the features of high-order spatial correlation with classical lights are…
Coherent vector beams with involved states of polarization (SOP) are widespread in the literature, having applications in laser processing, super-resolution imaging and particle trapping. We report novel vector beams obtained by…
We suggest a time-effective algorithm to calculate tight focusing of a collimated continuous-wave laser beam with an arbitrary cross-section light vector distribution by a high-aperture microscope objective into a planar microcavity. This…
Typical circuit implementations of Shor's algorithm involve controlled rotation gates of magnitude $\pi/2^{2L}$ where $L$ is the binary length of the integer N to be factored. Such gates cannot be implemented exactly using existing…
Duality in the entanglement of identical particles manifests that entanglement in only one variable can be revealed at a time. We demonstrate this using polarization and orbital angular momentum (OAM) variables of indistinguishable photons…
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…
Linear-optical systems can implement photonic quantum walks that simulate systems with nontrivial topological properties. Here, such photonic walks are used to jointly entangle polarization and winding number. This joint entanglement allows…
We consider how vectorial aspects (polarization) of light propagation can be implemented, and its origin, within a Feynman path integral approach. A key part of this scheme is in generalising the standard optical path length integral from a…
A scheme is discussed for measuring Nth-order coherences of two orthogonally polarized light fields in a single spatial mode at very limited experimental cost. To implement the scheme, the only measurements needed are the Nth-order…