6 pags., 4 figs. ; We study the effect of action noise on state-to-state control protocols. Action noise creates dephasing in the instantaneous eigenbasis of the Hamiltonian and hampers the fidelity of the final state with respect to the target state. We find that for shorter protocols the noise more strongly influences the dynamics and degrades fidelity. We suggest improving the fidelity by inducing stronger dephasing rates along the process. The effects of action noise on the dynamics and its manipulation is described for a general Hamiltonian and is then studied by examples. ; This work was funded by the US Army Research Office under Contract W911NF- 15-1-0250 and the Basque Government (Grant No. IT986-16), MINECO/FEDER,UE (Grants No. FIS2015-67161-P and No. FIS2015-70856-P), and QUITEMAD+CM S2013-ICE2801. ; Peer Reviewed
6 pags., 4 figs. ; We demonstrate that it is possible to implement a quantum perceptron with a sigmoid activation function as an efficient, reversible many-body unitary operation. When inserted in a neural network, the perceptron's response is parameterized by the potential exerted by other neurons. We prove that such a quantum neural network is a universal approximator of continuous functions, with at least the same power as classical neural networks. While engineering general perceptrons is a challenging control problem - also defined in this work - the ubiquitous sigmoid-response neuron can be implemented as a quasi-adiabatic passage with an Ising model. In this construct, the scaling of resources is favorable with respect to the total network size and is dominated by the number of layers. We expect that our sigmoid perceptron will have applications also in quantum sensing or variational estimation of many-body Hamiltonians. ; We acknowledge funding from MINECO/FEDER Project FIS2015-70856-P, CAM PRICYT project QUITEMAD+CM S2013-ICE2801, and Basque Government (Grant No. IT986-16).
14 pags., 4 figs., 4 apps. -- Open Access funded by Creative Commons Atribution Licence 3.0 ; A systematic approach to design robust control protocols against the influence of different types of noise is introduced. We present control schemes which protect the decay of the populations avoiding dissipation in the adiabatic and nonadiabatic regimes and minimize the effect of dephasing. The effectiveness of the protocols is demonstrated in two different systems. Firstly, we present the case of population inversion of a two-level system in the presence of either one or two simultaneous noise sources. Secondly, we present an example of the expansion of coherent and thermal states in harmonic traps, subject to noise arising from monitoring and modulation of the control, respectively. ; Funding by the Israeli Science Foundation, the US Army Research Office under Contract W911NF- 15-1-0250, the Basque Government (Grant No. IT986-16), MINECO/FEDER,UE (Grants No. FIS2015-70856-P and No. FIS2015-67161-P), and QUITEMAD+CM S2013-ICE2801.
10 pags., 6 figs., 2 apps. -- Open Access funded by Creative Commons Atribution Licence 3.0 ; We propose speeding up a single ion heat pump based on a tapered ion trap. If a trapped ion is excited in an oscillatory motion axially the radial degrees of freedom are cyclically expanded and compressed such that heat can be pumped between two reservoirs coupled to the ion at the turning points of oscillation. Through the use of invariant-based inverse engineering we can speed up the process without sacrificing the efficiency of each heat pump cycle. This additional control can be supplied with additional control electrodes or it can be encoded into the geometry of the radial trapping electrodes. We present a novel insight into how speed up can be achieved through the use of inverted harmonic potentials and verify the stability of such trapping conditions. ; We acknowledge funding from MINECO/FEDER (Grants No. FIS2015-70856-P and No. FIS2015-67161-P), CAM PRICYT project QUITEMAD+CM S2013-ICE2801, and Basque Government (Grant No. IT986-16). KS acknowledges support by the German Science Foundation through the Single Ion Heat Engine project.
