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Continuous Time Open Quantum Random Walks and Non-Markovian Lindblad Master Equations

Clément Pellegrini

Journal of Statistical PhysicsJan 13, 201441 citations

On the equivalence between quantum and random walks on finite graphs

Matheus Guedes de Andrade, Franklin de Lima Marquezino, Daniel R. Figueiredo

arXiv:1912.06256Quantum Information ProcessingNov 1, 20207 citations

Quantum State Transfer and Periodicity in Discrete‐Time Quantum Walks Under Non‐Markovian Dephasing Noise

Monika Rani, Supriyo Dutta, Subhashish Banerjee

ABSTRACT In quantum communication, quantum state transfer from one location to another in a quantum network plays a prominent role, where the impact of noise could be crucial. The idea of state transfer can be fruitfully associated with quantum walk on graphs. We investigate the consequences of non‐Markovian quantum noises on periodicity and state transfer induced by a discrete‐time quantum walk on graphs, governed by the Grover coin operator. Different bipartite graphs, such as the path graph, cycle graph, star graph, and complete bipartite graph, present periodicity and state transfer in a discrete‐time quantum walk depending on the topology of the graph. We investigate the effect of quantum non‐Markovian dephasing noises, particularly quantum non‐Markovian Random Telegraph Noise (RTN) and modified non‐Markovian Ornstein‐Uhlenbeck Noise (OUN) on state transfer and periodicity. We demonstrate how the RTN and OUN noises allow state transfer and periodicity for a finite number of steps in a quantum walk. Our investigation brings out the feasibility of state transfer in a noisy environment.ABSTRACT In quantum communication, quantum state transfer from one location to another in a quantum network plays a prominent role, where the impact of noise could be crucial. The idea of state transfer can be fruitfully associated with quantum walk on graphs. We investigate the consequences of non‐Markovian quantum noises on periodicity and state transfer induced by a discrete‐time quantum walk on graphs, governed by the Grover coin operator. Different bipartite graphs, such as the path graph, cycle graph, star graph, and complete bipartite graph, present periodicity and state transfer in a discrete‐time quantum walk depending on the topology of the graph. We investigate the effect of quantum non‐Markovian dephasing noises, particularly quantum non‐Markovian Random Telegraph Noise (RTN) and modified non‐Markovian Ornstein‐Uhlenbeck Noise (OUN) on state transfer and periodicity. We demonstrate how the RTN and OUN noises allow state transfer and periodicity for a finite number of steps in a quantum walk. Our investigation brings out the feasibility of state transfer in a noisy environment.

arXiv:2506.24066Annalen der PhysikNov 21, 20250 citations

Quantum Markov Chains Associated with Open Quantum Random Walks

Ameur Dhahri, Chul Ki Ko, Hyun Jae Yoo

arXiv:1808.03479Journal of Statistical PhysicsJun 21, 201923 citations

Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks

Kenneth Rudinger, John King Gamble, Eric Bach +3 more

Berry and Wang [Phys. Rev. A {\bf 83}, 042317 (2011)] show numerically that a discrete-time quantum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting particles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle differences in the graph certificate construction algorithm can nontrivially impact the walk's distinguishing power. We also show that no continuous-time walk of a fixed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certificates we consider. We extend this constraint to discrete-time walks of fixed numbers of noninteracting particles for one kind of graph certificate; it remains an open question as to whether or not this constraint applies to the other graph certificates we consider.Berry and Wang [Phys. Rev. A {\bf 83}, 042317 (2011)] show numerically that a discrete-time quantum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting particles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle differences in the graph certificate construction algorithm can nontrivially impact the walk's distinguishing power. We also show that no continuous-time walk of a fixed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certificates we consider. We extend this constraint to discrete-time walks of fixed numbers of noninteracting particles for one kind of graph certificate; it remains an open question as to whether or not this constraint applies to the other graph certificates we consider.

arXiv:1207.4535Journal of Computational and Theoretical NanoscienceJun 20, 201319 citations

A novel graph clustering algorithm based on discrete-time quantum random walk

Swarnali Roy, Amlan Chakrabarti

Elsevier eBooksOct 7, 201618 citations

Non-Markovianity in discrete-time open quantum random walk on arbitrary graphs

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