Towards Non-Abelian Quantum Signal Processing: Efficient Control of Hybrid Continuous- and Discrete-Variable Architectures
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| Format: | Preprint |
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2025
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| _version_ | 1866917181715906560 |
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| author | Singh, Shraddha Royer, Baptiste Girvin, Steven M. |
| author_facet | Singh, Shraddha Royer, Baptiste Girvin, Steven M. |
| contents | Robust quantum control is crucial for achieving operations below the quantum error correction threshold. Quantum Signal Processing (QSP) transforms a unitary parameterized by $θ$ into one governed by a polynomial function $f(θ)$, a feature that underpins key quantum algorithms. Originating from composite pulse techniques in NMR, QSP enhances robustness against systematic control errors. We extend QSP to a new class, non-abelian QSP, which utilizes non-commuting control parameters, $\hatθ_1, \hatθ_2, \dots$, representing quantum harmonic oscillator positions and momenta. We introduce a fundamental non-abelian composite pulse sequence, the Gaussian-Controlled-Rotation (GCR), for entangling and disentangling a qubit from an oscillator. This sequence achieves at least a $4.5\times$ speedup compared to the state-of-the-art abelian QSP pulse BB1, while maintaining performance. Though quantum fluctuations in the control parameters are unavoidable, the richer commutator algebra of non-abelian QSP enhances its power and efficiency. Non-abelian QSP represents the highest tier of QSP variants tailored for hybrid oscillator-qubit architectures, unlocking new possibilities for such systems. We demonstrate the utility of GCR in high-fidelity preparation of continuous-variable oscillator states, including squeezed, Fock, cat, and GKP states, using fully analytical schemes that match numerically optimized methods in fidelity and depth while enabling mid-circuit error detection. Furthermore, we propose a high-fidelity QSP-based end-of-the-line GKP readout and a measurement-free, error-corrected gate teleportation protocol for logical operations on GKP bosonic qudits, bridging the gap between idealized theoretical and experimentally realistic versions of the GKP code. Finally, we showcase a GCR-based phase estimation algorithm for oscillator-based quantum computing. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_19992 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards Non-Abelian Quantum Signal Processing: Efficient Control of Hybrid Continuous- and Discrete-Variable Architectures Singh, Shraddha Royer, Baptiste Girvin, Steven M. Quantum Physics Robust quantum control is crucial for achieving operations below the quantum error correction threshold. Quantum Signal Processing (QSP) transforms a unitary parameterized by $θ$ into one governed by a polynomial function $f(θ)$, a feature that underpins key quantum algorithms. Originating from composite pulse techniques in NMR, QSP enhances robustness against systematic control errors. We extend QSP to a new class, non-abelian QSP, which utilizes non-commuting control parameters, $\hatθ_1, \hatθ_2, \dots$, representing quantum harmonic oscillator positions and momenta. We introduce a fundamental non-abelian composite pulse sequence, the Gaussian-Controlled-Rotation (GCR), for entangling and disentangling a qubit from an oscillator. This sequence achieves at least a $4.5\times$ speedup compared to the state-of-the-art abelian QSP pulse BB1, while maintaining performance. Though quantum fluctuations in the control parameters are unavoidable, the richer commutator algebra of non-abelian QSP enhances its power and efficiency. Non-abelian QSP represents the highest tier of QSP variants tailored for hybrid oscillator-qubit architectures, unlocking new possibilities for such systems. We demonstrate the utility of GCR in high-fidelity preparation of continuous-variable oscillator states, including squeezed, Fock, cat, and GKP states, using fully analytical schemes that match numerically optimized methods in fidelity and depth while enabling mid-circuit error detection. Furthermore, we propose a high-fidelity QSP-based end-of-the-line GKP readout and a measurement-free, error-corrected gate teleportation protocol for logical operations on GKP bosonic qudits, bridging the gap between idealized theoretical and experimentally realistic versions of the GKP code. Finally, we showcase a GCR-based phase estimation algorithm for oscillator-based quantum computing. |
| title | Towards Non-Abelian Quantum Signal Processing: Efficient Control of Hybrid Continuous- and Discrete-Variable Architectures |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.19992 |