Identifying an Experimental Two-State Hamiltonian to Arbitrary Accuracy

Abstract

Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on these parameters. This method requires only one measurement basis and the ability to initialise the system in some arbitrary state which is not an eigenstate of the Hamiltonian in question. The scaling of the uncertainty is studied for large numbers of measurements and found to be proportional to one on the square-root of the number of measurements.

Minor corrections, Accepted for publication in Physical Review A

References in corpus (10)

• On the Measurement of Qubits
• NMR Techniques for Quantum Control and Computation
• Reliable Quantum Computers
• Prescription for experimental determination of the dynamics of a quantum black box
• Complete Characterization of a Quantum Process: the Two-Bit Quantum Gate
• Tackling Systematic Errors in Quantum Logic Gates with Composite Rotations
• Arbitrarily accurate composite pulses
• Experimental Hamiltonian identification for controlled two-level systems
• Dressed Qubits
• Parameters estimation in quantum optics

Cited by in corpus (52)

• Quantum Error Correction for Beginners
• Spin transport and quasi 2D architectures for donor-based quantum computing
• Gate Set Tomography
• Learning Quantum Systems
• Sensing of Fluctuating Nanoscale Magnetic Fields Using NV Centres in Diamond
• Quantum Hamiltonian identification from measurement time traces
• Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements
• Experimental estimation of one-parameter qubit gates in the presence of phase diffusion
• Scanning Quantum Decoherence Microscopy
• Hamiltonian tomography in an access-limited setting without state initialization
• A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis
• Efficient estimation of nearly sparse many-body quantum Hamiltonians
• Integrated tool-set for Control, Calibration and Characterization of quantum devices applied to superconducting qubits
• Characterization of a qubit Hamiltonian using adaptive measurements in a fixed basis
• Hamiltonian Tomography via Quantum Quench
• Approximate controllability, exact controllability, and conical eigenvalue intersections for quantum mechanical systems
• Identification of open quantum systems from observable time traces
• Two-Qubit Hamiltonian Tomography by Bayesian Analysis of Noisy Data
• Hamiltonian tomography for quantum many-body systems with arbitrary couplings
• Coherent electron transport by adiabatic passage in an imperfect donor chain
• Scheme for direct measurement of a general two-qubit Hamiltonian
• Identifying a Two-State Hamiltonian in the Presence of Decoherence
• Learning Quantum Hamiltonians from Single-qubit Measurements
• Scalable Hamiltonian learning for large-scale out-of-equilibrium quantum dynamics
• Optimal quantum multi-parameter estimation and application to dipole- and exchange-coupled qubits
• Equivalence classes and local asymptotic normality in system identification for quantum Markov chains
• Subspace Confinement: How good is your qubit?
• Reconstructing the Profile of Time-Varying Magnetic Fields With Quantum Sensors
• Compressed sensing for Hamiltonian reconstruction
• Precision characterisation of two-qubit Hamiltonians via entanglement mapping
• Quantum System Identification by Bayesian Analysis of Noisy Data: Beyond Hamiltonian Tomography
• The ubiquitous problem of learning system parameters for dissipative two-level quantum systems: Fourier analysis versus Bayesian estimation
• Quantum Hamiltonian Identification with Classical Colored Measurement Noise
• Direct Estimation of Single- and Two-Qubit Hamiltonians and Relaxation Rates
• Robustly learning the Hamiltonian dynamics of a superconducting quantum processor
• Physics-based mathematical models for quantum devices via experimental system identification
• Active Learning of Quantum System Hamiltonians yields Query Advantage
• Optimizing qubit Hamiltonian parameter estimation algorithms using PSO
• High-accuracy Hamiltonian learning via delocalized quantum state evolutions
• Spectroscopy of a Cooper-Pair box in the Autler-Townes configuration
• Inferring interpretable dynamical generators of local quantum observables from projective measurements through machine learning
• An interleaved sampling scheme for the characterization of single qubit dynamics
• Maximum likelihood versus likelihood-free quantum system identification in the atom maser
• Quantum System Identification: Hamiltonian Estimation using Spectral and Bayesian Analysis
• On open quantum systems, effective Hamiltonians and device characterization
• Improving quantum gate fidelities using optimized Euler angles
• Differentiable master equation solver for quantum device characterisation
• Model discrimination for dephasing two-level systems
• Efficient Quantum State Tracking in Noisy Environments
• Characterization and Control of Quantum Spin Chains and Rings
• Time-dependent Hamiltonian estimation for Doppler velocimetry of trapped ions
• Effective Strategies for Identifying Model Parameters for Open Quantum Systems