Effective quantum state reconstruction using compressive sensing in NMR quantum computing

Abstract

The number of measurements required to reconstruct the states of quantum systems increases exponentially with the quantum system dimensions, which makes the state reconstruction of high-qubit quantum systems have a great challenge in physical quantum computing experiments. Compressive sensing (CS) has been verified as a effective technique in the reconstruction of quantum state, however, it is still unknown that if CS can reconstruct quantum states given the less data measured by nuclear magnetic resonance (NMR). In this paper, we propose an effective NMR quantum state reconstruction method based on CS. Different from the conventional CS-based quantum state reconstruction, our method uses the actual observation data from NMR experiments rather than the data measured by the Pauli operators. We implement measurements on quantum states in practical NMR computing experiments and reconstruct states of 2,3,4 qubits using fewer number of measurements, respectively. The proposed method is easy to implement and performs more efficiently with the increase of the system dimension size. The performance reveals both efficiency and accuracy, which provides an alternative for the quantum state reconstruction in practical NMR.

7 pages, 5 figures

References in corpus (18)

• Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance
• Quantum state tomography via compressed sensing
• Experimental realization of a quantum algorithm
• Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
• Implementation of a Quantum Algorithm to Solve Deutsch's Problem on a Nuclear Magnetic Resonance Quantum Computer
• Efficient measurement of quantum dynamics via compressive sensing
• Benchmarking quantum control methods on a 12-qubit system
• Experimental quantum compressed sensing for a seven-qubit system
• Quantum Tomography under Prior Information
• Experimental realization of quantum algorithm for solving linear systems of equations
• Quantum Tomography Protocols with Positivity are Compressed Sensing Protocols
• Experimental Comparison of Efficient Tomography Schemes for a Six-Qubit State
• Quantum state tomography by continuous measurement and compressed sensing
• Preparation of pseudo-pure states by line-selective pulses in Nuclear Magnetic Resonance
• Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
• Application of compressed sensing to the simulation of atomic systems
• Experimental NMR Realization of A Generalized Quantum Search Algorithm
• Fast Reconstruction of High-qubit Quantum States via Low Rate Measurements

Cited by in corpus (5)

• Gradient-descent methods for fast quantum state tomography
• Neural network assisted quantum state and process tomography using limited data sets
• Efficient experimental characterization of quantum processes via compressed sensing on an NMR quantum processor
• Group Sparse Matrix Optimization for Efficient Quantum State Transformation
• True experimental reconstruction of quantum states and processes via convex optimization