Quantum process tomography of unitary and near-unitary maps

Abstract

We study quantum process tomography given the prior information that the map is a unitary or close to a unitary process. We show that a unitary map on a $d$-level system is completely characterized by a minimal set of $d^2+d$ elements associated with a collection of POVMs, in contrast to the $d^4-d^2$ elements required for a general completely positive trace-preserving map. To achieve this lower bound, one must probe the map with a particular set of $d$ pure states. We further compare the performance of different compressed sensing algorithms used to reconstruct a near-unitary process from such data. We find that when we have accurate prior information, an appropriate compressed sensing method reduces the required data needed for high-fidelity estimation, and different estimators applied to the same data are sensitive to different types of noise. Compressed sensing techniques can therefore be used both as indicators of error models and to validate the use of the prior assumptions.

arXiv comment11 pages, 3 figures

References in corpus (19)

• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Quantum state tomography via compressed sensing
• Randomized Benchmarking of Quantum Gates
• Robust randomized benchmarking of quantum processes
• Scalable Noise Estimation with Random Unitary Operators
• Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
• Characterization of addressability by simultaneous randomized benchmarking
• Randomized benchmarking and process tomography for gate errors in a solid-state qubit
• Efficient measurement of quantum dynamics via compressive sensing
• Quantum Tomography under Prior Information
• Randomized Benchmarking of Multi-Qubit Gates
• Minimal Informationally Complete Measurements for Pure States
• Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing
• Random Quantum Operations
• Quantum state tomography by continuous measurement and compressed sensing
• Randomized benchmarking of atomic qubits in an optical lattice
• Quantum Control in the Cs 6S_{1/2} Ground Manifold Using rf and μw Magnetic Fields
• Minimum number of input states required for quantum gate characterization
• Process tomography for unitary quantum channels

Cited by in corpus (52)

• Eigenstate Thermalization Hypothesis
• Quantum enhanced measurements without entanglement
• Experimental quantum compressed sensing for a seven-qubit system
• Compressed sensing quantum process tomography for superconducting quantum gates
• Experimental Benchmarking of Quantum Control in Zero-Field Nuclear Magnetic Resonance
• Recovering quantum gates from few average gate fidelities
• Supervised Quantum Learning without Measurements
• Robust and Efficient Hamiltonian Learning
• Scalable reconstruction of unitary processes and Hamiltonians
• Quantum gate identification: error analysis, numerical results and optical experiment
• Guaranteed recovery of quantum processes from few measurements
• Objective Compressive Quantum Process Tomography
• Universal compressive characterization of quantum dynamics
• Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly
• Gradient-descent quantum process tomography by learning Kraus operators
• Two-photon tomography using on-chip quantum walks
• Compressive gate set tomography
• Query-optimal estimation of unitary channels in diamond distance
• Experimental realization of self-guided quantum process tomography
• Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice
• Compressed sensing for Hamiltonian reconstruction
• Single-preparation unsupervised quantum machine learning: concepts and applications
• Quantum algorithm for universal implementation of projective measurement of energy
• Quantum Process Fidelity Bounds from Sets of Input States
• Certifying quantum memories with coherence
• Compressively certifying quantum measurements
• Quantum process tomography with unknown single-preparation input states
• The Role of Topology in Quantum Tomography
• Density-Matrix Renormalization Group study of Many-Body Localization in Floquet Eigenstates
• Modern compressive tomography for quantum information science
• Quantum SWAP gate realized with CZ and iSWAP gates in a superconducting architecture
• Quantum tomography of noisy ion-based qudits
• Process tomography in general physical theories
• Estimation of high-dimensional unitary transformations saturating the Quantum Cramér-Rao bound
• Quantum Process Tomography of Unitary Maps from Time-Delayed Measurements
• Machine learning of quantum channels on NISQ devices
• Context Aware Fidelity Estimation
• Group Sparse Matrix Optimization for Efficient Quantum State Transformation
• Universal compiling and (No-)Free-Lunch theorems for continuous variable quantum learning
• Parameterized quantum comb and simpler circuits for reversing unknown qubit-unitary operations
• Unitary quantum process tomography with unreliable pure input states
• Certifying Temporal Correlations
• Benchmarking quantum tomography completeness and fidelity with machine learning
• Beyond the density operator and Tr(ρA): Exploiting the higher-order statistics of random-coefficient pure states for quantum information processing
• Using non-convex optimization in quantum process tomography: Factored gradient descent is tough to beat
• Statistical intrusion detection and eavesdropping in quantum channels with coupling: Multiple-preparation and single-preparation methods
• Learning the structure of any Hamiltonian from minimal assumptions
• Characterizing a high-dimensional unitary transformation without measuring the qudit it transforms
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations
• Multi-core fiber integrated multi-port beamsplitters for quantum information processing
• A sparse-sampling approach for the fast computation of matrices: application to molecular vibrations
• Parameterized process characterization with reduced resource requirements