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Indian Control Conference

Feedback-Based Quantum Control of Nuclei Spin in Ensembles

Vishesh Kaushik, Navin Khaneja

Published Dec 9, 2024• 2 citations
Publisher

Abstract

In this paper, we present a feedback-based framework for controlling the evolution of quantum spin states of nuclei within an ensemble. This approach allows for the selective excitation of nuclear spin states within specific pass bands of Larmor frequencies while leaving the nuclei outside the pass bands undisturbed. The control input sequence is designed in simulation and implemented using radio frequency pulses in the real system.

DOI
10.1109/icc64753.2024.10883723

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In this paper, we present a feedback-based framework for controlling the evolution of quantum spin states of nuclei within an ensemble. This approach allows for the selective excitation of nuclear spin states within specific pass bands of Larmor frequencies while leaving the nuclei outside the pass bands undisturbed. The control input sequence is designed in simulation and implemented using radio frequency pulses in the real system.
Purifying a high-temperature ensemble of quantum particles towards a known state is a key requirement to exploit quantum many-body effects. An alternative to passive cooling, which brings a system to its ground state, is based on feedback to stabilise the system actively around a target state. This alternative, if realised, offers additional control capabilities for the design of quantum states. Here we present a quantum feedback algorithm capable of stabilising the collective state of an ensemble from an infinite-temperature state to the limit of single quanta. We implement this on ~50,000 nuclei in a semiconductor quantum dot, and show that the nuclear-spin fluctuations are reduced 83-fold down to 10 spin macrostates. While our algorithm can purify a single macrostate, system-specific inhomogeneities prevent reaching this limit. Our feedback algorithm further engineers classically correlated ensemble states via macrostate tuning, weighted bimodality, and latticed multistability, constituting a pre-cursor towards quantum-correlated macrostates.
Purifying a high-temperature ensemble of quantum particles toward a known state is a key requirement to exploit quantum many-body effects.An alternative to passive cooling, which brings a system to its ground state, is active feedback, which stabilizes the system at a chosen target state.This alternative, if realized, offers additional control capabilities for the design of quantum states.Here we present a feedback algorithm applied to a quantum system, which is capable of stabilizing the collective state of an ensemble from its maximum entropy state to the limit of single quantum fluctuations.Our algorithmic approach maximizes the rate of state purification given the system's physical constants; thus it remains the optimal feedback approach even in the presence of dissipation and disorder.We test experimentally the robustness of this feedback on the highly inhomogeneous nuclear-spin ensemble of a semiconductor quantum dot, reducing nuclear-spin fluctuations 83-fold, down to 5.7(2) spin macrostates.Simulations demonstrate that without system-specific inhomogeneities, our algorithm can purify the system down to single-spin fluctuations.Further, we exploit our algorithmic approach to tailor nontrivial nuclear-spin distributions that go beyond simple polarization, including weighted bimodality and latticed multistability.This control is a precursor toward quantum-correlated macrostates, which an extended version of our algorithm could generate in homogeneous systems.
Nuclear magnetic resonance (NMR) spectroscopy has proven to be a facile means of achieving small-scale demonstrations of quantum information processing. This was in large part made possible by the sophisticated methods of quantum control that have been developed by the NMR community over a span of more than 50 years. The traditional control methods, already perhaps the most complex examples of open-loop control available, were nevertheless designed primarily to assist in identifying the physical parameters of the underlying spin system, rather than to control the system with high precision. We have therefore extended the traditional methods in a variety of ways so as to achieve precise control, by taking advantage of prior knowledge of the physical parameters as determined by traditional methods. Due to the experimental challenges of real-time control, these developments relied upon our ability to simulate the evolution of the system under the action of radio-frequency control fields with essentially arbitrary precision, subject only to the available computing power. This talk presents an overview of our work in quantum control together with some of the on-going challenges still facing us
We propose a new approach to the measurement of a single spin state, based on nuclear magnetic resonance (NMR) techniques and inspired by the coherent control over many-body systems envisaged by quantum information processing. A single target spin is coupled via the magnetic dipolar interaction to a large ensemble of spins. Applying radio frequency pulses, we can control the evolution so that the spin ensemble reaches one of two orthogonal states whose collective properties differ depending on the state of the target spin and are easily measured. We first describe this measurement process using quantum gates; then we show how equivalent schemes can be defined in terms of the Hamiltonian and thus implemented under conditions of real control, using well established NMR techniques. We demonstrate this method with a proof of principle experiment in ensemble liquid state NMR and simulations for small spin systems.
Controlling ensembles of weakly coupled spins typically requires computationally expensive multispin optimisations. We present a compact framework that enables control of weakly coupled spin systems (of any spin), but using RF pulses optimised for a single spin-1/2. We do this by explicitly creating a GRAPE pulse with fixed 'active' evolution times using single spin-1/2 methods, and pulsing on one spin at a time. By enforcing this form uniformly across offsets ('band-schematic' pulses),chemical shift and scalar coupling evolution of the entire system can be precisely controlled. We demonstrate the approach by constructing band-schematic pulses and a continuously irradiated joint INEPT (JINEPT) that achieves band-selective transfer Iz→2IzSzI_z \rightarrow 2I_zS_zIz​→2Iz​Sz​. The framework is implemented in the software Seedless, which both rapidly generates such pulses and analyses the schematic form of arbitrary pulses, enabling robust multi-spin control, without multi-spin optimisation.