The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution Pt(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, sigma(t) scales as sigma(t) ~ t, unlike the classical random walk for which sigma(t) ~ sqrt{t}. It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be T ~ alpha^(-2) where alpha is the standard deviation of the noise.
Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0> in space without interference, instead of two coin states |1>, |0> .For the case of no boundary conditions, the model is similar to a Markov chain with a stochastic matrix, i.e., it conserves the population distribution of the four coin states, and by using a proper transformation, yield probability distributions of the two quantum states |1>, |0> in space,…
In this work we explain the necessity for consistently labeled rotation maps for efficiently computing coined discrete time quantum walks on regular graphs.
This study investigates the unitary equivalence of split-step quantum walks (SSQW). We consider a new class of quantum walks which includes all SSQWs. We show the explicit form of quantum walks in this class, and clarify their unitary equivalence classes. Unitary equivalence classes of Suzuki's SSQW are also given.
In this paper, we work on a quantum walk whose system is manipulated by a five-diagonal unitary matrix, and present long-time limit distributions. The quantum walk launches off a location and delocalizes in distribution as its system is getting updated. The five-diagonal matrix contains a phase term and the quantum walk becomes a standard coined walk when the phase term is fixed at special values. Or, the phase term gives an effect on the quantum walk. As a result, we will see an explicit form of a long-time limit distribution for a quantum walk driven by the matrix, and thanks to the exact fo…
Diverse tunable dynamics of two quantum random walkers
量子漫步的研究主要集中在由于重复应用时间无关的酉硬币算子而引起的演化。然而，使用依赖于时间的幺正硬币控制单粒子演化的想法仍然是多个研究的主题，因为它不仅为量子信息处理提供了有趣的可能性，而且还开启了一系列更丰富的现象，包括静态和动态局域化。到目前为止，这种研究只针对单个量子步行者进行。在多步行者系统的情况下，由于步行者之间的纠缠和相互作用，时间相关的硬币可能会产生单粒子模型无法描述的可测量现象。在这种情况下，我们在这里提出了一个全面的数值研究的一维系统的两个量子步行者表现出丰富的集体动力学控制的简单的时间相关的酉硬币中提出的[Phys. Rev. A \textbf{80}，042332（2009）]和[Phys. Rev. A \textbf{73}，062304（2006）]。我们研究了硬币的时间依赖性，简单的相互作用方案，纠缠和粒子的硬币状态之间的相对相位的相互作用如何影响量子行走的演化。结果表明，该系统提供了丰富多样的集体动力学行为，同时控制的时间依赖硬币。特别是，我们发现和表征迷人的两体局域化现象与可调准周期动力学的相关性和纠缠量的量子起源。
We calculate the hybrid entanglement entropy between coin and walker degrees of freedom in a non-unitary quantum walk. The model possesses a joint parity and time-reversal symmetry or PT-symmetry and supports topological phases when this symmetry is unbroken by its eigenstates. An asymptotic analysis at long times reveals that the quantum walk can indefinitely sustain hybrid entanglement in the unbroken symmetry phase even when gain and loss mechanisms are present. However, when the gain-loss strength is too large, the PT-symmetry of the model is spontaneously broken and entanglement vanishes.…
We investigate the dynamics of discrete-time quantum walk subject to time correlated noise. Noise is described as an unitary coin-type operator before each step, and attention is focused on the noise generated by a Gaussian Ornstein Uhlenbeck process, going beyond the usual telegraph noise, where the random variables are consist of only -1 and 1. Under the first-order approximation of BCH formula, the master equation of noisy discrete-time quantum walk is derived. The dynamics given by the master equation are in good agreement with those given by numerical simulations within a certain period o…
We study the effects of quantum noise in hybrid quantum-classical solver for sparse systems of linear equations using quantum random walks, applied to stoquastic Hamiltonian matrices. In an ideal noiseless quantum computer, sparse matrices achieve solution vectors with lower relative error than dense matrices. However, we find quantum noise reverses this effect, with overall error increasing as sparsity increases. We identify invalid quantum random walks as the cause of this increased error and propose a revised linear solver algorithm which improves accuracy by mitigating these invalid walks.
This study investigate the unitary equivalence classes of quantum walks on cycles. We show that unitary equivalence classes of quantum walks on a cycle with $N$ vertices are parameterized by $2N$ real parameters. Moreover, the ranges of two of the parameters are restricted, and the ranges depend on the parity of $N$.
We investigate robustness of probabilistic storage and retrieval device optimized for phase gates to noise. We use noisy input composed of convex combination of unitary channel with either depolarizing or dephasing channel. We find out that the resistance to dephasing noise is higher than to depolarization. Interestingly, for the depolarisation the retrieval reduces the degree of noise. We also examine the possible realizations showing that their performance is different when the noise is present.
