Quantum dynamical decoupling is a procedure to cancel the effective coupling between two systems by applying sequences of fast actuations, under which the coupling Hamiltonian averages out to leading order(s). One of its prominent uses is to drive a target system in such a way as to decouple it from a less protected one. The present manuscript investigates the dual strategy: acting on a noisy "environment" subsystem such as to decouple it from a target system. The potential advantages are that actions on the environment commute with system operations, and that imprecisions in the decoupling actuation are harmless to the target. We consider two versions of environment-side decoupling: adding an imprecise Hamiltonian drive which stirs the environment components; and, increasing the decoherence rates on the environment. The latter can be viewed as driving the environment with pure noise and our conclusions establish how, maybe counterintuitively, isolating the environment from noise sources as much as possible is often not the best option. We explicitly analyze the induced decoherence on the target system and establish how it is influenced by the parameters in both cases. The analysis combines Lindbladian derivation, adiabatic elimination, and Floquet modeling in a way that may be of independent interest.
A quantum particle in a slowly-changing potential well $V(x,t)=V(x-x_0(εt))$, periodically shaken in time at a slow frequency $ε$, provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than $ \sim 1 / ε$. Specifically, we consider a double-well potential $V(x)$ sustaining two bound states spaced in frequency by $ω_0$ and periodically-shaken in complex plane. Two different spatial displacements $x_0(t)$ are assumed: the real spatial displacement $x_0(εt)=A \sin (εt)$, corresponding to ordinary Hermitian shaki…
I revisit the ideas underlying dynamical decoupling methods within the framework of quantum information processing, and examine their potential for direct implementations in terms of encoded rather than physical degrees of freedom. The usefulness of encoded decoupling schemes as a tool for engineering both closed- and open-system encoded evolutions is investigated based on simple examples.
Dynamical decoupling is a powerful technique for extending the coherence time (T$_2$) of qubits. We apply this technique to the electron spin qubit of a single nitrogen-vacancy center in type IIa diamond. In a crystal with natural abundance of $^{13}$C nuclear spins, we extend the decoherence time up to 2.2 ms. This is close to the T$_1$ value of this NV center (4 ms). Since dynamical decoupling must perform well for arbitrary initial conditions, we measured the dependence on the initial state and compared the performance of different sequences with respect to initial state dependence and robu…
We prove an achievability result for privacy amplification and decoupling in terms of the sandwiched Rényi entropy of order $α\in (1,2]$; this extends previous results which worked for $α=2$. The fact that this proof works for $α$ close to 1 means that we can bypass the smooth min-entropy in the many applications where the bound comes from the fully quantum AEP or entropy accumulation, and carry out the whole proof using the Rényi entropy, thereby easily obtaining an error exponent for the final task. This effectively replaces smoothing, which is a difficult high-dimensional optimization probl…
An optimal dynamical decoupling of a quantum system coupled to a noisy environment must take into account also the imperfections of the control pulses. We present a new formalism which describes, in a closed-form expression, the evolution of the system, including the spectral function of both the environment and control noise. We show that by measuring these spectral functions, our expression can be used to optimize the decoupling pulse sequence. We demonstrate this approach with an ensemble of optically trapped ultra-cold Rubidium atoms, and use quantum process tomography to identify the effe…
We address the issue of dephasing effects in flying polarization qubits propagating through optical fiber by using the method of dynamical decoupling. The control pulses are implemented with half waveplates suitably placed along the realistic lengths of the single mode optical fiber. The effects of the finite widths of the waveplates on the polarization rotation are modeled using tailored refractive index profiles inside the waveplates. We show that dynamical decoupling is effective in preserving the input qubit state with the fidelity close to one when the polarization qubit is subject to the…
We analyze the suppression of decoherence by means of dynamical decoupling in the pure-dephasing spin-boson model for baths with power law spectra. The sequence of ideal $π$ pulses is optimized according to the power of the bath. We expand the decoherence function and separate the cancelling divergences from the relevant terms. The proposed sequence is chosen to be the one minimizing the decoherence function. By construction, it provides the best performance. We analytically derive the conditions that must be satisfied. The resulting equations are solved numerically. The solutions are very clo…
Synthesizing an effective identity evolution in a target system subjected to unwanted unitary or non-unitary dynamics is a fundamental task for both quantum control and quantum information processing applications. Here, we investigate how single-bit, discrete-time feedback capabilities may be exploited to enact or to enhance quantum procedures for effectively suppressing unwanted dynamics in a finite-dimensional open quantum system. An explicit characterization of the joint unitary propagators correctable by a single-bit feedback strategy for arbitrary evolution time is obtained. For a two-dim…
The need for strategies able to accurately manipulate quantum dynamics is ubiquitous in quantum control and quantum information processing. We investigate two scenarios where randomized dynamical decoupling techniques become more advantageous with respect to standard deterministic methods in switching off unwanted dynamical evolution in a closed quantum system: when dealing with decoupling cycles which involve a large number of control actions and/or when seeking long-time quantum information storage. Highly effective hybrid decoupling schemes, which combine deterministic and stochastic featur…
The use of the nuclear spins surrounding electron spin qubits as quantum registers and long-lived memories opens the way to new applications in quantum information and biological sensing. Hence, there is a need for generic and robust forms of control of the nuclear registers. Although adiabatic gates are widely used in quantum information, they can become too slow to outpace decoherence. Here, we introduce a technique whereby adiabatic gates arise from the dynamical decoupling protocols that simultaneously extend coherence. We illustrate this pulse-based adiabatic control for nuclear spins aro…
