Achieving high-fidelity universal two-qubit gates is a central requisite of any implementation of quantum information processing. The presence of spurious fluctuators of various physical origin represents a limiting factor for superconducting nanodevices. Operating qubits at optimal points, where the qubit-fluctuator interaction is transverse with respect to the single qubit Hamiltonian, considerably improved single qubit gates. Further enhancement has been achieved by dynamical decoupling (DD). In this article we investigate DD of transverse random telegraph noise acting locally on each of the qubits forming an entangling gate. Our analysis is based on the exact numerical solution of the stochastic Schrödinger equation. We evaluate the gate error under local periodic, Carr–Purcell and Uhrig DD sequences. We find that a threshold value of the number, n , of pulses exists above which the gate error decreases with a sequence-specific power-law dependence on n . Below threshold, DD may even increase the error with respect to the unconditioned evolution, a behaviour reminiscent of the anti-Zeno effect.
Controlling the dynamics of entanglement and preventing its disappearance are central requisites for any implementation of quantum information processing. Solid state qubits are frequently affected by random telegraph noise due to bistable impurities of different nature coupled to the device. In this paper, we investigate the possibility to achieve an efficient universal two-qubit gate in the presence of random telegraph noise by periodic dynamical decoupling. We find an analytic form of the gate error as a function of the number of applied pulses valid when the gate time is much shorter then the telegraphic process correlation time. The analysis is further supplemented by exact numerical results demonstrating the feasibility of a highly-efficient universal two-qubit gate.
We investigate the possibility of achieving high-fidelity universal two-qubit gates by supplementing optimal tuning of individual qubits with dynamical decoupling (DD) of local
1/f noise. We consider simultaneous local pulse sequences applied during the gate operation and compare the efficiencies of periodic, Carr-Purcell, and Uhrig DD with hard $\ensuremath{\pi}$ pulses along two directions (${\ensuremath{\pi}}_{z/y}$ pulses). We present analytical perturbative results (Magnus expansion) in the quasistatic noise approximation combined with numerical simulations for realistic
1/f noise spectra. The gate efficiency is studied as a function of the gate duration, of the number
n of pulses, and of the high-frequency roll-off. We find that the gate error is nonmonotonic in
n, decreasing as ${n}^{\ensuremath{-}\ensuremath{\alpha}}$ in the asymptotic limit, $\ensuremath{\alpha}\ensuremath{\ge}2$, depending on the DD sequence. In this limit ${\ensuremath{\pi}}_{z}$-Urhig is the most efficient scheme for quasistatic
1/f noise, but it is highly sensitive to the soft UV cutoff. For small number of pulses, ${\ensuremath{\pi}}_{z}$ control yields anti-Zeno behavior, whereas ${\ensuremath{\pi}}_{y}$ pulses minimize the error for a finite
n. For the current noise figures in superconducting qubits, two-qubit gate errors $\ensuremath{\sim}{10}^{\ensuremath{-}6}$, meeting the requirements for fault-tolerant quantum computation, can be achieved. The Carr-Purcell-Meiboom-Gill sequence is the most efficient procedure, stable for
1/f noise with UV cutoff up to gigahertz.
We study the dissipative dynamics of a qubit that is afflicted by classical random telegraph noise and is subject to dynamical decoupling. We derive exact formulas for the qubit dynamics at arbitrary working points in the limit of infinitely strong control pulses (bang-bang control), and we investigate in great detail the efficiency of the dynamical decoupling techniques for both Gaussian and non-Gaussian (slow) noise at qubit pure dephasing and at optimal point. We demonstrate that control sequences can be successfully implemented as diagnostic tools to infer spectral properties of a few fluctuators interacting with the qubit. The analysis is extended in order to include the effect of noise in the pulses, and we give upper bounds on the noise levels that can be tolerated in the pulses while still achieving an efficient dynamical decoupling performance.
In this paper, we study how to preserve entanglement and nonlocality under dephasing produced by classical noise with large low-frequency components, such as
1/f noise, using 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 us to assess the efficiency of pulse-based dynamical decoupling for protecting nonlocal quantum correlations between two qubits subject to pure-dephasing local random telegraph and
1/f noise. We investigate the efficiency of an ``entanglement memory'' element under two-pulse echo and under sequences of periodic, Carr-Purcell, and Uhrig dynamical decoupling. The Carr-Purcell sequence is shown to outperform the other sequences in preserving entanglement against both random telegraph and
1/f noise. For typical
1/f flux-noise figures in superconducting nanocircuits, we show that entanglement and its nonlocal features can be efficiently stored up to times one order of magnitude longer than natural entanglement disappearance times employing pulse timings of current experimental reach.
Dynamical decoupling (DD) refers to a well-established family of methods for error mitigation, comprising pulse sequences aimed at averaging away slowly evolving noise in quantum systems. Here we revisit the question of its efficacy in the presence of noisy pulses in scenarios important for quantum devices today: pulses with gate control errors, and the computational setting where DD is used to reduce noise in every computational gate. We focus on the well-known schemes of periodic (or universal) DD and its extension, concatenated DD, for scaling up its power. The qualitative conclusions from our analysis of these two schemes nevertheless apply to other DD approaches. In the presence of noisy pulses, DD does not always mitigate errors. It does so only when the added noise from the imperfect DD pulses does not outweigh the increased ability in averaging away the original background noise. We present break-even conditions that delineate when DD is useful, and further find that there is a limit in the performance of concatenated DD, specifically in how far one can concatenate the DD pulse sequences before the added noise no longer offers any further benefit in error mitigation.
In quantum information processing, it is vital to protect the coherence of qubits in noisy environments. Dynamical decoupling (DD), which applies a sequence of flips on qubits and averages the qubit-environment coupling to zero, is a promising strategy compatible with other desired functionalities, such as quantum gates. Here, we review the recent progresses in theories of dynamical decoupling and experimental demonstrations. We give both semiclassical and quantum descriptions of the qubit decoherence due to coupling to noisy environments. Based on the quantum picture, a geometrical interpretation of DD is presented. The periodic Carr-Purcell-Meiboom-Gill DD and the concatenated DD are reviewed, followed by a detailed exploration of the recently developed Uhrig DD, which employs the least number of pulses in an unequally spaced sequence to suppress the qubit-environment coupling to a given order of the evolution time. Some new developments and perspectives are also discussed.