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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.13450 |
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| _version_ | 1866909531997470720 |
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| author | Bhattacharya, Aranya Sahu, Himanshu Zahed, Ahmadullah Sen, Kallol |
| author_facet | Bhattacharya, Aranya Sahu, Himanshu Zahed, Ahmadullah Sen, Kallol |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13450 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Complexity for one-dimensional discrete time quantum walk circuits Bhattacharya, Aranya Sahu, Himanshu Zahed, Ahmadullah Sen, Kallol Quantum Physics 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. |
| title | Complexity for one-dimensional discrete time quantum walk circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2307.13450 |