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Europhysics Letters (EPL)

Universal dynamical decoupling from slow noise with minimal control

Guy Bensky, E. Brion, F. Carlier, V. M. Akulin, Gershon Kurizki

Published Jan 1, 2010• 9 citations
Publisher

Abstract

We propose a technique that allows to simultaneously perform universal control of the evolution operator of a system and compensate for the first-order contribution of any Hermitian constant noise and the action of the environment. We show that, at least, a three-valued Hamiltonian is needed in order to protect the system against any such noise and propose an explicit algorithm for finding an appropriate control sequence. This algorithm is applied to numerically design a safe gate in an atomic qutrit.

DOI
10.1209/0295-5075/89/10011

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We propose a technique that allows to simultaneously perform universal control of the evolution operator of a system and compensate for the first-order contribution of any Hermitian constant noise and the action of the environment. We show that, at least, a three-valued Hamiltonian is needed in order to protect the system against any such noise and propose an explicit algorithm for finding an appropriate control sequence. This algorithm is applied to numerically design a safe gate in an atomic qutrit.
Abstract A protocol for implementing a universal set of quantum gates, which are safeguarded from noise through geometric, dephasing‐free, and dynamical‐decoupling approaches is proposed. With properly designed Hamiltonians, the desired interactions are realized directly within the Schrödinger picture rather than relying on the interaction picture. This design confers two advantages. One is that the system's evolution remains continuously protected by the noise‐mitigation strategies at every stage, eliminating the need to revert to the Schrödinger picture. The other one is that the dynamical decoupling technique effectively averages out small residual free terms in the system's Hamiltonian, thus reducing the stringent requirements for precise control of system parameters to avoid errors. Furthermore, numerical results are presented to support our protocol by finding gate fidelities in the absence (presence) of noises or errors, without or with dynamical decoupling technique.
Realistic quantum computing is subject to noise. Therefore, an important frontier in quantum computing is to implement noise-resilient quantum control over qubits. At the same time, dynamical decoupling can protect the coherence of qubits. Here we demonstrate non-trivial quantum evolution steered by dynamical decoupling control, which simultaneously suppresses noise effects. We design and implement a self-protected controlled-NOT gate on the electron spin of a nitrogen-vacancy centre and a nearby carbon-13 nuclear spin in diamond at room temperature, by employing an engineered dynamical decoupling control on the electron spin. Final state fidelity of 0.91(1) is observed in preparation of a Bell state using the gate. At the same time, the qubit coherence time is elongated at least 30 fold. The design scheme does not require the dynamical decoupling control to commute with the qubit interaction and therefore works for general qubit systems. This work marks a step towards implementing realistic quantum computing systems. Realistic quantum computers require a high degree of qubit control and must also be resilient to noise. Using dynamical decoupling control techniques, Liuet al.implement a self-protected controlled-NOT gate for electron and nuclear spins that retains a high final state fidelity.
Parity-time (PT\mathcal{PT}PT)-symmetric non-Hermitian Hamiltonians bring about many novel features and interesting applications such as quantum gates faster than those in Hermitian systems and topological state transfer. The performance of evolutions under PT\mathcal{PT}PT-symmetric Hamiltonians is degraded by the inevitable noise and errors due to system-environment interaction and experimental imperfections. In contrast to Hermitian Hamiltonians, the fluctuations in dissipative beams that are utilized to generate non-Hermitian contributions in the PT\mathcal{PT}PT-symmetric Hamiltonians cause additional errors. Here we achieve the protection of PT\mathcal{PT}PT-symmetric Hamiltonians against noise acting along the qubit's quantization axis by combining quantum evolutions with dynamical decoupling sequences. We demonstrate the performance of our method by numerical simulations. Realistic noise sources and parameters are chosen including constant detuning error, time-varying detuning noise, and dissipative-beam noise. The fidelity of states after protected evolutions is well above those after unprotected evolutions under all the above situations. Our work paves the way for further studies and applications of non-Hermitian PT\mathcal{PT}PT-symmetric physics in noisy quantum systems.
In the field of quantum information, a major challenge is to protect and shield quantum systems from environmental influences, which cause dissipation and decoherence. One approach to address this problem is called dynamical decoupling, where we act on a quantum system with a series of fast and strong local control operations. If done correctly, the system's state gets rotated in discrete steps in its state space in such a way that the effects of the environment cancel up to a certain order. In the first part of this thesis, we will introduce the basics of dynamical decoupling and present a new approach for constructing dynamical decoupling schemes based on sequences of Weyl operators on networks of qudits. This approach goes beyond merely protecting a quantum system, as it is also capable of altering existing Hamiltonian interactions in ways suitable for quantum simulation purposes. We will also investigate how imperfect controls influence the effectiveness of dynamical decoupling and focus particularly on stochastic noise. In the second part of the thesis, we study concrete scenarios for the application of dynamical decoupling. First, we consider the task of quantum state transfer on a linear chain of qubits and use decoupling to protect the transfer from detrimental influences caused by a bend in the chain. We also look at how to design the specific interaction strengths required on the chain to make the state transfer work and extend this result to chains of qudits. Another chapter deals with decoupling the atomic centre-of-mass motion of a trapped atom or ion in a cavity interacting with a radiation field. Finally, we use decoupling to execute sequences of one- and two-qubit quantum gates on a chain of coupled qubits. Particular care is taken to ensure high fidelity operations in the presence of imperfect decoupling pulses.
We explore a strategy for protecting the evolution of a qubit against the effects of environmental noise based on the application of controlled time-dependent perturbations. In the case of a purely decohering coupling, an explicit sequence of control operations is designed, able to average out the decoherence of the qubit with high efficiency. We argue that, in principle, the effects of arbitrary qubit-environment interactions can be removed through suitable decoupling perturbations acting on the system dynamics over time scales comparable to the correlation time of the environment.