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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
The paper develops a quantum-learning protocol that uses an entanglement-based silicon-photonic device to evaluate likelihoods for Hamiltonian learning. The approach implements forward-time evolutions for interactive quantum learning, with additional system–ancilla entanglement as a trade-off.
Problem
Hamiltonian-learning likelihoods must be obtained from quantum operations and measurements in an experimentally implementable protocol.
Method
The protocol uses an entanglement-based quantum channel in a silicon-photonic device to evaluate likelihoods for quantum and interactive quantum learning.
Results
The entanglement-based implementation realizes interactive quantum learning using only forward-time evolutions instead of backwards time evolution.
Takeaways & Limitations
The approach is amenable to analogue quantum simulators, while requiring additional entanglement between the system and an ancillary qubit.
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 methods combine an aligned diamond NV− centre with an integrated photonic device and use entanglement-based measurements to obtain QLE and IQLE likelihoods. The protocol estimates these likelihoods from single-qubit control operations and photon-coincidence measurements.
- Diamond NV− centre and setup: A CVD-grown electronic-grade diamond hosts the negative NV− centre at room temperature in a 5mT magnetic field aligned to its axis.The sample has natural-abundance nitrogen impurities of 1 ppb, and alignment is performed using optically detected magnetic resonance.
- Photonic implementation: An entanglement-based technique in the integrated photonic device produces the entangled states required to calculate the photonic inner product.The realised scheme uses control states and device operations denoted U and V.
- Likelihood estimation: QLE uses the likelihood LQLE = |⟨ψ|e−i H(x)t|ψ⟩|2, obtained by setting U = 1 and V = e−i H(x)t.The likelihood is obtained through the entanglement-based measurement scheme described for the photonic device.
- Likelihood estimation: IQLE uses LIQLE = |⟨ψ|ei H(x−)te−i H(x)t|ψ⟩|2 with U = e−i H(x−)t and V = e−i H(x)t.The IQLE quantum channel is supplied by entanglement generated in the sources, with all evolutions forward in time.
- Measurement procedure: The probabilities p+ and p+i are obtained through single-qubit operations on the control qubit followed by photon-coincidence measurements.These probabilities correspond to projective measurements in the relevant control-qubit eigenbases.