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.

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.

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.

GENERATION OF GRAPH-STATE ENTANGLEMENT WITH ATOMIC ENSEMBLES VIA THE DIPOLE BLOCKADE MECHANISM

2011 ◽  
Vol 09 (01) ◽  
pp. 547-554
Author(s):  
HONG XIE ◽  
MEI-XIANG CHEN
Keyword(s):  
Dipole Interaction ◽  
Entangled State ◽  
Linear Optics ◽  
Atomic Ensembles ◽  
Graph State ◽  
Single Spin ◽  
Generating Graph ◽  
Spin Excitations ◽  
Dipole Blockade ◽  
The Many

A scheme is proposed for generating graph-state entanglement between many atomic ensembles. In this scheme, the photons are transferred from the single-"spin" excitations of the atomic ensembles via the dipole blockade mechanism, which act as ancillary qubits and interfere with each other on linear optics apparatus. The quantum-entangled state of the atomic ensembles can be obtained under the conditional detection of the photons. Since the single-"spin" excitations can be deterministically created via strong long-range dipole–dipole interaction and the transferred efficiency is enhanced by the many-atom interference effects, our scheme can work with a high probability of success.

scholarly journals Many-body topological invariants from randomized measurements in synthetic quantum matter

2020 ◽  
Vol 6 (15) ◽  
pp. eaaz3666 ◽  
Author(s):  
Andreas Elben ◽  
Jinlong Yu ◽  
Guanyu Zhu ◽  
Mohammad Hafezi ◽  
Frank Pollmann ◽  
...  
Keyword(s):  
Body Wave ◽  
Complete Classification ◽  
Theoretical Description ◽  
Spin Model ◽  
Topological Invariants ◽  
Topological Phases ◽  
Many Body ◽  
Topological Quantum ◽  
The Many ◽  
Symmetry Protected

Many-body topological invariants, as quantized highly nonlocal correlators of the many-body wave function, are at the heart of the theoretical description of many-body topological quantum phases, including symmetry-protected and symmetry-enriched topological phases. Here, we propose and analyze a universal toolbox of measurement protocols to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits. The protocol is based on extracting the many-body topological invariants from statistical correlations of randomized measurements, implemented with local random unitary operations followed by site-resolved projective measurements. We illustrate the technique and its application in the context of the complete classification of bosonic symmetry-protected topological phases in one dimension, considering in particular the extended Su-Schrieffer-Heeger spin model, as realized with Rydberg tweezer arrays.

IMPLEMENTATION OF SWAP GATE AND FREDKIN GATE USING LINEAR OPTICAL ELEMENTS

2013 ◽  
Vol 11 (03) ◽  
pp. 1350031 ◽  
Author(s):  
MENG-ZHENG ZHU ◽  
LIU YE
Keyword(s):  
Photon Number ◽  
Success Probability ◽  
Distinct Advantage ◽  
Single Photons ◽  
Linear Optics ◽  
Optical Elements ◽  
Present Scheme ◽  
Fredkin Gate ◽  
Swap Gate ◽  
Linear Optical Elements

A scheme is proposed to directly implement the optical swap gate and quantum Fredkin gate based on the Mach–Zehnder interferometer (MZI). The distinct advantage of the present scheme is that ancilla single-photons are not needed. The optical swap gate is deterministic and does not need the photon number resolving detectors. The total success probability of the present Fredkin gate can reach 1/16 by using basic linear-optics elements.

Wave equation for dissipative systems derived from a quantized many-body problem

1980 ◽  
Vol 58 (7) ◽  
pp. 1019-1025 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Body Problem ◽  
Body Wave ◽  
Time Dependent ◽  
Dissipative Systems ◽  
Many Body ◽  
Dependent Part ◽  
The Many

A classical many-body problem composed of an infinite number of mass points coupled together by springs is quantized. The masses and the spring constants in this system are chosen in such a way that the motion of each particle is exponentially damped. Because of the quadratic form of the Hamiltonian, the many-body wave function of the system can be written as a product of two terms: a time-dependent phase factor which contains correlations between the classical motions of the particles, and a stationary state solution of the Schrödinger equation. By assuming a Hartree type wave function for the many-particle Schrödinger equation, the contribution of the time-dependent part to the single particle wave function is determined, and it is shown that the time-dependent wave function of each mass point satisfies the nonlinear Schrödinger–Langevin equation. The characteristic decay time of any part of the subsystem, in this model, is related to the stiffness of the springs, and is the same for all particles.

scholarly journals Approximating Ground States by Neural Network Quantum States

2018 ◽  
Author(s):  
Ying Yang ◽  
Chengyang Zhang ◽  
Huaixin Cao
Keyword(s):  
Neural Network ◽  
Relative Error ◽  
Ground State ◽  
Quantum Physics ◽  
Body Problem ◽  
Body Wave ◽  
Quantum States ◽  
Many Body ◽  
The Many ◽  
Exponential Complexity

The many-body problem in quantum physics originates from the difficulty of describing the non-trivial correlations encoded in the exponential complexity of the many-body wave function. Motivated by the Giuseppe Carleo's work titled solving the quantum many-body problem with artificial neural networks [Science, 2017, 355: 602], we focus on finding the NNQS approximation of the unknown ground state of a given Hamiltonian $H$ in terms of the best relative error and explore the influences of sum, tensor product, local unitary of Hamiltonians on the best relative error. Besides, we illustrate our method with some examples.

