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arXiv:2206.00246 · Physical Review A

Optimizing measurement-based cooling by reinforcement learning

Jia‐shun Yan, Jun Jing

Published Sep 30, 2022• 2 citations
arXivHTMLPDF

Abstract

Conditional cooling-by-measurement holds a significant advantage over its unconditional (nonselective) counterpart in the average-population-reduction rate. However, it has a clear weakness with respect to the limited success probability of finding the detector in the measured state. In this work, we propose an optimized architecture to cool down a target resonator, which is initialized as a thermal state, using an interpolation of conditional and unconditional measurement strategies. An optimal measurement-interval ${\ensuremath{\tau}}_{\mathrm{opt}}^{u}$ for unconditional measurement is analytically derived, which is inversely proportional to the collective dominant Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{d}$ as a function of the resonator's population in the end of the last round. A cooling algorithm under global optimization by reinforcement learning results in the maximum value for the cooperative cooling performance, an indicator to measure the comprehensive cooling efficiency for arbitrary cooling-by-measurement architecture. In particular, the average population of the target resonator under only 16 rounds of measurements can be reduced by four orders in magnitude with a success probability of about $30%$.

DOI
10.1103/physreva.106.033124

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•Jun 15, 2021•0 citations
Conditional cooling-by-measurement holds a significant advantage over its unconditional (nonselective) counterpart in the average-population-reduction rate. However, it has a clear weakness with respect to the limited success probability of finding the detector in the measured state. In this work, we propose an optimized architecture to cool down a target resonator, which is initialized as a thermal state, using an interpolation of conditional and unconditional measurement strategies. An optimal measurement-interval \ensuremathτoptu{\ensuremath{\tau}}_{\mathrm{opt}}^{u}\ensuremathτoptu​ for unconditional measurement is analytically derived, which is inversely proportional to the collective dominant Rabi frequency \ensuremathΩd{\mathrm{\ensuremath{\Omega}}}_{d}\ensuremathΩd​ as a function of the resonator's population in the end of the last round. A cooling algorithm under global optimization by reinforcement learning results in the maximum value for the cooperative cooling performance, an indicator to measure the comprehensive cooling efficiency for arbitrary cooling-by-measurement architecture. In particular, the average population of the target resonator under only 16 rounds of measurements can be reduced by four orders in magnitude with a success probability of about 3030%30.
We present a simultaneous-cooling protocol for a double-resonator system via projective measurements on an ancillary VVV-type qutrit. Through repeated measurements on the ground state of the ancillary system, the two resonators can be cooled down to their respective ground states from thermal states. With respect to the measurement-based cooling, an optimized measurement interval ${\ensuremath{\tau}}_{\mathrm{opt}}$ is analytically obtained, which is inversely proportional to the collective thermal Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{th}}$ as a function of the resonators' average population of the last round. Under about only 20 optimized measurements, the average population of the target resonators can be reduced by six orders in magnitude. Our simultaneous or collective cooling protocol is scalable to the systems with more numbers of resonators and robust to the fluctuation in the resonator frequency. Also we discuss the robustness of our cooling protocol against the thermal environment and the measurement error.
Abstract Nondeterministic measurement‐based techniques are efficient in reshaping the population distribution of a quantum system but suffer from a limited success probability of holding the system in the target state. To save the experimental cost, a two‐step protocol is proposed to cool a resonator down to the ground state with a near‐unit probability by exploiting the state‐engineering mechanisms of both conditional and unconditional measurements on an ancillary qubit. In the first step, the unconditional measurements on the ancillary qubit are applied to reshape the target resonator from a thermal state to a reserved Fock state. The measurement sequence can be efficiently optimized by reinforcement learning for maximum fidelity. In the second step, the population on the reserved state can be faithfully transferred in a stepwise way to the resonator's ground state with a near‐unit fidelity by the conditional measurements on the qubit. Properly designing the projection operator and the measurement interval enables the Kraus operator to act as a lowering operator for neighboring Fock states. Through dozens of measurements in all, the initial thermal average population of the resonator can be reduced by five orders in magnitude with a success probability of over 95%.