We introduce a task that we call partial decoupling, in which a bipartite quantum state is transformed by a unitary operation on one of the two subsystems and then is subject to the action of a quantum channel. We assume that the subsystem is decomposed into a direct-sum-product form, which often appears in the context of quantum information theory. The unitary is chosen at random from the set of unitaries having a simple form under the decomposition. The goal of the task is to make the final state, for typical choices of the unitary, close to the averaged final state over the unitaries. We co…
Realizing useful quantum operations with high fidelity is a two-task quantum control problem wherein decoherence is to be suppressed and desired unitary evolution is to be executed. The dynamical decoupling (DD) approach to decoherence suppression has been fruitful but synthesizing DD fields with certain quantum control fields may be experimentally demanding. In the context of spin squeezing, here we explore an unforeseen possibility that continuous DD fields may serve dual purposes at once. In particular, it is shown that a rather simple configuration of DD fields can suppress collective deco…
In this paper we study how to preserve entanglement and nonlocality under dephasing produced by classical noise with large low-frequency components, as $1/f$ noise, by Dynamical Decoupling techniques. We first show that quantifiers of entanglement and nonlocality satisfy a closed relation valid for two independent qubits locally coupled to a generic environment under pure dephasing and starting from a general class of initial states. This result allows to assess the efficiency of pulse-based dynamical decoupling for protecting nonlocal quantum correlations between two qubits subject to pure-de…
Dynamical decoupling is a coherent control technique where the intrinsic and extrinsic couplings of a quantum system are effectively averaged out by application of specially designed driving fields (refocusing pulse sequences). This entails pumping energy into the system, which can be especially dangerous when it has sharp spectral features like a cavity mode close to resonance. In this work we show that such an effect can be avoided with properly constructed refocusing sequences. To this end we construct the average Hamiltonian expansion for the system evolution operator associated with a sin…
Evolution of homonuclear J-coupling during t1 period creates Zero Quantum artefacts which seriously degrade the performance of 2D NOESY. In our previous work [28], it is demonstrated that creation of such artefacts can be prevented by incorporation of a perfect echo based broadband homo-nuclear decoupling technique during t1 period that also allows chemical shift encoding. However, such experiments have limited F1 resolution as the perfect echo based decoupling remains efficient for interpulse delay 2τ (=t1) short compared to 1/J. A solution to this problem is provided in the present work wher…
We report an optical memory in a rare earth doped crystal with long storage times, up to 20 ms, together with an optical bandwidth of 1.5 MHz. This is obtained by transferring optical coherences to nuclear spin coherences, which were then protected against environmental noise by dynamical decoupling. With this approach, we achieved a 33 fold increase in spin wave storage time over the intrinsic spin coherence lifetime. Comparison between different decoupling sequences indicates that sequences insensitive to initial spin coherence increase retrieval efficiency. Finally, an interference experime…
We show how dynamical decoupling (DD) and quantum error correction (QEC) can be optimally combined in the setting of fault tolerant quantum computing. To this end we identify the optimal generator set of DD sequences designed to protect quantum information encoded into stabilizer subspace or subsystem codes. This generator set, comprising the stabilizers and logical operators of the code, minimizes a natural cost function associated with the length of DD sequences. We prove that with the optimal generator set the restrictive local-bath assumption used in earlier work on hybrid DD-QEC schemes, …
Control scenarios have been identified where the use of randomized design may substantially improve the performance of dynamical decoupling methods [L. F. Santos and L. Viola, Phys. Rev. Lett. {\bf 97}, 150501 (2006)]. Here, by focusing on the suppression of internal unwanted interactions in closed quantum systems, we review and further elaborate on the advantages of randomization at long evolution times. By way of illustration, special emphasis is devoted to isolated Heisenberg-coupled chains of spin-1/2 particles. In particular, for nearest-neighbor interactions, two types of decoupling cycl…
We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective measurement on a typical subspace of a tensor power state. We show that, provided the rank of each measurement operator is sufficiently small, the transmitted data will with high probability be decoupled from the channel's environment. We also show that our construction leads to random codes whose average input is close to a product state and outline a modificat…
Long qubit coherence and efficient atom-photon coupling are essential for advanced applications in quantum communication. One technique to maintain coherence is dynamical decoupling, where a periodic sequence of refocusing pulses is employed to reduce the interaction of the system with the environment. We experimentally study the implementation of dynamical decoupling on an optically-trapped, spin-polarized $^{87}$Rb atom. We use the two magnetic-sensitive $5S_{1/2}$ Zeeman levels, $\lvert{F=2,\ m_{F}=-2}\rangle$ and $\lvert{F=1,\ m_{F}=-1}\rangle$ as qubit states, motivated by the possibility…
Quantum Error Correction and Dynamical Decoupling: Better Together or Apart?
University of Southern California（南加州大学）；Center for Quantum Information Science & Technology, University of Southern California（南加州大学量子信息科学与技术中心）；Quantum Elements, Inc.（量子元素公司）；Department of Physics & Astronomy, University of Southern California（南加州大学物理与天文学系）；Department of Chemistry, University of Southern California（南加州大学化学系）
Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where for instance it is employed in multiparameter estimation. While a sequence of equidistant control pulses (CPMG) has been ubiquitously used for decoupling, Uhrig recently proposed that a non-equidistant pulse sequence (UDD) may en…
Coherent optical control schemes exploit the coherence of laser pulses to change the phases of interfering dynamical pathways in order to manipulate dynamical processes. These active control methods are closely related to dynamical decoupling techniques, popularized in the field of Quantum Information. Inspired by Nuclear Magnetic Resonance (NMR) spectroscopy, dynamical decoupling methods apply sequences of unitary operations to modify the interference phenomena responsible for the system dynamics thus also belonging to the general class of coherent control techniques. Here we review related d…
