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arXiv:2111.04624

Optimal purification of a spin ensemble by quantum-algorithmic feedback

Jackson, Daniel M., Urs Haeusler, Leon Zaporski, Jonathan H. Bodey, Noah Shofer, Edmund Clarke, Maxime Hugues, Mete Atatüre, Claire Le Gall, Dorian A. Gangloff

Published Nov 8, 2021• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2111.04624

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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.
We propose a technique for polarizing and cooling finite many-body systems using feedback control. The technique requires the system to have one collective degree of freedom conserved by the internal dynamics. The fluctuations of other degrees of freedom are then converted into the growth of the conserved one. The proposal is validated using numerical simulations of classical and quantum spin systems in a setting representative of Nuclear Magnetic Resonance experiments. In particular, we were able to achieve 90 percent polarization for a lattice of 1000 classical spins starting from an unpolarized infinite temperature state.
We propose a technique for polarizing and cooling finite many-body classical systems using feedback control. The technique requires the system to have one collective degree of freedom conserved by the internal dynamics. The fluctuations of other degrees of freedom are then converted into the growth of the conserved one. The proposal is validated using numerical simulations of classical spin systems in a setting representative of nuclear magnetic resonance experiments. In particular, we were able to achieve 90% polarization for a lattice of 1000 classical spins starting from an unpolarized infinite temperature state.
Cooling techniques are essential to understand fundamental thermodynamic questions of the low-energy states of physical systems, furthermore they are at the core of practical applications of quantum information science. In quantum computing, this controlled preparation of highly pure quantum states is required from the state initialization of most quantum algorithms to a reliable supply of ancilla qubits that satisfy the fault-tolerance threshold for quantum error correction. Heat-bath algorithmic cooling has been shown to purify qubits by controlled redistribution of entropy and multiple contact with a bath, not only for ensemble implementations but also for technologies with strong but imperfect measurements. In this paper, we show that correlated relaxation processes between the system and environment during rethermalization when we reset hot ancilla qubits, can be exploited to enhance purification. We show that a long standing upper bound on the limits of algorithmic cooling Schulman et al (2005 Phys. Rev. Lett. 94 , 120501) can be broken by exploiting these correlations. We introduce a new tool for cooling algorithms, which we call 'state-reset', obtained when the coupling to the environment is generalized from individual-qubits relaxation to correlated-qubit relaxation. Furthermore, we present explicit improved cooling algorithms which lead to an increase of purity beyond all the previous work, and relate our results to the Nuclear Overhauser Effect.