Quantum walk on the Bloch sphere
arXiv:2201.11386 · doi:10.1103/PhysRevA.105.042215
Abstract
A scheme for implementing the discrete-time quantum walk on the Bloch sphere is proposed, which is closely related to the SU(2) group. A spin cluster serves as the walker, whereas its location on the Bloch sphere is described by the spin coherent state. An additional spin that interacts with the spin cluster plays the role of a coin, whose state determines the rotation of the spin cluster. The Wigner function is calculated to visualize the movement of the walker on the Bloch sphere, with which the probability distribution and the standard deviation are also achieved. The quadratic enhancement of variance for the quantum walk on the Bloch sphere is confirmed. Compared to the ideal quantum walk on a circle, the walker's states on the Bloch sphere are generally nonorthogonal, whose drawbacks can be eliminated by increasing the number of spins in the spin cluster.
arXiv comment6 pages, 3 figures
References in corpus (36)
- Quantum random walks - an introductory overview
- Quantum Computation and Decision Trees
- Quantum walks: a comprehensive review
- Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Observation of topologically protected bound states in a one dimensional photonic system
- Exploring Topological Phases With Quantum Walks
- Realization of a quantum walk with one and two trapped ions
- Quantum walk of a trapped ion in phase space
- Strongly Correlated Quantum Walks in Optical Lattices
- Discrete single-photon quantum walks with tunable decoherence
- Sub-Planck spots of Schroedinger cats and quantum decoherence
- Implementing the quantum random walk
- Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
- Quantum random walks in optical lattices
- Simulating dynamic quantum phase transitions in photonic quantum walks
- The quantum to classical transition for random walks
- Quantum quincunx in cavity quantum electrodynamics
- Measurements with prediction and retrodiction on the collective spin of 10^{11} atoms beat the standard quantum limit
- Sub-Planck phase-space structures and Heisenberg-limited measurements
- Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics
- Topological quantum walks in momentum space with a Bose-Einstein condensate
- Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks
- Quantum Walk in Momentum Space with a Bose-Einstein Condensate
- Quantum walk on a line for a trapped ion
- Disordered Quantum Walks in one lattice dimension
- Explicit definition of symmetry for non-unitary quantum walks with gain and loss
- Quantum entanglement and fixed-point bifurcations
- Split spin-squeezed Bose-Einstein Condensates
- Quantum walks on circles in phase space via superconducting circuit quantum electrodynamics
- Experimental simulation and limitations of quantum walks with trapped ions
- Wigner negativity in spin- systems
- Sub-Planck structures: Analogies between the Heisenberg-Weyl and SU(2) groups
- Discrete time quantum walk with nitrogen-vacancy centers in diamond coupled to a superconducting flux qubit
- Quantum walk on a toral phase space
- Quantum Walks with Non-Orthogonal Position States