scholarly journals Analysis of circuit imperfections in BosonSampling

2015 ◽  
pp. 489-512
Author(s):  
Anthony Leverrier ◽  
Raul Garcia-Patron
Keyword(s):  
Fault Tolerance ◽  
Quantum Computer ◽  
State Of The Art ◽  
Optical Element ◽  
Single Photons ◽  
Linear Optics ◽  
Tolerance Mechanism ◽  
Optical Elements ◽  
Full Quantum

BosonSampling is a problem where a quantum computer offers a provable speedup over classical computers. Its main feature is that it can be solved with current linear optics technology, without the need for a full quantum computer. In this work, we investigate whether an experimentally realistic BosonSampler can really solve BosonSampling without any fault-tolerance mechanism. More precisely, we study how the unavoidable errors linked to an imperfect calibration of the optical elements affect the final result of the computation. We show that the fidelity of each optical element must be at least 1 − O(1/n^2 ), where n refers to the number of single photons in the scheme. Such a requirement seems to be achievable with state-of-the-art equipment.

scholarly journals Resonant and Sensing Performance of Volume Waveguide Structures Based on Polymer Nanomaterials

Nanomaterials ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 2114
Author(s):  
Tatiana Smirnova ◽  
Volodymyr Fitio ◽  
Oksana Sakhno ◽  
Pavel Yezhov ◽  
Andrii Bendziak ◽  
...  
Keyword(s):  
Near Field ◽  
Linear Optics ◽  
Optical Elements ◽  
Resonant Structures ◽  
Analysis And Design ◽  
Non Linear Optics ◽  
Corrugated Surfaces ◽  
Proposed Model ◽  
New Strategy ◽  
Waveguide Gratings

Organic–inorganic photocurable nanocomposite materials are a topic of intensive research nowadays. The wide variety of materials and flexibility of their characteristics provide more freedom to design optical elements for light and neutron optics and holographic sensors. We propose a new strategy of nanocomposite application for fabricating resonant waveguide structures (RWS), whose working principle is based on optical waveguide resonance. Due to their resonant properties, RWS can be used as active tunable filters, refractive index (RI) sensors, near-field enhancers for spectroscopy, non-linear optics, etc. Our original photocurable organic–inorganic nanocomposite was used as a material for RWS. Unlike known waveguide structures with corrugated surfaces, we investigated the waveguide gratings with the volume modulation of the RI fabricated by a holographic method that enables large-size structures with high homogeneity. In order to produce thin photosensitive waveguide layers for their subsequent holographic structuring, a special compression method was developed. The resonant and sensing properties of new resonant structures were experimentally examined. The volume waveguide gratings demonstrate narrow resonant peaks with a bandwidth less than 0.012 nm. The Q-factor exceeds 50,000. The sensor based on waveguide volume grating provides detection of a minimal RI change of 1 × 10−4 RIU. Here we also present the new theoretical model that is used for analysis and design of developed RWS. Based on the proposed model, fairly simple analytical relationships between the parameters characterizing the sensor were obtained.

scholarly journals How many qubits are needed for quantum computational supremacy?

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 264 ◽  
Author(s):  
Alexander M. Dalzell ◽  
Aram W. Harrow ◽  
Dax Enshan Koh ◽  
Rolando L. La Placa
Keyword(s):  
Optical Networks ◽  
Quantum Computer ◽  
Circuit Simulation ◽  
Quantum Circuit ◽  
Deterministic Algorithm ◽  
Quantum Circuits ◽  
Polynomial Hierarchy ◽  
Optical Elements ◽  
Average Case ◽  
Classical Simulation

Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of classical computation. One common assumption is that the polynomial hierarchy (PH) does not collapse, a stronger version of the statement that P≠NP, which leads to the conclusion that any classical simulation of certain families of quantum circuits requires time scaling worse than any polynomial in the size of the circuits. However, the asymptotic nature of this conclusion prevents us from calculating exactly how many qubits these quantum circuits must have for their classical simulation to be intractable on modern classical supercomputers. We refine these quantum computational supremacy arguments and perform such a calculation by imposing fine-grained versions of the non-collapse conjecture. Our first two conjectures poly3-NSETH(a) and per-int-NSETH(b) take specific classical counting problems related to the number of zeros of a degree-3 polynomial in n variables over F2 or the permanent of an n×n integer-valued matrix, and assert that any non-deterministic algorithm that solves them requires 2cn time steps, where c∈{a,b}. A third conjecture poly3-ave-SBSETH(a′) asserts a similar statement about average-case algorithms living in the exponential-time version of the complexity class SBP. We analyze evidence for these conjectures and argue that they are plausible when a=1/2, b=0.999 and a′=1/2.Imposing poly3-NSETH(1/2) and per-int-NSETH(0.999), and assuming that the runtime of a hypothetical quantum circuit simulation algorithm would scale linearly with the number of gates/constraints/optical elements, we conclude that Instantaneous Quantum Polynomial-Time (IQP) circuits with 208 qubits and 500 gates, Quantum Approximate Optimization Algorithm (QAOA) circuits with 420 qubits and 500 constraints and boson sampling circuits (i.e. linear optical networks) with 98 photons and 500 optical elements are large enough for the task of producing samples from their output distributions up to constant multiplicative error to be intractable on current technology. Imposing poly3-ave-SBSETH(1/2), we additionally rule out simulations with constant additive error for IQP and QAOA circuits of the same size. Without the assumption of linearly increasing simulation time, we can make analogous statements for circuits with slightly fewer qubits but requiring 104 to 107 gates.

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