scholarly journals Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor

2021 ◽  
Vol 7 (9) ◽  
pp. eabb8375
Author(s):  
Xiaogang Qiang ◽  
Yizhi Wang ◽  
Shichuan Xue ◽  
Renyou Ge ◽  
Lifeng Chen ◽  
...  
Keyword(s):  
Large Scale ◽  
Quantum Algorithms ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Graph Theoretic ◽  
Two Photon ◽  
Full Control ◽  
Silicon Photonic ◽  
Vertex Graph ◽  
Particle Exchange

Applications of quantum walks can depend on the number, exchange symmetry and indistinguishability of the particles involved, and the underlying graph structures where they move. Here, we show that silicon photonics, by exploiting an entanglement-driven scheme, can realize quantum walks with full control over all these properties in one device. The device we realize implements entangled two-photon quantum walks on any five-vertex graph, with continuously tunable particle exchange symmetry and indistinguishability. We show how this simulates single-particle walks on larger graphs, with size and geometry controlled by tuning the properties of the composite quantum walkers. We apply the device to quantum walk algorithms for searching vertices in graphs and testing for graph isomorphisms. In doing so, we implement up to 100 sampled time steps of quantum walk evolution on each of 292 different graphs. This opens the way to large-scale, programmable quantum walk processors for classically intractable applications.

scholarly journals The role of coherence on two-particle quantum walks

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Li-Hua Lu ◽  
Shan Zhu ◽  
You-Quan Li
Keyword(s):  
Correlation Function ◽  
Average Distance ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Mixed States ◽  
Initial State ◽  
Photon Correlation ◽  
Two Photon ◽  
Degree Of Coherence

AbstractWe investigate the dynamical properties of the two-boson quantum walk in systems with different degrees of coherence, and where the effect of the coherence on the two-boson quantum walk can be naturally introduced. A general analytical expression for the two-boson correlation function, for both pure states and mixed states, is given.We propose a possible two-photon quantum-walk scheme with a mixed initial state, and find that the twophoton correlation function and the average distance between two photons can be influenced by the initial photon distribution, the relative phase, or the degree of coherence. The propagation features of our numerical results can be explained by our analytical two-photon correlation function.

scholarly journals Floquet-engineered quantum walks

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Haruna Katayama ◽  
Noriyuki Hatakenaka ◽  
Toshiyuki Fujii
Keyword(s):  
Quantum Computation ◽  
Computational Models ◽  
Quantum Algorithms ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Research Areas ◽  
Wide Range ◽  
Mechanical Analogue ◽  
Universal Quantum ◽  
Walking Mechanism

Abstract The quantum walk is the quantum-mechanical analogue of the classical random walk, which offers an advanced tool for both simulating highly complex quantum systems and building quantum algorithms in a wide range of research areas. One prominent application is in computational models capable of performing any quantum computation, in which precisely controlled state transfer is required. It is, however, generally difficult to control the behavior of quantum walks due to stochastic processes. Here we unveil the walking mechanism based on its particle-wave duality and then present tailoring quantum walks using the walking mechanism (Floquet oscillations) under designed time-dependent coins, to manipulate the desired state on demand, as in universal quantum computation primitives. Our results open the path towards control of quantum walks.

scholarly journals Quantum fast-forwarding: Markov chains and graph property testing

2019 ◽  
Vol 19 (3&4) ◽  
pp. 181-213 ◽  
Author(s):  
Simon Apers ◽  
Alain Scarlet
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Quantum State ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Walk ◽  
Transient Behavior ◽  
Quantum Walks ◽  
Learning Context

We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with P the Markov chain transition matrix and D = \sqrt{P\circ P^T} its discriminant matrix (D=P if P is symmetric), we construct a quantum walk algorithm that for any quantum state |v> and integer t returns a quantum state \epsilon-close to the state D^t|v>/\|D^t|v>. The algorithm uses O(|D^t|v>|^{-1}\sqrt{t\log(\epsilon\|D^t|v>})^{-1}}) expected quantum walk steps and O(\|D^t|v>|^{-1}) expected reflections around |v>. This shows that quantum walks can accelerate the transient dynamics of Markov chains, complementing the line of results that proves the acceleration of their limit behavior. We show that this tool leads to speedups on random walk algorithms in a very natural way. Specifically we consider random walk algorithms for testing the graph expansion and clusterability, and show that we can quadratically improve the dependency of the classical property testers on the random walk runtime. Moreover, our quantum algorithm exponentially improves the space complexity of the classical tester to logarithmic. As a subroutine of independent interest, we use QFF for determining whether a given pair of nodes lies in the same cluster or in separate clusters. This solves a robust version of s-t connectivity, relevant in a learning context for classifying objects among a set of examples. The different algorithms crucially rely on the quantum speedup of the transient behavior of random walks.

scholarly journals Spatial search on grids with minimum memory

2015 ◽  
Vol 15 (13&14) ◽  
pp. 1233-1247
Author(s):  
Andris Ambainis ◽  
Renato Portugal ◽  
Nikolay Nahimov
Keyword(s):  
Numerical Simulations ◽  
Quantum Algorithms ◽  
Success Probability ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Optimal Number ◽  
Rigorous Analysis ◽  
Spatial Search ◽  
Finite Dimensional

We study quantum algorithms for spatial search on finite dimensional grids. Patel \textit{et al.}~and Falk have proposed algorithms based on a quantum walk without a coin, with different operators applied at even and odd steps. Until now, such algorithms have been studied only using numerical simulations. In this paper, we present the first rigorous analysis for an algorithm of this type, showing that the optimal number of steps is $O(\sqrt{N\log N})$ and the success probability is $O(1/\log N)$, where $N$ is the number of vertices. This matches the performance achieved by algorithms that use other forms of quantum walks.

