Bhattacharya, A and Sahu, H and Zahed, A and Sen, K (2024) Complexity for one-dimensional discrete-time quantum walk circuits. In: Physical Review A, 109 (2).
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Abstract
We compute the complexity for the mixed-state density operator derived from a one-dimensional discrete-time quantum walk (DTQW). The complexity is computed using a two-qubit quantum circuit obtained from canonically purifying the mixed state. We demonstrate that the Nielson complexity for the unitary evolution oscillates around a mean circuit depth of k. Further, the complexity of the stepwise evolution operator grows cumulatively and linearly with the steps. From a quantum circuit perspective, this implies a succession of circuits of (near) constant depth to be applied to reach the final state. © 2024 American Physical Society.
| Item Type: | Journal Article |
|---|---|
| Publication: | Physical Review A |
| Publisher: | American Physical Society |
| Additional Information: | The copyright for this article belongs to the Author. |
| Keywords: | Density operators; Discrete time; Evolution operator; Mixed state; One-dimensional; Quantum circuit; Quantum walk; State densities; Time quantum; Two-qubit, Timing circuits |
| Department/Centre: | Division of Physical & Mathematical Sciences > Centre for High Energy Physics Division of Physical & Mathematical Sciences > Instrumentation Appiled Physics |
| Date Deposited: | 04 Apr 2024 12:29 |
| Last Modified: | 04 Apr 2024 12:29 |
| URI: | https://eprints.iisc.ac.in/id/eprint/84707 |
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