8 pags., 5 figs. ; The quantum perceptron is a fundamental building block for quantum machine learning. This is a multidisciplinary feld that incorporates abilities of quantum computing, such as state superposition and entanglement, to classical machine learning schemes. Motivated by the techniques of shortcuts to adiabaticity, we propose a speed-up quantum perceptron where a control feld on the perceptron is inversely engineered leading to a rapid nonlinear response with a sigmoid activation function. This results in faster overall perceptron performance compared to quasi-adiabatic protocols, as well as in enhanced robustness against imperfections in the controls. ; We acknowledge fnancial support from Spanish Government via PGC2018-095113-B-I00 (MCIU/AEI/FEDER, UE), Basque Government via IT986-16, as well as from QMiCS (820505) and OpenSuperQ (820363) of the EU Flagship on Quantum Technologies, and the EU FET Open Grant Quromorphic (828826). J. C. acknowledges the Ramón y Cajal program (RYC2018- 025197-I) and the EUR2020-112117 Project of the Spanish MICINN,as well as support from the UPV/EHU through the Grant EHUrOPE. X. C. acknowledges NSFC (12075145), SMSTC (2019SHZDZX01-ZX04, 18010500400 and 18ZR1415500), the Program for Eastern Scholar and the Ramón y Cajal program of the Spanish MICINN (RYC-2017-22482). E. T. acknowledges support from Project PGC2018-094792-B-I00 (MCIU/AEI/FEDER,UE), CSIC Research Platform PTI-001, and CAM/FEDER Project No. S2018/TCS-4342 (QUITEMAD-CM). ; Peer reviewed
7 pags., 3 figs., 1 tab. ; Two-dimensional (2D) systems with time-dependent controls admit a quadratic Hamiltonian modeling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some systems are not separable into independent modes by a point transformation. For these "coupled systems"2D invariants may still guide the Hamiltonian design. The theory to perform the inversion and two application examples are provided: (i) We control the deflection of wave packets in transversally harmonic wave guides and (ii) we design the state transfer from one coupled oscillator to another. ; This work was supported by the Basque Country Government (Grant No. IT986-16), and by PGC2018-101355- B-I00 (MCIU/AEI/FEDER,UE). E.T. acknowledges support from PGC2018-094792-B-I00 (MCIU/AEI/FEDER,UE), CSIC Research Platform PTI-001, and CAM/FEDER No. S2018/TCS- 4342 (QUITEMAD-CM).
6 pags., 4 figs. -- Correction: Missing information in Ref. [40] has been inserted (9 July 2021) ; We propose to optimally control the harmonic potential of a levitated nanoparticle to quantum delocalize its center-of-mass motional state to a length scale orders of magnitude larger than the quantum zero-point motion. Using a bang-bang control of the harmonic potential, including the possibility of inverting it, the initial ground-state-cooled levitated nanoparticle coherently expands to large scales and then contracts to the initial state in a time-optimal way. We show that this fast loop protocol can be used to enhance force sensing as well as to dramatically boost the entangling rate of two weakly interacting nanoparticles. We parameterize the performance of the protocol, and therefore the macroscopic quantum regime that could be explored, as a function of displacement and frequency noise in the nanoparticle's center-of-mass motion. This noise analysis accounts for the sources of decoherence relevant to current experiments. ; This work has received funding from the MaQSens project under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. [736943]). This work has received funding from the QXtreme project of the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. [951234]). T. W. acknowledges financial support from the Alexander von Humboldt foundation. E. T. acknowledges financial support from Project No. PGC2018-094792-B-I00 (MCIU/AEI/ FEDER,UE), CSIC Research Platform PTI-001, and CAM/ FEDER Project No. S2018/TCS-4342 (QUITEMAD-CM).
