Optimally combining dynamical decoupling and quantum error correction

Abstract

Quantum control and fault-tolerant quantum computing (FTQC) are two of the cornerstones on which the hope of realizing a large-scale quantum computer is pinned, yet only preliminary steps have been taken towards formalizing the interplay between them. Here we explore this interplay using the powerful strategy of dynamical decoupling (DD), and show how it can be seamlessly and optimally integrated with FTQC. To this end we show how to find the optimal decoupling generator set (DGS) for various subspaces relevant to FTQC, and how to simultaneously decouple them. We focus on stabilizer codes, which represent the largest contribution to the size of the DGS, showing that the intuitive choice comprising the stabilizers and logical operators of the code is in fact optimal, i.e., minimizes a natural cost function associated with the length of DD sequences. Our work brings hybrid DD-FTQC schemes, and their potentially considerable advantages, closer to realization.

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

“…This ideal 'bang-bang' DD setting has been extensively investigated in both single-qubit [3,5,6,33,34] and multi-qubit systems [4,15,16,37] (see [1] for a review). For the sake of completeness and consistency, we summarize the basic ingredients in this section, building in particular on [16,38]. In the process, we introduce a new composition rule which unifies existing high-order sequence constructions and may be of independent interest within DD theory.…”

Distinguishing decoherence from alternative quantum theories by dynamical decoupling

“…Many experiments, such as [28][29][30], demonstrate the applicability of dynamical decoupling in an impressive way by prolonging coherence times a few orders of magnitude. Additionally, dynamical decoupling can be combined with the implementation of quantum gates which makes it a viable option to error correction [31,32]. The idea of dynamical decoupling is to rapidly rotate the quantum system by means of classical fields to average the systemenvironment coupling to zero.…”

Protecting solid-state spins from a strongly coupled environment

“…Due to the strong hyperfine coupling A=2. 16 MHz between the electronic and nuclear spin of the NV, the condition (4) requires τ1 μs, which is not feasible given the slow control of the nuclear spin qubit (with typical π-pulse times 50 μs). However, as the hyperfine interaction is symmetric with respect to the state of both spins, applying π-pulses on either the qubit or the fluctuator modulates the hyperfine interaction sign and will lead to an effectively weaker averaged hyperfine coupling and thus a slower rate at which nuclear states acquire a random phase.…”

“…This is in contrast to other protocols where the electronic spin is inaccessible during protection of nuclear spins [25,31,45]. Proposals concatenating DD with active QEC [16][17][18] also makes it potentially a first layer of protection before applying QEC, enabling scaling-up with less overhead. Finally, the proposed control technique is also applicable to other solid-state systems, for example, superconducting qubits, where single or ensembles of fluctuators are believed to be the major noise source [21,37,46].…”

“…This technique, going back to NMR's spin echo [12], enjoys great success thanks to its ease of implementation. In addition, it is compatible with many quantum information processing protocols [13][14][15] and can be concatenated with active QEC [16][17][18]. Still, DD has traditionally been applied to refocus slow-varying, weakly coupled environments that can often be modeled as classical bath [19], while its usefulness to decouple from strongly interacting quantum environments is less clear [20].…”