Simple, reliable and noise-resilient continuous-variable quantum state tomography with convex optimization

Abstract

Precise reconstruction of unknown quantum states from measurement data, a process commonly called quantum state tomography, is a crucial component in the development of quantum information processing technologies. Many different tomography methods have been proposed over the years. Maximum likelihood estimation is a prominent example, being the most popular method for a long period of time. Recently, more advanced neural network methods have started to emerge. Here, we go back to basics and present a method for continuous variable state reconstruction that is both conceptually and practically simple, based on convex optimization. Convex optimization has been used for process tomography and qubit state tomography, but seems to have been overlooked for continuous variable quantum state tomography. We demonstrate high-fidelity reconstruction of an underlying state from data corrupted by thermal noise and imperfect detection, for both homodyne and heterodyne measurements. A major advantage over other methods is that convex optimization algorithms are guaranteed to converge to the optimal solution.

Code available at https://github.com/ingstra/cvx-tomography

References in corpus (10)

• Quantum Process Tomography: Resource Analysis of Different Strategies
• Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
• Diluted maximum-likelihood algorithm for quantum tomography
• Characterizing Quantum Microwave Radiation and its Entanglement with Superconducting Qubits using Linear Detectors
• Mapping coherence in measurement via full quantum tomography of a hybrid optical detector
• Quantum process tomography with coherent states
• Quantum state tomography by continuous measurement and compressed sensing
• Reconstructing quantum states with quantum reservoir networks
• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• Quantum efficiency, purity and stability of a tunable, narrowband microwave single-photon source

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• Digital homodyne and heterodyne detection for stationary bosonic modes
• Entanglement of photonic modes from a continuously driven two-level system
• Deterministic generation of frequency-bin-encoded microwave photons
• On-demand shaped photon emission based on a parametrically modulated qubit
• Selective and efficient quantum state tomography for multi-qubit systems