scholarly journals QUANTUM HITTING TIME ON THE COMPLETE GRAPH

2010 ◽  
Vol 08 (05) ◽  
pp. 881-894 ◽  
Author(s):  
RAQUELINE AZEVEDO MEDEIROS SANTOS ◽  
RENATO PORTUGAL
Keyword(s):  
Markov Chain ◽  
Complete Graph ◽  
Quantum Algorithms ◽  
Success Probability ◽  
Natural Extension ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Hitting Time ◽  
Quantum Markov Chain ◽  
Definition Of

Quantum walks play an important role in the area of quantum algorithms. Many interesting problems can be reduced to searching marked states in a quantum Markov chain. In this context, the notion of quantum hitting time is very important, because it quantifies the running time of the algorithms. Markov chain-based algorithms are probabilistic, therefore the calculation of the success probability is also required in the analysis of the computational complexity. Using Szegedy's definition of quantum hitting time, which is a natural extension of the definition of the classical hitting time, we present analytical expressions for the hitting time and success probability of the quantum walk on the complete graph.

scholarly journals Scaling capacity of fiber-optic transmission systems via silicon photonics

Nanophotonics ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Shi ◽  
Ye Tian ◽  
Antoine Gervais
Keyword(s):  
Silicon Photonics ◽  
Communication Systems ◽  
Large Scale ◽  
Recent Progress ◽  
Fiber Optic ◽  
Rapid Evolution ◽  
System Capacity ◽  
Disruptive Technology ◽  
System Perspective ◽  
Silicon Photonic

AbstractThe tremendous growth of data traffic has spurred a rapid evolution of optical communications for a higher data transmission capacity. Next-generation fiber-optic communication systems will require dramatically increased complexity that cannot be obtained using discrete components. In this context, silicon photonics is quickly maturing. Capable of manipulating electrons and photons on the same platform, this disruptive technology promises to cram more complexity on a single chip, leading to orders-of-magnitude reduction of integrated photonic systems in size, energy, and cost. This paper provides a system perspective and reviews recent progress in silicon photonics probing all dimensions of light to scale the capacity of fiber-optic networks toward terabits-per-second per optical interface and petabits-per-second per transmission link. Firstly, we overview fundamentals and the evolving trends of silicon photonic fabrication process. Then, we focus on recent progress in silicon coherent optical transceivers. Further scaling the system capacity requires multiplexing techniques in all the dimensions of light: wavelength, polarization, and space, for which we have seen impressive demonstrations of on-chip functionalities such as polarization diversity circuits and wavelength- and space-division multiplexers. Despite these advances, large-scale silicon photonic integrated circuits incorporating a variety of active and passive functionalities still face considerable challenges, many of which will eventually be addressed as the technology continues evolving with the entire ecosystem at a fast pace.

Optical Single-Event Transients Induced in Integrated Silicon-Photonic Waveguides by Two-Photon Absorption

2021 ◽  
pp. 1-1
Author(s):  
George N. Tzintzarov ◽  
Adrian Ildefonso ◽  
Jeffrey W. Teng ◽  
Milad Frounchi ◽  
Albert Djikeng ◽  
...  
Keyword(s):  
Photon Absorption ◽  
Single Event ◽  
Two Photon Absorption ◽  
Two Photon ◽  
Single Event Transients ◽  
Silicon Photonic ◽  
Photonic Waveguides

Global Optimization With Quantum Walk Enhanced Grover Search

2014 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Early Stage ◽  
Hybrid Approach ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Tunneling Effect ◽  
Grover’S Algorithm ◽  
Grover's Algorithm ◽  
Grover Search

One of the significant breakthroughs in quantum computation is Grover’s algorithm for unsorted database search. Recently, the applications of Grover’s algorithm to solve global optimization problems have been demonstrated, where unknown optimum solutions are found by iteratively improving the threshold value for the selective phase shift operator in Grover rotation. In this paper, a hybrid approach that combines continuous-time quantum walks with Grover search is proposed. By taking advantage of quantum tunneling effect, local barriers are overcome and better threshold values can be found at the early stage of search process. The new algorithm based on the formalism is demonstrated with benchmark examples of global optimization. The results between the new algorithm and the Grover search method are also compared.

Higher-dimensional open quantum walk in environment of quantum Bernoulli noises

2021 ◽  
pp. 2250001
Author(s):  
Ce Wang
Keyword(s):  
Quantum Walk ◽  
Quantum Walks ◽  
Initial State ◽  
Quantum Random Walks ◽  
Open Quantum ◽  
Higher Dimensional ◽  
Gauss Type ◽  
Open Quantum Random Walks ◽  
Limit Probability ◽  
Creation Operators

Open quantum walks (OQWs) (also known as open quantum random walks) are quantum analogs of classical Markov chains in probability theory, and have potential application in quantum information and quantum computation. Quantum Bernoulli noises (QBNs) are annihilation and creation operators acting on Bernoulli functionals, and can be used as the environment of an open quantum system. In this paper, by using QBNs as the environment, we introduce an OQW on a general higher-dimensional integer lattice. We obtain a quantum channel representation of the walk, which shows that the walk is indeed an OQW. We prove that all the states of the walk are separable provided its initial state is separable. We also prove that, for some initial states, the walk has a limit probability distribution of higher-dimensional Gauss type. Finally, we show links between the walk and a unitary quantum walk recently introduced in terms of QBNs.

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