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arXiv:1703.05654 · New Journal of Physics

Suppressing the geometric dephasing of Berry phase by using modified dynamical decoupling sequences

Xiao-Ke Qin, Guang‐Can Guo, Zheng-Wei Zhou

Published Dec 19, 2016• 4 citations
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Abstract

Even though traditional dynamical decoupling methods have the ability to resist dynamic dephasing caused by low frequency noise, they are not appropriate for suppressing the residual geometric dephasing, which arises from the disturbance of the geometric loop in the parameter space. This prevents the precision of quantum manipulation-based geometric quantum gates from being promoted further. In this paper, we design two kinds of modified dynamical decoupling schemes to suppress the residual geometric dephasing. The further numerical simulation demonstrates the validity of our schemes.

DOI
10.1088/1367-2630/aa5488

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Even though traditional dynamical decoupling methods have the ability to resist dynamic dephasing caused by low frequency noise, they are not appropriate for suppressing the residual geometric dephasing, which arises from the disturbance of the geometric loop in the parameter space. This prevents the precision of quantum manipulation-based geometric quantum gates from being promoted further. In this paper, we design two kinds of modified dynamical decoupling schemes to suppress the residual geometric dephasing. The further numerical simulation demonstrates the validity of our schemes.
In the quantum-computation scenario, the geometric phase gates are becoming increasingly attractive for their intrinsic fault tolerance to disturbance. With an adiabatic cyclic evolution, Berry phase appears to realize a geometric transformation. Performing the quantum gates as many as possible within the timescale of coherence, however, remains an inconvenient bottleneck due to the systematic errors. Here we propose an accelerated adiabatic quantum gate based on the Berry phase, the transitionless driving, and the dynamical decoupling. It reconciles a high fidelity with a high speed in the presence of control noise or imperfection. We optimize the dynamical-decoupling sequence in the time domain under a popular Gaussian noise spectrum following the inversely quadratic power law.
Scalable quantum information processing requires the ability to tune multiqubit interactions. This makes the precise manipulation of quantum states particularly difficult for multiqubit interactions because tunability unavoidably introduces sensitivity to fluctuations in the tuning parameters, leading to erroneous multiqubit gate operations. The performance of quantum algorithms may be severely compromised by coherent multiqubit errors. It is therefore imperative to understand how these fluctuations affect multiqubit interactions and, more importantly, to mitigate their influence. In this study, we demonstrate how to implement dynamical-decoupling techniques to suppress the two-qubit analogue of the dephasing on a superconducting quantum device featuring a compact tunable coupler, a trending technology that enables the fast manipulation of qubit-qubit interactions. The pure-dephasing time shows up to an approximate 14 times enhancement on average when using robust sequences. The results are in good agreement with the noise generated from room-temperature circuits. Our study further reveals the decohering processes associated with tunable couplers and establishes a framework to develop gates and sequences robust against two-qubit errors.
We demonstrate a protocol, that combines quantum uncollapsing and dynamical decoupling, to protect the quantum state stored in a qubit against decoherence errors. The protocol can simultaneously suppress the two kinds of decoherence processes: the energy relaxation and the low-frequency noise induced dephasing. We present the analytical derivation and numerical simulations in detail. We also provide a preliminary experimental test in superconducting phase qubits, using the process fidelity to calibrate the performance of the protocol. Our results suggest that the protocol can be effective against errors due to both energy relaxation and the low-frequency dephasing noise, except at a reduced probability of success.
The ability of geometric quantum gate against the fluctuations of control external field was researched.We replace the random fluctuations by the periodic perturbation.In this approximation,the result shows that no matter the Berry geometry phase or the Aharonov- Anandan(A-A)geometry phase has the same ability against the stochastic fluctuations as their corresponding dynamics phases.And numerical results also justify that the Berry phase is more powerful to resist the external field fluctuation than that of the A-A phase.We believe that this distinction is caused by adiabatic approximation purely.Lastly,it is validated that the geometry quantum gates constructed by an orthogonal state scheme are more powerful against the fluctuations.
We propose a novel method for constructing geometric quantum gates using three- or two-level systems, in which a controllable variable, the detuning between the driving frequency and the atomic energy spacing, is introduced to realize geometric transformations. In particular, we have two instantaneous eigenstates with opposite eigenvalues constituting a closed loop in the parameter space. The accumulated dynamical phase is then exactly cancelled when the loop is completed, which is beyond the traditional parallel-transport restriction. We apply the transitionless quantum driving method to enhance the speed and fidelity of geometric gates. Gate fidelity in the presence of decoherence is also estimated.
Recently, nonadiabatic geometric quantum computation has been received great attentions, due to its fast operation and intrinsic error resilience. However, compared with the corresponding dynamical gates, the robustness of implemented nonadiabatic geometric gates based on the conventional single-loop geometric scheme still has the same order of magnitude due to the requirement of strict multi-segment geometric controls, and the inherent geometric fault-tolerance characteristic is not fully explored. Here, we present an effective geometric scheme combined with a general dynamical-corrected technique, with which the super-robust nonadiabatic geometric quantum gates can be constructed over the conventional single-loop geometric and two-loop composite-pulse geometric strategies, in terms of resisting the systematic error, i.e., σx error. In addition, combined with the decoherence-free subspace (DFS) coding, the resulting geometric gates can also effectively suppress the σz error caused by the collective dephasing. Notably, our protocol is a general one with simple experimental setups, which can be potentially implemented in different quantum systems, such as Rydberg atoms, trapped ions and superconducting qubits. These results indicate that our scheme represents a promising way to explore large-scale fault-tolerant quantum computation.