Dynamical decoupling sequences for multi-qubit dephasing suppression and long-time quantum memory

Abstract

We consider a class of multi-qubit dephasing models that combine classical noise sources and linear coupling to a bosonic environment, and are controlled by arbitrary sequences of dynamical decoupling pulses. Building on a general transfer filter-function framework for open-loop control, we provide an exact representation of the controlled dynamics for arbitrary stationary non-Gaussian classical and quantum noise statistics, with analytical expressions emerging when all dephasing sources are Gaussian. This exact characterization is used to establish two main results. First, we construct multi-qubit sequences that ensure maximum high-order error suppression in both the time and frequency domain and that can be exponentially more efficient than existing ones in terms of total pulse number. Next, we show how long-time multi-qubit storage may be achieved by meeting appropriate conditions for the emergence of a fidelity plateau under sequence repetition, thereby generalizing recent results for single-qubit memory under Gaussian dephasing. In both scenarios, the key step is to endow multi-qubit sequences with a suitable displacement anti-symmetry property, which is of independent interest for applications ranging from environment-assisted entanglement generation to multi-qubit noise spectroscopy protocols.

Multiqubit spectroscopy of Gaussian quantum noise

“…II D contains our first result, namely, an exact analytical expression for the time-dependent expectations of arbitrary N -qubit Pauli observables, and hence the controlled reduced dynamics -valid under the sole assumptions that the noise has Gaussian statistics and the dephasing nature of the system-bath interaction is preserved by the applied control. To the best of our knowledge, this generalizes exact results derived under the explicit assumption of bosonic environments [17,36,47].…”

“…A paradigmatic M1 model is the well-known purely dephasing linear spin-boson model [48] in which case, relative to the interaction picture associated with the free oscillatorbath Hamiltonian H B = k Ω k a † k a k , Ω ≥ 0, the relevant time-dependent bath operators are [36] …”

“…Notably, interaction with a quantum bath can generate quantum correlations and entangle the qubits, even in the absence of direct coupling between them, see e.g. [30][31][32][33][34][35][36][37]. The quantum spectra relate directly to the ability of a quantum bath to mediate such entangling interaction.…”

“…Several schemes have been proposed for using quantum environments as a resource, notably, for entangling two or more qubits via their interaction with a common bath [30][31][32][33][34][35][36][37]. While no detailed knowledge of the bath is necessary to generate entanglement, full knowledge of the power spectra is instrumental to generate controlled entanglement, i.e., to retrieve it on-demand or perform a precise entangling gate.…”

Arbitrarily Accurate Pulse Sequences for Robust Dynamical Decoupling

“…Nevertheless, protection of quantum systems from unwanted interactions with the environment remains a major challenge. Dynamical decoupling (DD) is a widely used approach that aims to do this by nullifying the average effect of the unwanted qubit-environment coupling through the application of appropriate sequences of pulses [1][2][3][4].Most DD schemes focus on dephasing processes because they have maximum contribution to information loss in many systems, e.g., in nuclear magnetic resonance and quantum information [5,6]. Then, the major limitation to DD are pulse imperfections whose impact often exceeds the effect of the perturbations from the environment [6][7][8].…”