Inference-Based Quantum Sensing

Abstract

In a standard Quantum Sensing (QS) task one aims at estimating an unknown parameter $\theta$, encoded into an $n$-qubit probe state, via measurements of the system. The success of this task hinges on the ability to correlate changes in the parameter to changes in the system response $\mathcal{R}(\theta )$ (i.e., changes in the measurement outcomes). For simple cases the form of $\mathcal{R}(\theta )$ is known, but the same cannot be said for realistic scenarios, as no general closed-form expression exists. In this work we present an inference-based scheme for QS. We show that, for a general class of unitary families of encoding, $\mathcal{R}(\theta )$ can be fully characterized by only measuring the system response at $2n+1$ parameters. This allows us to infer the value of an unknown parameter given the measured response, as well as to determine the sensitivity of the scheme, which characterizes its overall performance. We show that inference error is, with high probability, smaller than $\delta$, if one measures the system response with a number of shots that scales only as $\Omega ({\log }^3(n)/{\delta }^2)$. Furthermore, the framework presented can be broadly applied as it remains valid for arbitrary probe states and measurement schemes, and, even holds in the presence of quantum noise. We also discuss how to extend our results beyond unitary families. Finally, to showcase our method we implement it for a QS task on real quantum hardware, and in numerical simulations.

arXiv comment7+13 pages, 3+7 figures

References in corpus (37)

• Quantum sensing
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum metrology
• High-sensitivity diamond magnetometer with nanoscale resolution
• Quantum metrology with nonclassical states of atomic ensembles
• Quantum Convolutional Neural Networks
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• On the Improvement of Frequency Stardards with Quantum Entanglement
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Optical magnetic detection of single-neuron action potentials using quantum defects in diamond
• Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond
• Absence of Barren Plateaus in Quantum Convolutional Neural Networks
• Individual quantum probes for optimal thermometry
• General parameter-shift rules for quantum gradients
• Learning the quantum algorithm for state overlap
• A Geometric Perspective on Quantum Parameter Estimation
• Stochastic gradient descent for hybrid quantum-classical optimization
• Sequential minimal optimization for quantum-classical hybrid algorithms
• Frequency-Dependent Squeezing for Advanced LIGO
• Trainability of Dissipative Perceptron-Based Quantum Neural Networks
• Fisher Information in Noisy Intermediate-Scale Quantum Applications
• A variational toolbox for quantum multi-parameter estimation
• Local quantum thermal susceptibility
• Quantum Variational Optimization of Ramsey Interferometry and Atomic Clocks
• Variational-State Quantum Metrology
• Variational Quantum Algorithm for Estimating the Quantum Fisher Information
• Directional Detection of Dark Matter using Spectroscopy of Crystal Defects
• Simulating the performance of a distance-3 surface code in a linear ion trap
• Maximal Quantum Fisher Information for Mixed States
• Quantum Fisher information and symmetric logarithmic derivative via anti-commutators
• Characterizing local noise in QAOA circuits
• Sub-Quantum Fisher Information
• Quantifying precision loss in local quantum thermometry via diagonal discord
• Quantum magnetometry using two-stroke thermal machines
• Nonclassical correlations for quantum metrology in thermal equilibrium
• Generalized Measure of Quantum Fisher Information

Cited by in corpus (10)

• Quantum Simulating Nature's Fundamental Fields
• Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
• Does provable absence of barren plateaus imply classical simulability?
• Effects of noise on the overparametrization of quantum neural networks
• Optimal protocols for quantum metrology with noisy measurements
• On the universality of $S_n$-equivariant $k$-body gates
• A Hierarchy of Multipartite Correlations Based on Concentratable Entanglement
• Efficient quantum-enhanced classical simulation for patches of quantum landscapes
• More buck-per-shot: Why learning trumps mitigation in noisy quantum sensing
• Interferometric binary phase estimations