Statistical Inference with Quantum Measurements: Methodologies for Nitrogen Vacancy Centers in Diamond

Abstract

The analysis of photon count data from the standard nitrogen vacancy (NV) measurement process is treated as a statistical inference problem. This has applications toward gaining better and more rigorous error bars for tasks such as parameter estimation (eg. magnetometry), tomography, and randomized benchmarking. We start by providing a summary of the standard phenomenological model of the NV optical process in terms of Lindblad jump operators. This model is used to derive random variables describing emitted photons during measurement, to which finite visibility, dark counts, and imperfect state preparation are added. NV spin-state measurement is then stated as an abstract statistical inference problem consisting of an underlying biased coin obstructed by three Poisson rates. Relevant frequentist and Bayesian estimators are provided, discussed, and quantitatively compared. We show numerically that the risk of the maximum likelihood estimator is well approximated by the Cramer-Rao bound, for which we provide a simple formula. Of the estimators, we in particular promote the Bayes estimator, owing to its slightly better risk performance, and straight-forward error propagation into more complex experiments. This is illustrated on experimental data, where Quantum Hamiltonian Learning is performed and cross-validated in a fully Bayesian setting, and compared to a more traditional weighted least squares fit.

41 pages and 14 figures, including the appendices

References in corpus (24)

• The nitrogen-vacancy colour centre in diamond
• High-sensitivity diamond magnetometer with nanoscale resolution
• Sensing electric fields using single diamond spins
• Magnetometry with nitrogen-vacancy defects in diamond
• Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate
• Temperature dependence of the nitrogen-vacancy magnetic resonance in diamond
• Characterizing Quantum Gates via Randomized Benchmarking
• Theory of the ground state spin of the NV- center in diamond: II. Spin solutions, time-evolution, relaxation and inhomogeneous dephasing
• Theory of the ground state spin of the NV- center in diamond: I. Fine structure, hyperfine structure, and interactions with electric, magnetic and strain fields
• Ab initio supercell calculations on nitrogen-vacancy center in diamond: its electronic structure and hyperfine tensors
• Efficient readout of a single spin state in diamond via spin-to-charge conversion
• Robust Online Hamiltonian Learning
• Adaptive Bayesian Quantum Tomography
• Randomized Benchmarking with Confidence
• Investigating the limits of randomized benchmarking protocols
• High resolution spectroscopy of single NV defects coupled with nearby ${}^{13}$C nuclear spins in diamond
• Practical Bayesian Tomography
• Robust Control of Quantum Information
• Quantum Hamiltonian Learning Using Imperfect Quantum Resources
• Continuous dynamical decoupling magnetometry
• Accelerated Randomized Benchmarking
• QInfer: Statistical inference software for quantum applications
• Characterization of control noise effects in optimal quantum unitary dynamics
• Fidelity enhancement by logical qubit encoding

Cited by in corpus (12)

• Learning Quantum Systems
• Quantum diamond spectrometer for nanoscale NMR and ESR spectroscopy
• Learning models of quantum systems from experiments
• Bayesian estimation for quantum sensing in the absence of single-shot detection
• Magnetic-field-learning using a single electronic spin in diamond with one-photon-readout at room temperature
• Adversarial Hamiltonian learning of quantum dots in a minimal Kitaev chain
• Fast Quantum State Tomography in the Nitrogen Vacancy Center of Diamond
• Low-frequency quantum sensing
• Hamiltonian learning with real-space impurity tomography in topological moire superconductors
• Machine learning the Kondo entanglement cloud from local measurements
• Noisy Coherent Population Trapping: Applications to Noise Estimation and Qubit State Preparation
• Nuclear spin relaxation in solid state defect quantum bits via electron-phonon coupling in their optical excited state