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Experimental Quantum Hamiltonian Learning
Jianwei Wang, Stefano Paesani, Raffaele Santagati, Sebastian Knauer, Antonio A. Gentile, Nathan Wiebe, Maurangelo Petruzzella, Jeremy L. O'Brien, John G. Rarity, Anthony Laing, Mark G. Thompson
TL;DR
Validating theoretical models of quantum systems is challenging because classical machines cannot tractably predict their behavior across exponentially large configuration spaces. This paper uses a quantum photonic simulator and Bayesian inference to learn an NV-centre spin Hamiltonian, estimating its Rabi frequency and using a learning saturation to improve the model.
Problem
How to validate theoretical models of quantum systems when predicting their behavior across exponentially large configuration spaces is intractable for classical machines.
Source: p. 1Method
The authors use Bayesian quantum Hamiltonian learning, interfacing a silicon-photonics quantum simulator with an NV-centre electron spin through a classical channel.
Source: p. 1Results
6.93 ± 0.09 MHz was the learned Rabi frequency, consistent with the 6.90 MHz reference, and the data provided strong evidence for the improved model (Bayes factor K = 560).
Source: pp. 2–3Takeaways & Limitations
The experiments demonstrate QHL's capability to validate Hamiltonian models and verify quantum devices.
Source: p. 4QLE often requires short evolution times, which can preclude exponential reductions in experiment numbers and make the SMC approximation more error prone.
Source: p. 3
Abstract
from arXiv · showhide
Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of foundational physics. Machine-learning enhanced by quantum simulators has been proposed as a route to improve the computational cost of performing these studies. Here we interface two different quantum systems through a classical channel - a silicon-photonics quantum simulator and an electron spin in a diamond nitrogen-vacancy centre - and use the former to learn the latter's Hamiltonian via Bayesian inference. We learn the salient Hamiltonian parameter with an uncertainty of approximately $10^{-5}$. Furthermore, an observed saturation in the learning algorithm suggests deficiencies in the underlying Hamiltonian model, which we exploit to further improve the model itself. We go on to implement an interactive version of the protocol and experimentally show its ability to characterise the operation of the quantum photonic device. This work demonstrates powerful new quantum-enhanced techniques for investigating foundational physical models and characterising quantum technologies.
Methods
The experiment paired an NV− centre in diamond with a silicon-photonic device and used photonic measurements to estimate the likelihoods needed for Bayesian Hamiltonian learning. An entanglement-based scheme implemented both standard and interactive quantum likelihood evaluation, with all IQLE evolutions forward in time.
Diamond NV−centre and setup
- The diamond NV− centre was measured at room temperature in a 5 mT magnetic field aligned to its axis, lifting the ms = ±1 spin-state degeneracy.ODMR was used to align the field and indicated the ms = 0 to ms = −1 transition.Source: Methods · p. 4
Silicon quantum photonic device and setup
- The SOI photonic device used silicon waveguides, single-photon-pair sources, thermo-optical phase shifters and near-0.5-reflectivity MMI beam splitters; a classical computer processed photon statistics and used Bayesian inference to update the Hamiltonian model.Each phase-shifter was individually controlled by an electronic driver with 12-bit resolution.Source: Methods · p. 4
Estimation of the likelihoods on the photonic chip
- In the photonic device, QLE likelihood is LQLE = |⟨ψ|e−iH(x)t|ψ⟩|², obtained by setting U = 1 and V = e−iH(x)t in an entanglement-based technique [35].Source: Methods · p. 5
- For IQLE, the chip implemented U = e^(iH(x−)t) and V = e^(-iH(x)t), keeping every evolution forward in time at the cost of added system–ancilla entanglement.The required IQLE quantum channel was provided by entanglement generated in the photon sources.Source: Methods · p. 5