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.

11 pages, 3 figures

References in corpus (10)

• Randomized Benchmarking of Quantum Gates
• Robust randomized benchmarking of quantum processes
• 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
• Randomized Benchmarking of Multi-Qubit Gates
• 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

Cited by in corpus (7)

• Compressed sensing quantum process tomography for superconducting quantum gates
• Scalable reconstruction of unitary processes and Hamiltonians
• Objective Compressive Quantum Process Tomography
• Universal compressive characterization of quantum dynamics
• The Role of Topology in Quantum Tomography
• Quantum tomography of noisy ion-based qudits
• A sparse-sampling approach for the fast computation of matrices: application to molecular vibrations