We present a general control-theoretic framework for constructing and analyzing random decoupling schemes, applicable to quantum dynamical control of arbitrary finite-dimensional composite systems. The basic idea is to design the control propagator according to a random rather than deterministic path on a group. We characterize the performance of random decoupling protocols, and identify control scenarios where they can significantly weaken time scale requirements as compared to cyclic counterparts. Implications for reliable quantum computation are discussed.
We present a general control-theoretic framework for constructing and analyzing random decoupling schemes, applicable to quantum dynamical control of arbitrary finite-dimensional composite systems. The basic idea is to design the control propagator according to a random rather than deterministic path on a group. We characterize the performance of random decoupling protocols, and identify control scenarios where they can significantly weaken time scale requirements as compared to cyclic counterparts. Implications for reliable quantum computation are discussed.
We demonstrate the advantages of randomization in coherent quantum dynamical control. For systems which are either time-varying or require decoupling cycles involving a large number of operations, we find that simple randomized protocols offer superior convergence and stability as compared to deterministic counterparts. In addition, we show how randomization may allow us to outperform purely deterministic schemes at long times, including combinatorial and concatenated methods. General criteria for optimally interpolating between deterministic and stochastic design are proposed and illustrated in explicit decoupling scenarios relevant to quantum information storage.
We reexamine the problem of switching off unwanted phase evolution and decoherence in a single two-state quantum system in the light of recent results on random dynamical decoupling methods [L. Viola and E. Knill, Phys. Rev. Lett. 94, 060502 (2005)]. A systematic comparison with standard cyclic decoupling is effected for a variety of dynamical regimes, including the case of both semiclassical and fully quantum decoherence models. In particular, exact analytical expressions are derived for randomized control of decoherence from a bosonic environment. We investigate quantitatively control protocols based on purely deterministic, purely random, as well as hybrid design, and identify their relative merits and weaknesses at improving system performance. We find that for time-independent systems, hybrid protocols tend to perform better than pure random and may improve over standard asymmetric schemes, whereas random protocols can be considerably more stable against fluctuations in the system parameters. Beside shedding light on the physical requirements underlying randomized control, our analysis further demonstrates the potential for explicit control settings where the latter may significantly improve over conventional schemes.
We propose a general procedure for implementing dynamical decoupling of quantum systems without requiring arbitrarily strong, impulsive control actions. This is accomplished by designing continuous decoupling propagators according to Eulerian paths in the decoupling group for the system. Such Eulerian decoupling schemes offer two important advantages over their impulsive counterparts: they are able to enforce the same dynamical symmetrization but with more realistic control resources and, at the same time, they are intrinsically tolerant against a large class of systematic implementation errors.
Control scenarios have been identified where the use of randomized design may substantially improve the performance of dynamical decoupling methods (Santos and Viola 2006 Phys. Rev. Lett. 97 150501). Here, by focusing on the suppression of internal unwanted interactions in closed quantum systems, we review and further elaborate on the advantages of randomization at long evolution times. By way of illustration, special emphasis is devoted to isolated Heisenberg chains of coupled spin-1/2 particles. In particular, for nearest-neighbor interactions, two types of decoupling cycles are contrasted: inefficient averaging, whereby the number of control actions increases exponentially with the system size, and efficient averaging associated to a fixed-size control group. The latter allows for analytical and numerical studies of efficient decoupling schemes created by exploiting and merging together randomization and deterministic strategies, such as symmetrization, concatenation and cyclic permutations. Notably, sequences capable of removing interactions up to third order in the achievable control timescale are explicitly constructed, and a numerical algorithm to search for optimal decoupling sequences is proposed. The consequences of faulty controls in deterministic versus randomized schemes are also analyzed.
The fundamental goal of quantum computing is to precisely control quantum systems to perform meaningful tasks, including implementing high-fidelity quantum gates for reliable quantum computation and accurately simulating complex quantum many- body dynamics. In this dissertation, we develop improved quantum control protocols for three distinct objectives, quantum error suppression, quantum optimal control, and analog quantum algorithms, achieving performance beyond standard approaches. First, we introduce new dynamical decoupling protocols, including both determin- istic and randomized constructions, that can substantially outperform conventional deterministic sequences. We then extend the randomized approach to dynamically corrected gates. Second, we propose a randomized quantum optimal control frame- work that offers advantages over deterministic optimal control protocols. Finally, we develop new control protocols for analog quantum algorithms to perform high-order Hamiltonian simulation and learning unknown quantum states.
The need for strategies able to accurately manipulate quantum dynamics is ubiquitous in quantum control and quantum information processing. We investigate two scenarios where randomized dynamical decoupling techniques become more advantageous with respect to standard deterministic methods in switching off unwanted dynamical evolution in a closed quantum system: when dealing with decoupling cycles which involve a large number of control actions and/or when seeking long-time quantum information storage. Highly effective hybrid decoupling schemes, which combine deterministic and stochastic features are discussed, as well as the benefits of sequentially implementing a concatenated method, applied at short times, followed by a hybrid protocol, employed at longer times. A quantum register consisting of a chain of spin-1/2 particles interacting via the Heisenberg interaction is used as a model for the analysis throughout.