Quantum-enhanced magnetometry by phase estimation algorithms with a single artificial atom

S Danilin,G B Lesovik,A V Lebedev,G Blatter,G S Paraoanu,A Vepsäläinen

doi:10.1038/s41534-018-0078-y

Abstract

Phase estimation algorithms are key protocols in quantum information processing. Besides applications in quantum computing, they can also be employed in metrology as they allow for fast extraction of information stored in the quantum state of a system. Here, we implement two suitably modified phase estimation procedures, the Kitaev and the semiclassical Fourier-transform algorithms, using an artificial atom realized with a superconducting transmon circuit. We demonstrate that both algorithms yield a flux sensitivity exceeding the classical shot-noise limit of the device, allowing one to approach the Heisenberg limit. Our experiment paves the way for the use of superconducting qubits as metrological devices which are potentially able to outperform the best existing flux sensors with a sensitivity enhanced by few orders of magnitude.

Highlights

Phase estimation algorithms are building elements for many important quantum algorithms,[1] such as Shor’s factorization algorithm[2,3] or Lloyd’s algorithm[4] for solving systems of linear equations
Phase estimation is a natural concept in quantum metrology,[5] where one aims at evaluating an unknown parameter λ that typically enters into the Hamiltonian of a probe quantum system and defines its energy states En(λ)
In the superconducting quantum interference devices (SQUIDs) loop geometry, the relative phase of the superconducting wavefunctions across the Josephson junctions acquires a dependence on magnetic flux by the frequency mismatch Δω(Φ) = ωd−ω01(Φ) between the transition frequency ω01(Φ) of the transmon qubit and the fixed drive frequency ωd of the π/2 pulses

Summary

Introduction

Phase estimation algorithms are building elements for many important quantum algorithms,[1] such as Shor’s factorization algorithm[2,3] or Lloyd’s algorithm[4] for solving systems of linear equations. Phase estimation is a natural concept in quantum metrology,[5] where one aims at evaluating an unknown parameter λ that typically enters into the Hamiltonian of a probe quantum system and defines its energy states En(λ). The Heisenberg limit can be achieved with the help of entanglement resources, e.g., using NOON photon states in optics.[6,7,8] these states are difficult to create in general and they typically have a short coherence time. One can reach the Heisenberg limit without exploiting entanglement, by using the coherence of the wavefunction of a single quantum system as a dynamical resource. A further improvement has to make use of an alternative measurement strategy with a precision following the standard quantum limit but with a better prefactor. The unknown parameter λ can be estimated from the phase φ

Methods

Results

Conclusion