Quantum Computing in Discrete- and Continuous-Variable Architectures
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913922128281600 |
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| author | Singh, Shraddha |
| author_facet | Singh, Shraddha |
| contents | This thesis develops a theoretical framework for hybrid continuous-variable (CV) and discrete-variable (DV) quantum systems, with emphasis on quantum control, state preparation, and error correction. A central contribution is non-abelian quantum signal processing (NA-QSP), a generalization of quantum signal processing to settings where control parameters are non-commuting operators. Within this framework, we introduce the Gaussian-Controlled-Rotation (GCR) protocol, which enables high-fidelity control of CV states using DV ancillae. This approach allows for deterministic preparation of squeezed, cat, and Gottesman-Kitaev-Preskill (GKP) states without numerical optimization.
Two previously unpublished contributions are included: (i) Chapter 2.3 introduces the Gaussian hierarchy, a classification of CV operations analogous to the Clifford hierarchy, offering a new lens for understanding CV gate sets; (ii) Chapter 5 presents an analytical framework for correcting photon loss in finite-energy GKP codes, introducing the notion of probabilistic error correction, providing insight into recent GKP experiments surpassing break-even thresholds.
Overall, this work lays the groundwork for scalable, fault-tolerant quantum computation in hybrid CV-DV architectures, with applications to logical gate synthesis, readout, and hybrid algorithm design using ancilla oscillators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01146 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Computing in Discrete- and Continuous-Variable Architectures Singh, Shraddha Quantum Physics This thesis develops a theoretical framework for hybrid continuous-variable (CV) and discrete-variable (DV) quantum systems, with emphasis on quantum control, state preparation, and error correction. A central contribution is non-abelian quantum signal processing (NA-QSP), a generalization of quantum signal processing to settings where control parameters are non-commuting operators. Within this framework, we introduce the Gaussian-Controlled-Rotation (GCR) protocol, which enables high-fidelity control of CV states using DV ancillae. This approach allows for deterministic preparation of squeezed, cat, and Gottesman-Kitaev-Preskill (GKP) states without numerical optimization. Two previously unpublished contributions are included: (i) Chapter 2.3 introduces the Gaussian hierarchy, a classification of CV operations analogous to the Clifford hierarchy, offering a new lens for understanding CV gate sets; (ii) Chapter 5 presents an analytical framework for correcting photon loss in finite-energy GKP codes, introducing the notion of probabilistic error correction, providing insight into recent GKP experiments surpassing break-even thresholds. Overall, this work lays the groundwork for scalable, fault-tolerant quantum computation in hybrid CV-DV architectures, with applications to logical gate synthesis, readout, and hybrid algorithm design using ancilla oscillators. |
| title | Quantum Computing in Discrete- and Continuous-Variable Architectures |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.01146 |