Guy Bensky

Reversible state transfer between superconducting qubits and atomic ensembles

We examine the possibility of coherent, reversible information transfer between solid-state superconducting qubits and ensembles of ultra-cold atoms. Strong coupling between these systems is mediated by a microwave transmission line resonator that interacts near-resonantly with the atoms via their optically excited Rydberg states. The solid-state qubits can then be used to implement rapid quantum logic gates, while collective metastable states of the atoms can be employed for long-term storage and optical read-out of quantum information.

Bath-optimized minimal-energy protection of quantum operations from decoherence.

The quest for strategies for combatting decoherence is of paramount importance to the control of open quantum systems, particularly for quantum information operations [1]. A prevailing unitary strategy aimed at suppressing decoherence is dynamical decoupling (DD) [2, 3, 4], which consists, in the case of a qubit, in the application of strong and fast pulses alternating along orthogonal Bloch-sphere axes, e.g., X and Z. In the frequency domain, where the decoherence rate can be described as overlap between the spectra of the pulse-driven (modulated) system and the bath [5], DD is tantamount to shifting the driven-system resonances beyond the bath cutoff frequencies. The DD efficacy can be enhanced for certain bath spectra upon choosing the timings of the pulses so as to reduce the low-frequency parts in the system spectrum and thus its overlap with the low-frequency portion of the bath spectrum [4]. DD sequences are inherently binary, i.e., their pulsed control parameters are discretely switched on or off. Realistically, the finiteness of pulse durations and spacings sets an upper limit on the speed and fidelity of DD-assisted quantum gate operations [2, 3, 4]. An alternative strategy formulated here in full generality is analog unitary control of multidimensional systems subject to any noise or decoherence. It is effected by a system Hamiltonian whose time-dependence is variationally tailored to optimally perform a desired gate operation. The vast additional freedom of non-discrete (smooth) Hamiltonian parametrization significantly enhances the efficacy of decoherence control under realistic constraints compatible with the non-Markov time scales required for such control. Its formulation meets the longstanding conceptual challenge of simultaneously controlling non-commuting system operators subject to noise along orthogonal axes. This is here achieved by working in an optimally rotated, different basis at each instant. The price we pay for such general optimal control is the need for at least partial knowledge of the bath or noise

Direct measurement of the system–environment coupling as a tool for understanding decoherence and dynamical decoupling

Decoherence is a major obstacle to any practical implementation of quantum information processing. One of the leading strategies to reduce decoherence is dynamical decoupling—the use of an external field to average out the effect of the environment. The decoherence rate under any control field can be calculated if the spectrum of the coupling to the environment is known. We present a direct measurement of the bath-coupling spectrum in an ensemble of optically trapped ultra-cold atoms, by applying a spectrally narrow-band control field. The measured spectrum follows a Lorentzian shape at low frequencies but exhibits non-monotonic features at higher frequencies due to the oscillatory motion of the atoms in the trap. These features agree with our analytical models and numerical Monte Carlo simulations of the collisional bath. From the inferred bath-coupling spectrum, we predict the performance of some well-known dynamical decoupling sequences. We then apply these sequences in experiment and compare the results to predictions, finding good agreement in the weak-coupling limit. Thus, our work establishes experimentally the validity of the overlap integral formalism and is an important step towards the implementation of an optimal dynamical decoupling sequence for a given measured bath spectrum.

Optimized control of quantum state transfer from noisy to quiet qubits

Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel(Dated: October 26, 2010)We analyze quantum state-transfer optimization within hybrid open systems, from a “noisy”(write-in) qubit to its “quiet” counterpart (storage qubit). Intriguing interplay is revealed betweenour ability to avoid bath-induced errors that profoundly depend on the bath-memory time andthe limitations imposed by leakage out of the operational subspace. Counterintuitively, under nocircumstances is the fastest transfer optimal (for a given transfer energy).