A quantum resonator in a thermal-equilibrium state with a high temperature has a large average population and is featured with significant occupation over Fock states with a high excitation number. The resonator could be cooled down via continuous measurements on the ground state of a coupled two-level system (qubit). We find, however, that the measurement-induced cooling might become inefficient in the high-temperature regime. Beyond the conventional strategy, we introduce strong driving between the excited state of the qubit and an external level. It can remarkably broaden the cooling range in regard to the nonvanishing populated Fock states of the resonator. Without any precooling procedure, our strategy allows a significant reduction of the populations over Fock states with a high excitation number, giving rise to nondeterministic ground-state cooling after a sequence of measurements. The driving-induced fast transition constrains the resonator and the ancillary qubit at their ground state upon measurement and then simulates the quantum Zeno effect. Our protocol is applied to cool down a high-temperature magnetic resonator. Additionally, it is generalized to a hybrid cooling protocol by interpolating the methods with and without strong driving, which can accelerate the cooling process and increase the overlap between the final state of the resonator and its ground state.
Reinforcement learning with neural networks (RLNN) has recently demonstrated great promise for many problems, including some problems in quantum information theory. In this work, we apply RLNN to quantum hypothesis testing and determine the optimal measurement strategy for distinguishing between multiple quantum states {ρj} while minimizing the error probability. In the case where the candidate states correspond to a quantum system with many qubit subsystems, implementing the optimal measurement on the entire system is experimentally infeasible. We use RLNN to find locally-adaptive measurement strategies that are experimentally feasible, where only one quantum subsystem is measured in each round. We provide numerical results which demonstrate that RLNN successfully finds the optimal local approach, even for candidate states up to 20 subsystems. We additionally demonstrate that the RLNN strategy meets or exceeds the success probability for a modified locally greedy approach in each random trial.While the use of RLNN is highly successful for designing adaptive local measurement strategies, in general a significant gap can exist between the success probability of the optimal locally-adaptive measurement strategy and the optimal collective measurement. We build on previous work to provide a set of necessary and sufficient conditions for collective protocols to strictly outperform locally adaptive protocols. We also provide a new example which, to our knowledge, is the simplest known state set exhibiting a significant gap between local and collective protocols. This result raises interesting new questions about the gap between theoretically optimal measurement strategies and practically implementable measurement strategies.
Reinforcement learning with neural networks (RLNN) has recently demonstrated great promise for many problems, including some problems in quantum information theory. In this work, we apply reinforcement learning to quantum hypothesis testing, where one designs measurements that can distinguish between multiple quantum states {ρj}|j=1mwhile minimizing the error probability. Although the Helstrom measurement is known to be optimal when there are m=2 states, the general problem of finding a minimal-error measurement is challenging. Additionally, in the case where the candidate states correspond to a quantum system with many qubit subsystems, implementing the optimal measurement on the entire system may be impractical. In this work, we develop locally-adaptive measurement strategies that are experimentally feasible in the sense that only one quantum subsystem is measured in each round. RLNN is used to find the optimal measurement protocol for arbitrary sets of tensor product quantum states. Numerical results for the network performance are shown. In special cases, the neural network testing-policy achieves the same probability of success as the optimal collective measurement.
A quantum resonator in a thermal-equilibrium state with a high temperature has a large average exciton number and has a significant occupation over the high Fock-states. The resonator could be cooled down through constant measurements on the ground state of a coupled two-level system (qubit). We find, however, that the measurement-induced cooling might become inefficient in the high-temperature regime. Beyond the conventional strategy, we propose a measurement-induced-cooling protocol via acting a strong interaction outside the space of the resonator-qubit system. In particular, the excited state of the two-level system is coupled to an outside state through a driving field. The strong interaction between these two states can greatly enlarge the cooling range in regard to the non-vanishing populated Fock-states of the resonator. Without any pre-cooling procedure, acting outside allows a significant reduction on the populations over the high Fock-states and then the ground-state cooling after a sequence of measurements. The fast transition induced by a strong acting-outside constrains the ancillary system at its ground state and then simulates a quantum Zeno effect, that consistently provides a possible realization for measurements required for cooling. Our protocol is applied to cool down a high-temperature magnetic resonator. It is then generalized to a hybrid cooling protocol by interpolating the methods with and without acting on the outside, which can accelerate the cooling process and promote the overlap between the final state of the resonator and its ground state.