54 pags., 15 figs., 5 tabs., 2 apps. ; Shortcuts to adiabaticity (STA) are fast routes to the final results of slow, adiabatic changes of the controlling parameters of a system. The shortcuts are designed by a set of analytical and numerical methods suitable for different systems and conditions. A motivation to apply STA methods to quantum systems is to manipulate them on timescales shorter than decoherence times. Thus shortcuts to adiabaticity have become instrumental in preparing and driving internal and motional states in atomic, molecular, and solid-state physics. Applications range from information transfer and processing based on gates or analog paradigms to interferometry and metrology. The multiplicity of STA paths for the controlling parameters may be used to enhance robustness versus noise and perturbations or to optimize relevant variables. Since adiabaticity is a widespread phenomenon, STA methods also extended beyond the quantum world to optical devices, classical mechanical systems, and statistical physics. Shortcuts to adiabaticity combine well with other concepts and techniques, in particular, with optimal control theory, and pose fundamental scientific and engineering questions such as finding speed limits, quantifying the third law, or determining process energy costs and efficiencies. Concepts, methods, and applications of shortcuts to adiabaticity are reviewed and promising prospects are outlined, as well as open questions and challenges ahead. ; This work was supported by the Basque Country Government (Grant No. IT986-16); PGC2018-101355-B-100 (MCIU/AEI/FEDER, UE); PGC2018-094792-B-100 (MCIU/AEI/FEDER, EU); CAM/ FEDER Project No. S2018/TCS-4342 (QUITEMAD-CM); and by Programme Investissements d'Avenir under the Grant ANR-11-IDEX-0002-02, reference ANR-10-LABX0037-NEXT, as well as the Grant ANR-18-CE30-0013.
We propose an inverse method to accelerate without final excitation the adiabatic transport of a Bose-Einstein condensate. The method is based on a partial extension of the Lewis-Riesenfeld invariants and provides transport protocols that satisfy exactly the no-excitation conditions without approximations. This inverse method is complemented by optimizing the trap trajectory with respect to different physical criteria and by studying the effect of perturbations such as anharmonicities and noise. ; Basque Government/IT472-10 ; Ministerio de Ciencia e Innovacion/FIS2009-12773-C02-01 ; Basque Government/BFI08.151 ; Juan de la Cierva Programme ; National Natural Science Foundation of China/60806041
We develop energy efficient, continuous microwave schemes to couple electron and nuclear spins, using phase or amplitude modulation to bridge their frequency difference. These controls have promising applications in biological systems, where microwave power should be limited, as well as in situations with high Larmor frequencies due to large magnetic fields and nuclear magnetic moments. These include nanoscale NMR where high magnetic fields achieves enhanced thermal nuclear polarization and larger chemical shifts. Our controls are also suitable for quantum information processors and nuclear polarization schemes. ; E. S. and J. C. acknowledge financial support from Spanish MINECO/FEDER FIS2015-69983-P, Basque Government IT986-16, as well as from QMiCS (820505) and OpenSuperQ (820363) of the EU Flagship on Quantum Technologies. J. C. acknowledges support by the Juan de la Cierva Grant No. IJCI-2016-29681. E. T. and J. J. G. R. acknowledge support from Spanish MINECO/FEDER Project No. FIS2015-70856-P, No. FIS2016-81891-REDT and CAMPRICYT ProjectQUITEMAD þ CMNo. S2013- ICE2801. M. B. P. acknowledges support by the ERC Synergy grant BioQ (Grant No. 319130), the EU project HYPERDIAMOND, the QuantERA project NanoSpin, the BMBF project DiaPol, the state of Baden-Württemberg through bwHPC, and the German Research Foundation (DFG) through Grant No. INST 40/467-1 FUGG. This material is also based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advance Scientific Computing Research (ASCR), Quantum Algorithms Teams project under field work proposal ERKJ335. ; Peer Reviewed
7 págs., 6 figs. ; Shortcuts to adiabaticity let a system reach the results of a slow adiabatic process in a shorter time. We propose to quantify the >energy cost> of the shortcut by the energy consumption of the system enlarged by including the control device. A mechanical model where the dynamics of the system and control device can be explicitly described illustrates that a broad range of possible values for the consumption is possible, including zero (above the adiabatic energy increment) when friction is negligible and the energy given away as negative power is stored and reused by perfect regenerative braking. ; We acknowledge funding from the Basque government (Grant No. IT986-16), MINECO/FEDER, UE (Grants No. FIS2015- 67161-P and No. FIS2015-70856-P), and QUITEMAD+CM S2013-ICE2801. ; Peer Reviewed