Optimized dynamical control of state transfer through noisy spin chains

We propose a method of optimally controlling the tradeoff of speed and fidelity of state transfer through a noisy quantum channel (spin-chain). This process is treated as qubit state-transfer through a fermionic bath. We show that dynamical modulation of the boundary-qubits levels can ensure state transfer with the best tradeoff of speed and fidelity. This is achievable by dynamically optimizing the transmission spectrum of the channel. The resulting optimal control is robust against both static and fluctuating noise in the channelʼs spin–spin couplings. It may also facilitate transfer in the presence of diagonal disorder (on site energy noise) in the channel.

Shift-driven modulations of spin-echo signals

Since the pioneering works of Carr-Purcell and Meiboom-Gill [Carr HY, Purcell EM (1954) Phys Rev 94:630; Meiboom S, Gill D (1985) Rev Sci Instrum 29:688], trains of π-pulses have featured amongst the main tools of quantum control. Echo trains find widespread use in nuclear magnetic resonance spectroscopy (NMR) and imaging (MRI), thanks to their ability to free the evolution of a spin-1/2 from several sources of decoherence. Spin echoes have also been researched in dynamic decoupling scenarios, for prolonging the lifetimes of quantum states or coherences. Inspired by this search we introduce a family of spin-echo sequences, which can still detect site-specific interactions like the chemical shift. This is achieved thanks to the presence of weak environmental fluctuations of common occurrence in high-field NMR—such as homonuclear spin-spin couplings or chemical/biochemical exchanges. Both intuitive and rigorous derivations of the resulting “selective dynamical recoupling” sequences are provided. Applications of these novel experiments are given for a variety of NMR scenarios including determinations of shift effects under inhomogeneities overwhelming individual chemical identities, and model-free characterizations of chemically exchanging partners.

Optimizing inhomogeneous spin ensembles for quantum memory

We propose a method to maximize the fidelity of quantum memory implemented by a spectrally inhomogeneous spin ensemble. The method is based on preselecting the optimal spectral portion of the ensemble by judiciously designed pulses. This leads to significant improvement of the transfer and storage of quantum information encoded in the microwave or optical field.

Task-optimized control of open quantum systems

We develop a general optimization strategy for performing a chosen unitary or nonunitary task on an open quantum system. The goal is to design a controlled time-dependent system Hamiltonian by variationally minimizing or maximizing a chosen function of the system state, which quantifies the task success (score), such as fidelity, purity, or entanglement. If the time dependence of the system Hamiltonian is fast enough to be comparable to or shorter than the response time of the bath, then the resulting non-Markovian dynamics is shown to optimize the chosen task score to second order in the coupling to the bath. This strategy can protect a desired unitary system evolution from bath-induced decoherence, but can also take advantage of the system-bath coupling so as to realize a desired nonunitary effect on the system.

Controlling quantum information processing in hybrid systems on chips

We investigate quantum information processing, transfer and storage in hybrid systems comprised of diverse blocks integrated on chips. Strong coupling between superconducting (SC) qubits and ensembles of ultracold atoms or NV-center spins is mediated by a microwave transmission-line resonator that interacts near-resonantly with the atoms or spins. Such hybrid devices allow us to benefit from the advantages of each block and compensate for their disadvantages. Specifically, the SC qubits can rapidly implement quantum logic gates, but are “noisy” (prone to decoherence), while collective states of the atomic or spin ensemble are “quiet”(protected from decoherence) and thus can be employed for storage of quantum information. To improve the overall performance (fidelity) of such devices we discuss dynamical control to optimize quantum state-transfer from a “noisy” qubit to the “quiet” storage ensemble. We propose to maximize the fidelity of transfer and storage in a spectrally inhomogeneous spin ensemble, by pre-selecting the optimal spectral portion of the ensemble. Significant improvements of the overall fidelity of hybrid devices are expected under realistic conditions. Experimental progress towards the realization of these schemes is discussed.

Universal dynamical decoupling from slow noise with minimal control

We propose a technique that allows to simultaneously perform universal control of the evolution operator of a system and compensate for the first-order contribution of any Hermitian constant noise and the action of the environment. We show that, at least, a three-valued Hamiltonian is needed in order to protect the system against any such noise and propose an explicit algorithm for finding an appropriate control sequence. This algorithm is applied to numerically design a safe gate in an atomic qutrit.