Limits on preserving quantum coherence using multipulse control

Abstract

We explore the physical limits of pulsed dynamical decoupling methods for decoherence control as determined by finite timing resources. By focusing on a decohering qubit controlled by arbitrary sequences of π pulses, we establish a nonperturbative quantitative upper bound to the achievable coherence for specified maximum pulsing rate and noise spectral bandwidth. We introduce numerically optimized control "bandwidth-adapted" sequences that saturate the performance bound and show how they outperform existing sequences in a realistic excitonic-qubit system where timing constraints are significant. As a by-product, our analysis reinforces the impossibility of fault-tolerance accuracy thresholds for generic open quantum systems under purely reversible error control.Building on the discovery of spin-echo and multiple-pulse techniques in nuclear magnetic resonance [1], dynamical decoupling (DD) methods for open quantum systems [2] have become a versatile tool for decoherence control in quantum engineering and fault-tolerant quantum computation. DD involves "open-loop" (feedback-free) quantum control based on the application of a time-dependent Hamiltonian which, in the simplest setting, effects a predetermined sequence of unitary operations (pulses) drawn from a basic repertoire. Physically, DD relies on the ability to access control time scales that are short relative to the correlation time scale of the interaction to be removed. The reduction in decoherence is achieved perturbatively, by ensuring that sufficiently high orders of the error-inducing Hamiltonian are removed. Recently, a number of increasingly powerful pulsed DD schemes have been proposed and validated in the laboratory. Uhrig DD (UDD) sequences [3], for instance, perturbatively cancel pure dephasing in a single qubit up to an arbitrarily high order n while using a minimal number (n) of pulses, paving the way to further optimization for given sequence duration [4,5] and/or specific noise environments [6], to nearly optimal protocols for generic single-qubit decoherence [7]. Experimentally, UDD has been employed to prolong coherence time in systems ranging from trapped ions [4,5,8] and atomic ensembles [9] to spin-based devices [10], and to enhance contrast in magnetic resonance imaging of tissue [11].In a realistic DD setting, the achievable performance is inevitably influenced by errors due to limited control as well as by deviations from the intended decoherence model. Since it is conceivable that both model uncertainty and pulse nonidealities can be largely removed by more accurate system identification and control design, some of these limitations may be regarded as nonfundamental in nature. Compositepulse [12] and pulse-shaping [13] techniques can be used, for instance, to cancel to high accuracy the effects of both systematic control errors and finite-width corrections. We argue, however, that, even in a situation where pulses may be assumed perfect and instantaneous, an ultimate constraint is implied by the fact that the rate at which control ope...

Quadratic dynamical decoupling with nonuniform error suppression

“…The order of error suppression can then be quantified by the scaling of the single-axis error as a function of either the total evolution time or the minimum pulse interval. We choose the minimum pulse interval since experimentally this quantity is always lower-bounded, and plays an important role in the ultimate performance limits of UDD [31] and DD in general [32].…”

The Size of Exponential Sums on Intervals of the Real Line

“…Physically, however, a minimum growth condition is always imposed by the fact that the separation between any two consecutive pulses cannot be made arbitrarily small due to finite timing resources, thus t j+1 − t j > τ > 0 for all j. As shown in [6], the results established here may then be used to obtain a nonperturbative lower bound on χ {t j } , determined solely in terms of the parameter ω c τ . As an additional implication of our analysis, we find that Uhrig decoupling arises naturally as a consequence of representing certain polynomials of degree at most 2n + 1 in terms of Lagrange interpolation at the extreme points of the Chebyshev polynomials U 2n+1 .…”

“…In addition to being interesting on its own, this extension is motivated by physical applications in the context of decoherence control in open quantum systems using dynamical decoupling methods [6]. In the paradigmatic case of a single two-level quantum system undergoing pure dephasing due to coupling to a quantum bosonic environment, for instance, the residual decoherence error at a time t after the application of n ideal "spin-flip" pulses at times 0 < t 1 < t 2 < .…”

Dynamical decoupling in optical fibers: Preserving polarization qubits from birefringent dephasing

“…This analysis assumes ideal pulses having zero width, in which case it has been shown that DD sequences can be designed to make higher-order system-bath coupling terms vanish [4,22,27]. However, such ideal, instantaneous pulses are not achievable in actual physical systems, and some researchers have considered finite-width pulses, which decouple to higher order than simple rectanglular pulses [28,29].…”