Quantum logic using correlated one-dimensional quantum walks

Abstract

Quantum Walks are unitary processes describing the evolution of an initially localized wavefunction on a lattice potential. The complexity of the dynamics increases significantly when several indistinguishable quantum walkers propagate on the same lattice simultaneously, as these develop non-trivial spatial correlations that depend on the particle's quantum statistics, mutual interactions, initial positions, and the lattice potential. We show that even in the simplest case of a quantum walk on a one dimensional graph, these correlations can be shaped to yield a complete set of compact quantum logic operations. We provide detailed recipes for implementing quantum logic on one-dimensional quantum walks in two general cases. For non-interacting bosons-such as photons in waveguide lattices-we find high-fidelity probabilistic quantum gates that could be integrated into linear optics quantum computation schemes. For interacting quantum-walkers on a one-dimensional lattice-a situation that has recently been demonstrated using ultra-cold atoms-we find deterministic logic operations that are universal for quantum information processing. The suggested implementation requires minimal resources and a level of control that is within reach using recently demonstrated techniques. Further work is required to address error-correction.npj Quantum Information (2018) 4:2 ;

Transport Efficiency of Continuous-Time Quantum Walks on Graphs

“…Experimentally [ 3 ], CTQWs can be implemented on nuclear-magnetic-resonance quantum computers [ 4 ], optical lattices of ultracold Rydberg atoms [ 5 ], quantum processors [ 6 ], and photonic chips [ 7 ]. The applications of CTQWs range from implementing fast and efficient quantum algorithms [ 8 , 9 ], e.g., for spatial search [ 10 ] and image segmentation [ 11 ], to implementing quantum logic gates by multi-particle CTQWs in one-dimension (1D) [ 12 ], from universal computation [ 13 ] to modeling and simulating quantum phenomena, e.g., state transfer [ 14 , 15 , 16 ], quantum transport, and for characterizing the behavior of many-body systems [ 17 , 18 ].…”

Quantum Walks in Periodic and Quasiperiodic Fibonacci Fibers

“…That is a huge advantage of photonics as compared to other technologies used in quantum applications such as ion-trapped, superconducting operating at extremely low temperatures, often at tens of millikelvin (mK). In light of that direction, quantum simulations with light [15] and photonics quantum gates [16] have been proposed and developed recently. Beam splitter arrays have been used to perform discrete-time QWs (DTQW) [17,18], and evanescently coupled parallel arrays of waveguides have been proven to be excellent platform to perform continuous-time QWs (CTQW) [1][2][3][4][5].…”

A Rout to Protect Quantum Gates constructed via quantum walks from Noises

“…Here we used a single-particle quantum walk to construct quantum gates, which is different from the cases of refs 22 , 24 where multiparticles were introduced in those systems. We considered a continuous-time quantum walk on a finite graph and utilized the qusi-momentum eigenstates of the quantum-walk system in the process of constructing the quantum gates.…”

“…As we aware, there are several works that studied the universal quantum computation with the help of quantum walks. For example, In refs 2 , 3 , 20 – 24 , the authors presented suggestions to realize different quantum operations based on the continuous-time quantum walk model. Whereas, in ref.…”