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Register a new userConservation-law-based global bounds to quantum optimal control
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Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related inequalities, but such bounds utilize only coarse system information, and loosen significantly in the presence of constraints and complex interaction dynamics. We show that an integral-equation-based formulation of conservation laws in quantum dynamics leads to a systematic framework for identifying fundamental limits to any quantum control scenario. We demonstrate the utility of our bounds in three scenarios -- three-level driving, decoherence suppression, and maximum-fidelity gate implementations -- and show that in each case our bounds are tight or nearly so. Global bounds complement local-optimization-based designs, illuminating performance levels that may be possible as well as those that cannot be surpassed.
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Fundamental quantum electrodynamical (QED) processes such as spontaneous emission and electron-photon scattering encompass a wealth of phenomena that form one of the cornerstones of modern science and technology. Conventionally, calculations in QED and in other field theories assume that incoming particles are single-momentum states. The possibility that coherent superposition states, i.e. shaped wavepackets, will alter the result of fundamental scattering processes is thereby neglected, and is instead assumed to sum to an incoherent (statistical) distribution in the incoming momentum. Here, we show that free-electron wave-shaping can be used to engineer quantum interferences that alter the results of scattering processes in QED. Specifically, the interference of two or more pathways in a QED process (such as photon emission) enables precise control over the rate of that process. As an example, we apply our concept to Bremsstrahlung, a ubiquitous phenomenon that occurs, for instance, in X-ray sources for state-of-the-art medical imaging, security scanning, materials analysis, and astrophysics. We show that free electron wave-shaping can be used to tailor both the spatial and the spectral distribution of emitted photons, enhancing their directionality and monochromaticity, and adding more degrees of freedom that make emission processes like Bremsstrahlung more versatile. The ability to tailor the spatiotemporal attributes of photon emission via quantum interference provides a new degree of freedom in shaping radiation across the entire electromagnetic spectrum. More broadly, the ability to tailor general QED processes through the shaping of free electrons opens up new avenues of control in processes ranging from optical excitation processes (e.g., plasmon and phonon emission) in electron microscopy to free electron lasing in the quantum regime.
The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering. Today, the increasing demand for applied quantum technologies requires to adapt this level of control to individual quantum systems. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback. Successful implementations thus far include experiments on the level of optical and atomic systems. Here we demonstrate real-time optimal control of the quantum trajectory of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3 times the zero point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of $n=0.56pm0.02$ quanta, realizing quantum ground state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems.
The atmospheric turbulence is the main factor that influences quantum properties of propagating optical signals and may sufficiently degrade the performance of quantum communication protocols. The probability distribution of transmittance (PDT) for free-space channels is the main characteristics of the atmospheric links. Applying the law of total probability, we derive the PDT by separating the contributions from turbulence-induced beam wandering and beam-spot distortions. As a result, the obtained PDT varies from log-negative Weibull to truncated log-normal distributions depending on the channel characteristics. Moreover, we show that the method allows one to consistently describe beam tracking, a procedure which is typically used in practical long-distance free-space quantum communication. We analyze the security of decoy-state quantum key exchange through the turbulent atmosphere and show that beam tracking does not always improves quantum communication.
In Ref. [Katz et al., arXiv:2007.08770 (2020)], we present a mechanism and optimal procedures for mapping the quantum state of photons onto an optically inaccessible macroscopic state of noble-gas spins, which functions as a quantum memory. Here we introduce and analyze a detailed model of the memory operation. We derive the equations of motion for storage and retrieval of non-classical light and design optimal control strategies. The detailed model accounts for quantum noise and for thermal atomic motion, including the effects of optical mode structure and imperfect anti-relaxation wall coating. We conclude with proposals of practical experimental configurations of the memory, with lifetimes ranging from seconds to hours.
We study the minimum time to implement an arbitrary two-qubit gate in two heteronuclear spins systems. We give a systematic characterization of two-qubit gates based on the invariants of local equivalence. The quantum gates are classified into four classes, and for each class the analytical formula of the minimum time to implement the quantum gates is explicitly presented. For given quantum gates, by calculating the corresponding invariants one easily obtains the classes to which the quantum gates belong. In particular, we analyze the effect of global phases on the minimum time to implement the gate. Our results present complete solutions to the optimal time problem in implementing an arbitrary two-qubit gate in two heteronuclear spins systems. Detailed examples are given to typical two-qubit gates with or without global phases.
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