A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis
arXiv:1610.08841 · doi:10.1109/TAC.2017.2747507
Abstract
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum Hamiltonian identification algorithm is developed within the framework of quantum process tomography. In the identification method, different probe states are inputted into quantum systems and the output states are estimated using the quantum state tomography protocol via linear regression estimation. The time-independent system Hamiltonian is reconstructed based on the experimental data for the output states. The Hamiltonian identification method has computational complexity O(d^6) where d is the dimension of the system Hamiltonian. An error upper bound O(d^3/N^(1/2))$ is also established, where N is the resource number for the tomography of each output state, and several numerical examples demonstrate the effectiveness of the proposed TSO Hamiltonian identification method.
13 pages, 4 figures
References in corpus (11)
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Entanglement-enhanced measurement of a completely unknown phase
- Quantum-enhanced optical phase tracking
- Choice of Measurement Sets in Qubit Tomography
- Knowledge and ignorance in incomplete quantum state tomography
- Hamiltonian tomography in an access-limited setting without state initialization
- Identifying an Experimental Two-State Hamiltonian to Arbitrary Accuracy
- Indirect Quantum Tomography of Quadratic Hamiltonians
- Hamiltonian identifiability assisted by single-probe measurement
- Optimal two-qubit tomography based on local and global measurements: Maximal robustness against errors as described by condition numbers
- Two-Qubit Hamiltonian Tomography by Bayesian Analysis of Noisy Data
Cited by in corpus (25)
- Learning a local Hamiltonian from local measurements
- Control-enhanced multiparameter quantum estimation
- Learning-based Quantum Robust Control: Algorithm, Applications and Experiments
- Hamiltonian Learning for Quantum Error Correction
- Learning the dynamics of open quantum systems from their steady states
- Quantum gate identification: error analysis, numerical results and optical experiment
- Quantum Hamiltonian Identifiability via a Similarity Transformation Approach and Beyond
- Exact dimension estimation of interacting qubit systems assisted by a single quantum probe
- Quantifying precision loss in local quantum thermometry via diagonal discord
- Learning control of quantum systems using frequency-domain optimization algorithms
- Single-preparation unsupervised quantum machine learning: concepts and applications
- Two-stage Estimation for Quantum Detector Tomography: Error Analysis, Numerical and Experimental Results
- A gradient algorithm for Hamiltonian identification of open quantum systems
- The advantage of quantum control in many-body Hamiltonian learning
- Quantum Hamiltonian Identification with Classical Colored Measurement Noise
- An inverse-system method for identification of damping rate functions in non-Markovian quantum systems
- Reconstructing effective Hamiltonians from nonequilibrium (pre-)thermal steady states
- On the capability of a class of quantum sensors
- A greedy reconstruction algorithm for the identification of spin distribution
- Learning a quantum channel from its steady-state
- When can a local Hamiltonian be recovered from a steady state?
- Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
- Modelling and Control of Quantum Measurement Induced Backaction in Double Quantum Dots
- Simulation-assisted learning of open quantum systems
- Beyond the density operator and Tr(ρA): Exploiting the higher-order statistics of random-coefficient pure states for quantum information processing