Heralded high-dimensional module-based quantum computation

• URL: http://arxiv.org/abs/2607.20895v1
• Date: Thu, 23 Jul 2026 03:33:43 GMT
• Title: Heralded high-dimensional module-based quantum computation
• Abstract summary: We first develop two alternative high-dimensional generalized parity modules, and then propose a procedure for constructing high-dimensional generalized module-based controlled-NOT gate.<n>The construction of module-based quantum computing introduced here is deterministic, heralded, insensitive to the dimensionality of the computing basis, and postselection technique is not required.
• Score: 7.401515703261687
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Parity measurements have been explored as building blocks for preparing and discriminating entangled states, as well as for implementing quantum computation. We first develop two alternative high-dimensional generalized parity modules, and then propose a procedure for constructing high-dimensional generalized module-based controlled-NOT gate. The construction of module-based quantum computing introduced here is deterministic, heralded, insensitive to the dimensionality of the computing basis, and postselection technique is not required. The result shows that out of $(d-1)!$ generalized parity modules, only modules $ \mathcal{P}=(j\ominus i)\bmod d$ and $ \mathcal{P}=(j \oplus i)\bmod d$ can be used as building blocks for high-dimensional quantum computing. Furthermore, we proposed an optical nondestructive scheme for implementing generalized parity module through quantum nondemolition measurements, and the success of the parity module is heralded by photon-number-resolving detectors and single-photon detectors.

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