Quantum Process Tomography of Unitary Maps from Time-Delayed Measurements
arXiv:2112.09021 · doi:10.1007/s11128-023-04008-y
Abstract
Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternative approach which requires only a single (or few) known initial states together with time-delayed measurements for reconstructing the unitary map and corresponding Hamiltonian of the time dynamics. The overarching mathematical framework and feasibility guarantee of our method is provided by the Takens embedding theorem. We explain in detail how the reconstruction of a single qubit Hamiltonian works in this setting, and provide numerical methods and experiments for general few-qubit and lattice systems with local interactions. In particular, the method allows to find the Hamiltonian of a two qubit system by observing only one of the qubits.
arXiv comment10 pages, 9 figures
References in corpus (28)
- Efficient simulation of one-dimensional quantum many-body systems
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Many-body quantum state tomography with neural networks
- Efficient quantum state tomography
- Quantum process tomography of a controlled-NOT gate
- Optimal Creation of Entanglement Using a Two--Qubit Gate
- A geometric theory of non-local two-qubit operations
- Quantum Process Tomography of a Universal Entangling Gate Implemented with Josephson Phase Qubits
- Realization of quantum process tomography in NMR
- Gate Set Tomography
- Quantum Process Tomography of the Quantum Fourier Transform
- Quantum Hamiltonian identification from measurement time traces
- On Learning Hamiltonian Systems from Data
- Entangled Bloch Spheres: Bloch Matrix and Two Qubit State Space
- Quantum process tomography of unitary and near-unitary maps
- Quantum process tomography via completely positive and trace-preserving projection
- Compressed sensing quantum process tomography for superconducting quantum gates
- Local-measurement-based quantum state tomography via neural networks
- Quantum tomography of electrical currents
- Identification of open quantum systems from observable time traces
- Projected Least-Squares Quantum Process Tomography
- Learning Quantum Hamiltonians from Single-qubit Measurements
- On the Koopman operator of algorithms
- Tracking the dynamics of an ideal quantum measurement
- An Emergent Space for Distributed Data with Hidden Internal Order through Manifold Learning
- Manifold Learning for Organizing Unstructured Sets of Process Observations
- Efficient quantum circuit simulation using a multi-qubit Bloch vector representation of density matrices
- Numerical Model Construction with Closed Observables