Characterizing the performance of continuous-variable Gaussian quantum gates
arXiv:1810.12335 · doi:10.1103/PhysRevResearch.2.013126
Abstract
The required set of operations for universal continuous-variable quantum computation can be divided into two primary categories: Gaussian and non-Gaussian operations. Furthermore, any Gaussian operation can be decomposed as a sequence of phase-space displacements and symplectic transformations. Although Gaussian operations are ubiquitous in quantum optics, their experimental realizations generally are approximations of the ideal Gaussian unitaries. In this work, we study different performance criteria to analyze how well these experimental approximations simulate the ideal Gaussian unitaries. In particular, we find that none of these experimental approximations converge uniformly to the ideal Gaussian unitaries. However, convergence occurs in the strong sense, or if the discrimination strategy is energy bounded, then the convergence is uniform in the Shirokov-Winter energy-constrained diamond norm and we give explicit bounds in this latter case. We indicate how these energy-constrained bounds can be used for experimental implementations of these Gaussian unitaries in order to achieve any desired accuracy.
v3: 26 pages, 10 figures, final version accepted for publication in Physical Review Research
References in corpus (28)
- Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency
- Coding Theorem and Strong Converse for Quantum Channels
- Performance and structure of single-mode bosonic codes
- Fault-tolerant bosonic quantum error correction with the surface-GKP code
- Repetition Cat Qubits for Fault-Tolerant Quantum Computation
- Quantum Error Correction with the Toric-GKP Code
- Demonstration of a quantum nondemolition sum gate
- Non-Gaussian and Gottesman-Kitaev-Preskill state preparation by photon catalysis
- Demonstration of deterministic and high fidelity squeezing of quantum information
- Encoding an oscillator into many oscillators
- Pair-cat codes: autonomous error-correction with low-order nonlinearity
- Quantum-limited loss sensing: Multiparameter estimation and Bures distance between loss channels
- Continuous-Variable Instantaneous Quantum Computing is hard to sample
- Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
- Modular Bosonic Subsystem Codes
- Protecting an optical qubit against photon loss
- Experimentally feasible quantum erasure-correcting code for continuous variables
- Energy-constrained diamond norm with applications to the uniform continuity of continuous variable channel capacities
- Sine distance for quantum states
- Convergence rates for quantum evolution & entropic continuity bounds in infinite dimensions
- All phase-space linear bosonic channels are approximately Gaussian dilatable
- Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels
- Quantum Error Correction with the GKP Code and Concatenation with Stabilizer Codes
- Strong quantitative benchmarking of quantum optical devices
- On approximation of quantum channels
- Designing good bosonic quantum codes via creating destructive interference
- Coherent Communication with Linear Optics
- Quantum supremacy and high-dimensional integration
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- Flow conditions for continuous variable measurement-based quantum computing
- Bosonic randomized benchmarking with passive transformations
- Certification of continuous-variable gates using average channel-fidelity witnesses