arXiv subjects

Ilki Kim

Publications and source records attributed to Ilki Kim.

24 records · Page 2Linked to original sources

arXiv2000

Quantum network architecture of tight-binding models with substitution sequences

We study a two-spin quantum Turing architecture, in which discrete local rotations α_m of the Turing head spin alternate with quantum controlled NOT-operations. Substitution sequences are known to underlie aperiodic structures. We show that parameter inputs α_m described by such sequences can lead here to a quantum dynamics, intermediate between the regular and the chaotic variant. Exponential parameter sensitivity characterizing chaotic quantum Turing machines turns out to be an adequate criterion for induced quantum chaos in a quantum network.

quant-ph↗

arXiv1999

Quantum chaos in small quantum networks

We study a 2-spin quantum Turing architecture, in which discrete local rotations α_m of the Turing head spin alternate with quantum controlled NOT-operations. We show that a single chaotic parameter input α_m leads to a chaotic dynamics in the entire Hilbert space. The instability of periodic orbits on the Turing head and `chaos swapping' onto the Turing tape are demonstrated explicitly as well as exponential parameter sensitivity of the Bures metric.

quant-ph↗

arXiv1999

Quantum chaos in quantum Turing machines

We investigate a 2-spin quantum Turing architecture, in which discrete local rotations α_m of the Turing head spin alternate with quantum controlled NOT-operations. We demonstrate that a single chaotic parameter input α_m leads to a chaotic dynamics in the entire Hilbert-space.

quant-ph↗

arXiv1999

Correlation between Correlations: Process and Time in Quantum Networks

We study a special inhomogeneous quantum network consisting of a ring of $M$ pseudo-spins (here $M = 4$) sequentially coupled to one and the same central spin under the influence of given pulse sequences (quantum gate operations). This architecture could be visualized as a quantum Turing machine with a cyclic ``tape''. Rather than input-output-relations we investigate the resulting process, i.e. the correlation between one- and two-point expectation values (``correlations'') over various time-steps. The resulting spatio-temporal pattern exhibits many non-classical features including Zeno-effects, violation of temporal Bell-inequalities, and quantum parallelism. Due to the strange web of correlations being built-up, specific measurement outcomes for the tape may refer to one or several preparation histories of the head. Specific families of correlation functions are more stable with respect to dissipation than the total wave-function.

quant-ph↗

arXiv1999

Moving quantum agents in a finite environment

We investigate an all-quantum-mechanical spin network, in which a subset of spins, the $K$ ``moving agents'', are subject to local and pair unitary transformations controlled by their position with respect to a fixed ring of $M$ ``environmental''-spins. We demonstrate that a ``flow of coherence'' results between the various subsystems. Despite entanglement between the agents and between agent and environment, local (non-linear) invariants may persist, which then show up as fascinating patterns in each agent's Bloch-sphere. Such patterns disappear, though, if the agents are controlled by different rules. Geometric aspects thus help to understand the interplay between entanglement and decoherence.

quant-ph↗

arXiv1999

Pattern formation in quantum Turing machines

We investigate the iteration of a sequence of local and pair unitary transformations, which can be interpreted to result from a Turing-head (pseudo-spin $S$) rotating along a closed Turing-tape ($M$ additional pseudo-spins). The dynamical evolution of the Bloch-vector of $S$, which can be decomposed into $2^{M}$ primitive pure state Turing-head trajectories, gives rise to fascinating geometrical patterns reflecting the entanglement between head and tape. These machines thus provide intuitive examples for quantum parallelism and, at the same time, means for local testing of quantum network dynamics.

quant-ph↗