Dominant strategies in two-qubit quantum computations

Faisal Shah Khan, Simon J. D. Phoenix

Faisal Shah Khan

Nash equilibrium is a solution concept in non-strictly competitive, noncooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, noncooperative game model is presented here for two-qubit quantum computations that allows for the characterization of Nash equilibrium in these computations via the inner product of their state space. Nash equilibrium outcomes are optimal under given constraints and therefore offer a game-theoretic measure of constrained optimization of two-qubit quantum computations.

Frank K. Wilhelm

A measurement on a macroscopic quantum system does not, in general, lead to a projection of the wave function in the basis of the detector as predicted by von Neumann's postulate. Hence, it is a question of fundamental interest, how the preferred basis onto which the state is projected is selected out of the macroscopic Hilbert space of the system. Detector-dominated von Neumann measurements are also desirable for both quantum computation and verification of quantum mechanics on a macroscopic scale. The connection of these questions to the predictions of the spin-boson model is outlined. I propose a measurement strategy, which uses the entanglement of the qubit with a weakly damped harmonic oscillator. It is shown that the degree of entanglement controls the degree of renormalization of the qubit and identify that this is equivalent to the degree to which the measurement is detector dominated. This measurement very rapidly decoheres the initial state, but the thermalization is slow. The implementation in Josephson quantum bits is described and it is shown that this strategy also has practical advantages for the experimental realization.

Masashi Kimura

昌史 木村

Paolo Andrea Erdman, Robert Czupryniak, Bibek Bhandari +4 more

Abstract Feedback control of open quantum systems is of fundamental importance for practical applications in various contexts, ranging from quantum computation to quantum error correction and quantum metrology. Its use in the context of thermodynamics further enables the study of the interplay between information and energy. However, deriving optimal feedback control strategies is highly challenging, as it involves the optimal control of open quantum systems, the stochastic nature of quantum measurement, and the inclusion of policies that maximize a long-term time- and trajectory-averaged goal. In this work, we employ a reinforcement learning approach to automate and capture the role of a quantum Maxwell’s demon: the agent takes the literal role of discovering optimal feedback control strategies in qubit-based systems that maximize a trade-off between measurement-powered cooling and measurement efficiency. Considering weak or projective quantum measurements, we explore different regimes based on the ordering between the thermalization, the measurement, and the unitary feedback timescales, finding different and highly non-intuitive, yet interpretable, strategies. In the thermalization-dominated regime, we find strategies with elaborate finite-time thermalization protocols conditioned on measurement outcomes. In the measurement-dominated regime, we find that optimal strategies involve adaptively measuring different qubit observables reflecting the acquired information, and repeating multiple weak measurements until the quantum state is ‘sufficiently pure’, leading to random walks in state space. Finally, we study the case when all timescales are comparable, finding new feedback control strategies that considerably outperform more intuitive ones. We discuss a two-qubit example where we explore the role of entanglement and conclude discussing the scaling of our results to quantum many-body systems.