Universal dynamical decoupling of multiqubit states from environment

Abstract

We study the dynamical decoupling of multiqubit states from environment. For a system of m qubits, the nested Uhrig dynamical decoupling (NUDD) sequence can efficiently suppress generic decoherence induced by the system-environment interaction to order N using (N + 1) 2m pulses. We prove that the NUDD sequence is universal, i.e., it can restore the coherence of an m-qubit quantum system independent of the details of the system-environment interaction. We also construct a general mapping between dynamical decoupling problems and discrete quantum walks in certain functional spaces. Dynamical decoupling (DD) is a powerful tool to protect quantum systems from decoherence induced by the inevitable system-environment interaction [1]. The idea of DD is to dynamically control the system (or environment) evolution to suppress the decoherence caused by interaction. For example, a static magnetic field with unknown magnitude B z σ z can induce dephasing of a qubit, but such dephasing can be fully eliminated by a spin flip σ x (i.e., Hahn echo) at half way of the evolution [2]. In practice, however, the Hahn echo only suppresses the dephasing to O(T 2 ) for total evolution time T , because the magnetic field may have complicated time dependence in both magnitude and orientation due to the evolution of the environment. Furthermore, if the environment consists of quantum degrees of freedom, it can become entangled with the system via the interaction. Hence it is a challenging task to design a universal DD scheme that can suppress decoherence to the desired order independent of the details of the system-environment interaction.One particularly interesting DD scheme is the concatenated DD (CDD), which has been shown to be universal for single qubits [3]. The limitation, however, is that the pulse number increases exponentially with the suppression order N [approximately 4 N pulses to suppress both bit-flip and dephasing processes to O(T N+1 )]. It is the discovery of the universality of the Uhrig DD (UDD) sequence [4][5][6][7][8] that makes the universal DD practically feasible. In contrast to the CDD's demand for exponentially many pulses [3], UDD uses only O(N) spin-flip pulses to suppress the dephasing processes to O(T N+1 ) [5,6]. The discovery of the UDD sequence has inspired many experimental efforts to further improve the coherence over a wide range of quantum systems, including trapped ions [9], electron spins [10], defect centers [10,11], quantum dots [12,13], and superconducting qubits [14]. However, UDD is restricted to pure dephasing errors of a single qubit. It is desirable to have an efficient DD scheme [with poly(N) pulses] to suppress both bit-flip and dephasing processes for multiple qubits to O (T N+1 ). Recently, the quadratic DD (QDD) scheme has been proposed [15], which uses (N + 1) 2 pulses to suppress both bitflip and dephasing errors of single qubits. As a generalization of QDD from a 1-qubit system to an m-qubit system, the nested UDD (NUDD) scheme has been proposed [16][17][18], which uses (N + 1) 2m...

Quadratic dynamical decoupling with nonuniform error suppression

“…[27], where the expected performance of QDD was proved for sequences with even N 1 (the proof was recently completed in Ref. [29]). We show that parity effects are absent in QDD only for the interaction that anti-commutes solely with the decoupling operator comprising the inner sequence.…”

“…NUDD applies to arbitrary multi-level systems coupled to arbitrary baths, as recently proved in Ref. [29].…”

Environmental noise spectroscopy with qubits subjected to dynamical decoupling

“…It is well known that the multi-qubit decoherence, and consequently entanglement dynamics [218], can depend qualitatively on the presence and degree of correlations between the noises affecting distinct qubits [75,210,[219][220][221][222], and when all the qubits are experiencing the same (common) noise, decoherence-free subspaces, hosting entangled states immune to such noise, appear [223,224]. It is also well understood that dynamical decoupling suppresses decoherence and disentanglement of multi-qubit states [75,[225][226][227][228][229][230], even if the unitary operations are applied to single qubits only [75,[230][231][232]. However, the DD-based spectroscopic characterization of cross-correlations of multiple noises has begun to be explored only quite recently [230,233,234].…”

Reducing sequencing complexity in dynamical quantum error suppression by Walsh modulation

“…While the grouptheoretic DD design is applicable only to first-order error suppression, concatenation allows us to combine DD sequences for different noise axes to produce a high order and generic decoupling procedure. This idea is the basis of a variety of recent DD schemes, such as quadratic DD (QDD) [66] and its multi-qubit variants [51,67].…”