Quantum walks with memory - goldfish, elephants and wise old men

  title={Quantum walks with memory - goldfish, elephants and wise old men},
  author={P. Rohde and Gavin K. Brennen and Alexei Gilchrist},
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with memory by endowing the walker with multiple recycled coins and using a physical memory function via a history dependent coin flip. By numerical simulation we observe several phenomena. First in one dimension, walkers with memory have persistent quantum ballistic… 
10 Citations
Quantum walks with tuneable self-avoidance in one dimension
A quantum walk in one dimension with tunable levels of self-avoidance is complemented with a memory register that records where the walker has previously resided and can be made to reproduce ideal quantum or classical random walk statistics, or a plethora of more elaborate diffusive phenomena.
Self-avoiding quantum walks
Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical
One-dimensional quantum walks with two-step memory
A general formula for the amplitudes of the two-step-memory walk with Hadamard coin is developed by using path integral approach, and the simulation shows that the probability distribution of this new walk is different from that of the hadamard quantum walk with one-step memory.
Szegedy quantum walks with memory on regular graphs
This paper presents general model of Szegedy QWM, a type of modified quantum walks that record the walker's latest path and reveals the relation of coined QWM and Szegdy QWM.
Quantum Walks with Memory Provided by Parity of Memory
This paper presents QWM-P, a kind of QWM whose evolution depends on the parity of memory, which has an identity coin shift function which helps in analyzing and designing algorithms.
Quantum walk under coherence non-generating channels* * Project supported by the National Natural Science Foundation of China (Grant No. 11774205) and the Young Scholars Program of Shandong University.
We investigate the probability distribution of the quantum walk under coherence non-generating channels. We define a model called generalized classical walk with memory. Under certain conditions,
Discrete-Time Quantum Walk with Memory on the Cayley Graph of the Dihedral Group
By adding one-step memory to enrich the model of discrete-time quantum walk on the Caylay graph of the dihedral group, the model of quantum walk with memory on the Cayley graph of the dihedral group
Quantum key distribution with quantum walks
This paper introduces a secure quantum key distribution protocol equipped with verification procedures against full man-in-the-middle attacks, and presents a one-way protocol and proves its security.
Negative correlations can play a positive role in disordered quantum walks
The results show that negatively correlated disorder plays a more important role in quantum entanglement than it has been assumed in the literature.
Quantum control using quantum memory
A new quantum numerical scheme to control the dynamics of a quantum walker in a two dimensional space–time grid is proposed, and analytically how to encode in the initial state any arbitrary walker’s mean trajectory and variance is proved.