We propose a scheme to control the evolution of a two-level quantum system in the strong coupling regime based on the idea of reverse-engineering. A coherent control field is designed to drive both closed and open two-level quantum systems along user predefined evolution trajectory without utilizing the rotating-wave approximation (RWA). As concrete examples, we show that complete population inversion, an equally weighted coherent superposition, and even oscillationlike dynamics can be achieved. As there are no limitations on the coupling strength between the control field and matter, the scheme is attractive for applications such as accelerating desired system dynamics and fast quantum information processing.
We show that specific quantum noise, acting as an open-system reservoir for non-locally entangled atoms, can serve to preserve rather than degrade joint coherence. This creates a new type of long-time control over hiding and recovery of quantum entanglement.
We put forward reverse engineering protocols to shape in time the components of the magnetic field to manipulate a single spin, two independent spins with different gyromagnetic factors, and two interacting spins in short amount of times. We also use these techniques to setup protocols robust against the exact knowledge of the gyromagnetic factors for the one spin problem, or to generate entangled states for two or more spins coupled by dipole-dipole interactions.
We develop models for the propagation of intense pulses in solid state media which can have either saturated absorption or exhibit reverse absorption . We show that the experiments of Bigelow {\it et al.}[Phys. Rev. Lett. {\bf 90}, 113903 (2003); Science {\bf 301}, 200 (2003).] on subluminal propagation in Ruby and superluminal propagation in Alexandrite are well explained by modelling them as three level and four level systems coupled to Maxwell equations. We present results well beyond the traditional pump-probe approach.
A protocol is proposed to generate singlet states of three logical qubits constructed by pairs of spins. Single and multiple operations of logical qubits are studied for the construction of an effective Hamiltonian, with which robust control fields are derived with invariant-based reverse engineering and optimal control. Moreover, systematic errors are further compensated by periodic modulation for better robustness. Furthermore, resistance to decoherence of the protocol is also shown with numerical simulations. Therefore, the protocol may provide useful perspectives for generations of logical…
We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost function which can be efficiently optimized to produce one-qubit control pulses that are robust against specified frequency bands of the noise power spectral density. We demonstrate the utility of our result by generating optimal control pulses that are designed to suppress broadband detuning and pulse amplitude noise. We report an order of magnitude improvement in gate fidelity in…
Estimation of unknown qubit elementary gates and alignment of reference frames are formally the same problem. Using quantum states made out of $N$ qubits, we show that the theoretical precision limit for both problems, which behaves as $1/N^{2}$, can be asymptotically attained with a covariant protocol that exploits the quantum correlation of internal degrees of freedom instead of the more fragile entanglement between distant parties. This cuts by half the number of qubits needed to achieve the precision of the dense covariant coding protocol.
We propose a protocol to realize nonadiabatic geometric quantum computation of small-amplitude Schrödinger cat qubits via invariant-based reverse engineering. We consider a system with a two-photon driven Kerr nonlinearity, which provides a pair of dressed even and odd coherent states, i.e., Schrödinger cat states for fault-tolerant quantum computations. An additional coherent field is applied to linearly drive a cavity mode, to induce oscillations between dressed cat states. By designing this linear drive with invariant-based reverse engineering, nonadiabatic geometric quantum computation wit…
We explore the electromagnetic field coupled to a mechanical resonator via quadratic optomechanical interaction in the reversed dissipation regime where the mechanical damping rate is much larger than the cavity field dissipation rate. It is shown that in this regime, the cavity field effectively acquires an additional reservoir which is conditioned by the temperature of the mechanical bath as well as the mechanical damping rate. We analytically find the steady-state mean photon number and the critical temperature of the mechanical oscillator to cool or heat the coupled electromagnetic field. …
We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum driving (TQD) [31], the present scheme is focus on only one or parts of moving states in a D-dimension (D > 3) system. The numerical simulation shows that the present scheme not only contains the results of TQD, but also has more free parameters, which make this scheme more flexible. An example is given by using this scheme to realize the population transfe…
Since 2005 there has been a huge growth in the use of engineered control pulses to perform desired quantum operations in systems such as NMR quantum information processors. These approaches, which build on the original gradient ascent pulse engineering (GRAPE) algorithm, remain computationally intensive because of the need to calculate matrix exponentials for each time step in the control pulse. Here we discuss how the propagators for each time step can be approximated using the Trotter--Suzuki formula, and a further speed up achieved by avoiding unnecessary operations. The resulting procedure…
We propose a scheme to engineer Schrödinger-cat states of propagating optical pulses. Multi-dimensional and multi-partite cat states can be generated simply by reflecting coherent optical pulses successively from a single-atom cavity. The influences of various sources of noise, including the atomic spontaneous emission and the pulse shape distortion, are characterized through detailed numerical simulation, which demonstrates practicality of this scheme within the reach of current experimental technology.
