Compressing measurements in quantum dynamic parameter estimation

Abstract

We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control methods to efficiently estimate time-dependent parameters in the system Hamiltonian. We show that incoherent measurement bases and, more generally, suitable random measurement matrices can be created by performing simple control sequences on the quantum system. Since random measurement matrices satisfying the restricted isometry property can be used to reconstruct any sparse signal in an efficient manner, and many physical processes are approximately sparse in some basis, these methods can potentially be useful in a variety of applications such as quantum sensing and magnetometry. We illustrate the theoretical results throughout the presentation with various practically relevant numerical examples.

15 pages, 4 figures

References in corpus (11)

• Quantum-enhanced measurements: beating the standard quantum limit
• Sparsity and Incoherence in Compressive Sampling
• High-sensitivity diamond magnetometer with nanoscale resolution
• Quantum state tomography via compressed sensing
• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• How to Enhance Dephasing Time in Superconducting Qubits
• Magnetic field imaging with NV ensembles
• Efficient measurement of quantum dynamics via compressive sensing
• Exact Results on Dynamical Decoupling by $\pi$-Pulses in Quantum Information Processes
• Reducing sequencing complexity in dynamical quantum error suppression by Walsh modulation
• Reconstructing the Profile of Time-Varying Magnetic Fields With Quantum Sensors

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