Collective unitary evolution with linear optics by Cartan decomposition

2022 ◽  
Author(s):  
Wen-Qiang Liu ◽  
Xin-Jie Zhou ◽  
Hai-Rui Wei
Keyword(s):  
Quantum Information Processing ◽  
Quantum Walk ◽  
Phase Shifters ◽  
Quantum Circuits ◽  
Unitary Operation ◽  
Linear Optics ◽  
Optical Elements ◽  
Unitary Evolution ◽  
Quantum Fourier Transformation ◽  
Specific Quantum

Abstract Unitary operation is an essential step for quantum information processing. We first propose an iterative procedure for decomposing a general unitary operation without resorting to controlled-NOT gate and single-qubit rotation library. Based on the results of decomposition, we design two compact architectures to deterministically implement arbitrary two-qubit polarization-spatial and spatial-polarization collective unitary operations, respectively. The involved linear optical elements are reduced from 25 to 20 and 21 to 20, respectively. Moreover, the parameterized quantum computation can be flexibly manipulated by wave plates and phase shifters. As an application, we construct the specific quantum circuits to realize two-dimensional quantum walk and quantum Fourier transformation. Our schemes are simple and feasible with the current technology.

scholarly journals Universal bound on sampling bosons in linear optics and its computational implications

2019 ◽  
Vol 6 (4) ◽  
pp. 719-729 ◽  
Author(s):  
Man-Hong Yung ◽  
Xun Gao ◽  
Joonsuk Huh
Keyword(s):  
Optical Networks ◽  
Body Wave ◽  
Randomized Algorithm ◽  
Phase Shifters ◽  
Linear Optics ◽  
Optical Elements ◽  
Universal Bound ◽  
General Bound ◽  
Transition Amplitudes ◽  
The Many

ABSTRACT In linear optics, photons are scattered in a network through passive optical elements including beam splitters and phase shifters, leading to many intriguing applications in physics, such as Mach–Zehnder interferometry, the Hong–Ou–Mandel effect, and tests of fundamental quantum mechanics. Here we present the fundamental limit in the transition amplitudes of bosons, applicable to all physical linear optical networks. Apart from boson sampling, this transition bound results in many other interesting applications, including behaviors of Bose–Einstein condensates (BEC) in optical networks, counterparts of Hong–Ou–Mandel effects for multiple photons, and approximating permanents of matrices. In addition, this general bound implies the existence of a polynomial-time randomized algorithm for estimating the transition amplitudes of bosons, which represents a solution to an open problem raised by Aaronson and Hance (Quantum Inf Comput 2012; 14: 541–59). Consequently, this bound implies that computational decision problems encoded in linear optics, prepared and detected in the Fock basis, can be solved efficiently by classical computers within additive errors. Furthermore, our result also leads to a classical sampling algorithm that can be applied to calculate the many-body wave functions and the S-matrix of bosonic particles.

scholarly journals Towards optimization of quantum circuits

Open Physics ◽  
2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Michal Sedlák ◽  
Martin Plesch
Keyword(s):  
Quantum Information ◽  
Quantum Information Processing ◽  
Quantum Circuit ◽  
Quantum Gate ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Unitary Operation ◽  
Short Sequence ◽  
Toffoli Gates ◽  
Universal Procedure

AbstractAny unitary operation in quantum information processing can be implemented via a sequence of simpler steps — quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, searching for a short sequence of gates — efficient quantum circuit for a given operation, is an important task. We contribute to this issue by proposing optimization of the well-known universal procedure proposed by Barenco et al. [Phys. Rev. A 52, 3457 (1995)]. We also created a computer program which realizes both Barenco’s decomposition and the proposed optimization. Furthermore, our optimization can be applied to any quantum circuit containing generalized Toffoli gates, including basic quantum gate circuits.

Efficient linear optics quantum computation

2001 ◽  
Vol 1 (Special) ◽  
pp. 13-19
Author(s):  
G.J. Milburn ◽  
T. Ralph ◽  
A. White ◽  
E. Knill ◽  
R. Laflamme
Keyword(s):  
Quantum Computation ◽  
Single Photon ◽  
Quantum Algorithms ◽  
Optical Nonlinearities ◽  
Linear Optics ◽  
Optical Elements ◽  
Particle Detectors ◽  
Feed Forward ◽  
Single Electrons ◽  
Photon Source

Two qubit gates for photons are generally thought to require exotic materials with huge optical nonlinearities. We show here that, if we accept two qubit gates that only work conditionally, single photon sources, passive linear optics and particle detectors are sufficient for implementing reliable quantum algorithms. The conditional nature of the gates requires feed-forward from the detectors to the optical elements. Without feed forward, non-deterministic quantum computation is possible. We discuss one proposed single photon source based on the surface acoustic wave guiding of single electrons.