An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.
Preparing highly entangled quantum states between remote parties is a major challenge for quantum communications [1-8]. Particularly promising in this context are the N00N states, which are entangled N-photon wavepackets delocalized between two different locations, providing measurement sensitivity limited only by the uncertainty principle [1, 10-15]. However, these states are notoriously vulnerable to losses, making it difficult both to share them between remote locations, and to recombine them to exploit interference effects. Here we address this challenge by utilizing the reverse version of…
We put forward a method for achieving fast and robust for magnetization reversal in a nanomagnet, by combining the inverse engineering and composite pulses. The magnetic fields, generated by microwave with time-dependent frequency, are first designed inversely within short operation time, and composite pulses are further incorporated to improve the fidelity through reducing the effect of magnetic anisotropy. The high-fidelity magnetization reversals are illustrated with numerical examples, and visualized on Bloch sphere. The influence of damping parameters, relevant to the pulse sequence, is f…
The quantum state of the photon pair generated from type-II spontaneous parametric down-conversion pumped by a ultrafast laser pulse exhibits strong decoherence in its polarization entanglement, an effect which can be attributed to the clock effect of the pump pulse or, equivalently, to distinguishing spectral information in the two-photon state. Here, we propose novel temporal and spectral engineering techniques to eliminate these detrimental decoherence effects. The temporal engineering of the two-photon wavefunction results in a universal Bell-state synthesizer that is independent of the ch…
The experimental optimization of a two-qubit controlled-Z (CZ) gate is realized following two different data-driven gradient ascent pulse engineering (GRAPE) protocols in the aim of optimizing the gate operator and the output quantum state, respectively. For both GRAPE protocols, the key computation of gradients utilizes mixed information of the input Z-control pulse and the experimental measurement. With an imperfect initial pulse in a flattop waveform, our experimental implementation shows that the CZ gate is quickly improved and the gate fidelities subject to the two optimized pulses are ar…
An interpretation of the probability flux is given, based on a derivation of its eigenstates and relating them to coherent state projections on a quantum wavefunction. An extended definition of the flux operator is obtained using coherent states. We present a "processed Husimi" representation, which makes decisions using many Husimi projections at each location. The processed Husimi representation reverse engineers or deconstructs the wavefunction, yielding the underlying classical ray structure. Our approach makes possible interpreting the dynamics of systems where the probability flux is uni…
We propose an all-electronic technique to manipulate and control interacting quantum systems by unitary single-jump feedback conditioned on the outcome of a capacitively coupled electrometer and in particular a single-electron transistor. We provide a general scheme to stabilize pure states in the quantum system and employ an effective Hamiltonian method for the quantum master equation to elaborate on the nature of stabilizable states and the conditions under which state purification can be achieved. The state engineering within the quantum feedback scheme is shown to be linked with the soluti…
We report some improvements to the gradient ascent pulse engineering (GRAPE) algorithm for optimal control of quantum systems. These include more accurate gradients, convergence acceleration using the BFGS quasi-Newton algorithm as well as faster control derivative calculation algorithms. In all test systems, the wall clock time and the convergence rates show a considerable improvement over the approximate gradient ascent.
