Continuous measurement-based holonomic quantum computation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916996126343168 |
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| author | Lanka, Anirudh Garcia-Nila, Juan Brun, Todd A. |
| author_facet | Lanka, Anirudh Garcia-Nila, Juan Brun, Todd A. |
| contents | We propose a scheme to generate holonomies using the Quantum Zeno effect, enabling logical unitary operations on quantum stabilizer codes purely through measurements. The quantum error-correcting code space is adiabatically rotated by measuring a succession of rotated stabilizer generators. When the rotation is sufficiently slow, the state remains confined to the instantaneous code space by the Zeno effect; otherwise, measurement-induced jumps can occur into a rotated orthogonal subspace. If the rotation completes a closed loop, the code state is transformed by a holonomy: a logical unitary transformation. We analytically derive the sequence of rotated stabilizer generators that produce a desired holonomy, and find the total time required to implement this procedure with a given success probability. If a measurement moves the state to the orthogonal subspace, we present a method to alter the path of the rotated observables to return the state either to the original code or the original error space with the desired holonomy; in the latter case, the holonomy is emulated. Finally, we establish conditions on the code and the measured observables that preserve the correctability of a given error set. When a code fails to meet the error-correcting conditions, our protocol remains applicable by augmenting the code with at most two ancilla qubits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06725 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous measurement-based holonomic quantum computation Lanka, Anirudh Garcia-Nila, Juan Brun, Todd A. Quantum Physics We propose a scheme to generate holonomies using the Quantum Zeno effect, enabling logical unitary operations on quantum stabilizer codes purely through measurements. The quantum error-correcting code space is adiabatically rotated by measuring a succession of rotated stabilizer generators. When the rotation is sufficiently slow, the state remains confined to the instantaneous code space by the Zeno effect; otherwise, measurement-induced jumps can occur into a rotated orthogonal subspace. If the rotation completes a closed loop, the code state is transformed by a holonomy: a logical unitary transformation. We analytically derive the sequence of rotated stabilizer generators that produce a desired holonomy, and find the total time required to implement this procedure with a given success probability. If a measurement moves the state to the orthogonal subspace, we present a method to alter the path of the rotated observables to return the state either to the original code or the original error space with the desired holonomy; in the latter case, the holonomy is emulated. Finally, we establish conditions on the code and the measured observables that preserve the correctability of a given error set. When a code fails to meet the error-correcting conditions, our protocol remains applicable by augmenting the code with at most two ancilla qubits. |
| title | Continuous measurement-based holonomic quantum computation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.06725 |