Optimal quantum multi-parameter estimation and application to dipole- and exchange-coupled qubits

Abstract

We consider the problem of quantum multi-parameter estimation with experimental constraints and formulate the solution in terms of a convex optimization. Specifically, we outline an efficient method to identify the optimal strategy for estimating multiple unknown parameters of a quantum process and apply this method to a realistic example. The example is two electron spin qubits coupled through the dipole and exchange interactions with unknown coupling parameters -- explicitly, the position vector relating the two qubits and the magnitude of the exchange interaction are unknown. This coupling Hamiltonian generates a unitary evolution which, when combined with arbitrary single-qubit operations, produces a universal set of quantum gates. However, the unknown parameters must be known precisely to generate high-fidelity gates. We use the Cramér-Rao bound on the variance of a point estimator to construct the optimal series of experiments to estimate these free parameters, and present a complete analysis of the optimal experimental configuration. Our method of transforming the constrained optimal parameter estimation problem into a convex optimization is powerful and widely applicable to other systems.

13 pages. Published version

References in corpus (10)

• Generalized Limits for Single-Parameter Quantum Estimation
• Symmetrised Characterisation of Noisy Quantum Processes
• Complete Characterization of Quantum-Optical Processes
• Electrical detection of 31P spin quantum states
• Direct Characterization of Quantum Dynamics
• Electrically-detected magnetic resonance in ion-implanted Si:P nanostructures
• Identifying an Experimental Two-State Hamiltonian to Arbitrary Accuracy
• Long spin coherence in silicon with an electrical spin trap readout
• Spin-Dependent Scattering off Neutral Antimony Donors in 28-Si Field-Effect Transistors
• Quantum non-demolition measurements of single donor spins in semiconductors

Cited by in corpus (19)

• Control of quantum phenomena: Past, present, and future
• Optimal estimation of joint parameters in phase space
• Quantum Hamiltonian identification from measurement time traces
• Evaluating the Holevo Cramér-Rao bound for multi-parameter quantum metrology
• The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation
• Efficient estimation of nearly sparse many-body quantum Hamiltonians
• Optimal Measurement on Noisy Quantum Systems
• Two-Qubit Hamiltonian Tomography by Bayesian Analysis of Noisy Data
• Optimal experiment design revisited: fair, precise and minimal tomography
• Multiple phase estimation in quantum cloning machines
• Robust Control of Quantum Dynamics under Input and Parameter Uncertainty
• The advantage of quantum control in many-body Hamiltonian learning
• High-dimensional cryptographic quantum parameter estimation
• Modelling the effect of charge noise on the exchange interaction between spins
• Invertible condition of quantum Fisher information matrix for a mixed qubit
• Experiment design and parameter estimation of Pauli channels using convex optimization
• Joint estimation of phase and phase diffusion for quantum metrology
• Quantum hypothesis testing via robust quantum control
• Pauli channel tomography with unknown channel directions