ERROR-REJECTING BENNETT–BRASSARD–MERMIN QUANTUM KEY DISTRIBUTION PROTOCOL BASED ON LINEAR OPTICS OVER A COLLECTIVE-NOISE CHANNEL

2010 ◽  
Vol 08 (07) ◽  
pp. 1141-1151 ◽  
Author(s):  
XI-HAN LI ◽  
XIAO-JIAO DUAN ◽  
FU-GUO DENG ◽  
HONG-YU ZHOU
Keyword(s):  
Quantum Entanglement ◽  
Quantum Key Distribution ◽  
Quantum Information Processing ◽  
Key Distribution ◽  
Entangled State ◽  
Collective Noise ◽  
Linear Optics ◽  
Entanglement Purification ◽  
Measurement Results ◽  
Entangled Quantum States

Quantum entanglement is an important element of quantum information processing. Sharing entangled quantum states between two remote parties is a precondition of most quantum communication schemes. We will show that the protocol proposed by Yamamoto et al. (Phys. Rev. Lett.95 (2005) 040503) for transmitting single quantum qubit against collective noise with linear optics is also suitable for distributing the components of entanglements with some modifications. An additional qubit is introduced to reduce the effect of collective noise, and the receiver can take advantage of the time discrimination and the measurement results of the assistant qubit to reconstruct a pure entanglement with the sender. Although the scheme succeeds probabilistically, the fidelity of the entangled state is almost unity in principle. The resource used in our protocol to get a pure entangled state is finite, which establishes entanglement more easily in practice than quantum entanglement purification. Also, we discuss its application in quantum key distribution over a collective channel in detail.

scholarly journals A limit theorem for a splitting distribution of a quantum walk

2018 ◽  
Vol 16 (03) ◽  
pp. 1850023
Author(s):  
Takuya Machida
Keyword(s):  
Limit Theorem ◽  
Probability Distribution ◽  
Random Walks ◽  
Discrete Time ◽  
Limit Distribution ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Unitary Evolution ◽  
Time Quantum ◽  
Long Time

Discrete-time quantum walks are considered a counterpart of random walks and their study has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to two parts. The quantum walker with two coin states spreads at points, represented by integers, and we analyze the chance of finding the walker at each position after it carries out a unitary evolution a lot of times. The result is reported as a long-time limit distribution from which one can see an approximation to the finding probability.

scholarly journals Human-Competitive Evolution of Quantum Computing Artefacts by Genetic Programming

2006 ◽  
Vol 14 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Paul Massey ◽  
John A. Clark ◽  
Susan Stepney
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Genetic Programming ◽  
Quantum Algorithms ◽  
Quantum Circuits ◽  
Quantum Fourier Transform ◽  
Competitive Evolution ◽  
Specific Quantum

We show how Genetic Programming (GP) can be used to evolve useful quantum computing artefacts of increasing sophistication and usefulness: firstly specific quantum circuits, then quantum programs, and finally system-independent quantum algorithms. We conclude the paper by presenting a human-competitive Quantum Fourier Transform (QFT) algorithm evolved by GP.

scholarly journals DECOHERENCE-FREE QUANTUM MEMORY FOR PHOTONIC STATE USING ATOMIC ENSEMBLES

2009 ◽  
Vol 07 (04) ◽  
pp. 811-820 ◽  
Author(s):  
FENG MEI ◽  
YA-FEI YU ◽  
ZHI-MING ZHANG
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Large Scale ◽  
Quantum Information Processing ◽  
Single Photon ◽  
Quantum Memory ◽  
Single Photon Detection ◽  
Atomic Ensembles ◽  
Optical Elements ◽  
Photonic State

Large scale quantum information processing requires stable and long-lived quantum memories. Here, using atom-photon entanglement, we propose an experimentally feasible scheme to realize decoherence-free quantum memory with atomic ensembles, and show one of its applications, remote transfer of unknown quantum state, based on laser manipulation of atomic ensembles, photonic state operation through optical elements, and single-photon detection with moderate efficiency. The scheme, with inherent fault-tolerance to the practical noise and imperfections, allows one to retrieve the information in the memory for further quantum information processing within the reach of current technology.

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