Complexity for one-dimensional discrete time quantum walk circuits
- URL: http://arxiv.org/abs/2307.13450v4
- Date: Wed, 18 Sep 2024 15:15:47 GMT
- Title: Complexity for one-dimensional discrete time quantum walk circuits
- Authors: Aranya Bhattacharya, Himanshu Sahu, Ahmadullah Zahed, Kallol Sen,
- Abstract summary: 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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-sa/4.0/
- 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 step-wise 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.
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