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.
Highlights
Characterizing and counteracting decoherence from noise environments which may exhibit both temporal and spatial correlations is a central challenge for realizing high-fidelity quantum information processing (QIP) and fault-tolerant quantum computation [1, 2]
Provided that the noise arises predominantly from low-frequency components, and that external control is available over time scales that are short compared to the resulting temporal correlations, open-loop techniques based on dynamical decoupling (DD) and dynamically error-corrected gates [1, 3,4,5,6,7,8] provide a powerful tool for boosting operational fidelities—potentially eliminating ‘coherent’ errors that dominate worst-case error estimates in rigorous threshold analyses [9, 10]
Once the state of the multi-qubit system after time Tg = Mg Tp is sufficiently close to an entangled state of interest, we may switch to a DD sequence with displacement anti-symmetry, in order to achieve protection for long storage times, say, Ts = Ms Tp¢, provided that the plateau conditions of equation (57) are satisfied, and where we allow for the duration of the storage base sequence to differ, in general
Summary
Characterizing and counteracting decoherence from noise environments which may exhibit both temporal and spatial correlations is a central challenge for realizing high-fidelity quantum information processing (QIP) and fault-tolerant quantum computation [1, 2]. Provided that selective control over individual qubits is available, we show that new multi-qubit DD sequences may be constructed, so that a displacement anti-symmetry property is obeyed by the control switching functions, both in the simplest case of N = 2 qubits (section 3.2) and, by appropriately orchestrating the sign pattern for every qubit pair, for general N (section 3.3) Such sequences ensure the same order of error suppression as the best known nested or concatenated protocols, while maximizing their ‘filtering order’ in the frequency domain [19]. Generalization of this result to dephasing scenarios that include bosonic noise sources again relies crucially on incorporating displacement anti-symmetry in the DD sequences used for repetition (section 4.2). We include in appendix B a discussion of the impact of timing errors on the ideal fidelity plateau, based on a simple error model that breaks the required underlying displacement anti-symmetry in a two-qubit system
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