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arXiv:1101.2942 · Superconductor Science and Technology

Protecting superconducting qubits with a universal quantum degeneracy point

X-H Deng, Yong Hu, Lin Tian

Published Sep 30, 2013• 6 citations
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Abstract

Low-frequency noise can induce serious decoherence in superconducting qubits. Due to its diverse physical origins, such noise can couple with the qubits either as transverse or as longitudinal noise. Here we present a universal quantum degeneracy point approach that can protect an encoded qubit from arbitrary low-frequency noise. We further show that universal quantum logic gates can be performed on the encoded qubits with high fidelity. The proposed scheme can be readily implemented with superconducting flux qubits or with a qubit coupling with a superconducting resonator. Meanwhile, the scheme is also robust against small parameter spreads due to errors of fabrication in the superconducting systems.

DOI
10.1088/0953-2048/26/11/114002

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Low-frequency noise can induce serious decoherence in superconducting qubits. Due to its diverse physical origins, such noise can couple with the qubits either as transverse or as longitudinal noise. Here we present a universal quantum degeneracy point approach that can protect an encoded qubit from arbitrary low-frequency noise. We further show that universal quantum logic gates can be performed on the encoded qubits with high fidelity. The proposed scheme can be readily implemented with superconducting flux qubits or with a qubit coupling with a superconducting resonator. Meanwhile, the scheme is also robust against small parameter spreads due to errors of fabrication in the superconducting systems.
We present a scheme for implementing quantum operations with superconducting qubits. Our approach uses a "coupler" qubit to mediate a controllable interaction between data qubits, pulse sequences which strongly mitigate the effects of 1/f flux noise, and a high-Q resonator-based local memory. We develop a Monte Carlo simulation technique capable of describing arbitrary noise-induced dephasing and decay, and demonstrate in this system a set of universal gate operations with O(10(-5)) error probabilities in the presence of experimentally measured levels of 1/f noise. We then add relaxation and quantify the decay times required to maintain this error level.
Quantum computers now show the promise of surpassing any possible classical machine. However, errors limit this ability and current machines do not have the ability to implement error correcting codes due to the limited number of qubits and limited control. Therefore, dynamical decoupling (DD) and encodings that limit noise with fewer qubits are more promising. For these reasons, we put forth a model of universal quantum computation that has many advantages over strategies that require a large overhead such as the standard quantum-error correcting codes. First, we separate collective noise from individual noises on physical qubits and use a decoherence-free subspace that uses just two qubits for its encoding to eliminate collective noise. Second, our bath model is very general as it uses a spin-boson-type bath but without any Markovian assumption. Third, we are able to either use a steady global magnetic field or to devise a set of DD pulses that remove much of the remaining noise and commute with the logical operations on the encoded qubit. This allows removal of noise while implementing gate operations. Numerical support is given for this hybrid protection strategy which provides an efficient approach to deal with the decoherence problems in quantum computation and is experimentally viable for several current quantum computing systems. This is emphasized by a recent experiment on superconducting qubits which shows promise for increasing the number of gates that can be implemented reliably with some realistic parameter assumptions.
Two-level system fluctuators in superconducting devices have demonstrated coherent coupling with superconducting qubits. Here, we show that universal quantum logic gates can be realized in these two-level systems solely by tuning a superconducting resonator in which they are imbedded. Because of the large energy separation between the fluctuators, conventional gate schemes in the cavity QED approach that are widely used for solid-state qubits cannot be directly applied to the fluctuators. We study a scheme to perform the gate operations by exploiting the controllability of the superconducting resonator with realistic parameters. Numerical simulation that takes into account the decay of the resonator mode shows that the quantum logic gates can be realized with high fidelity at moderate resonator decay rate. The quantum logic gates can also be realized between fluctuators inside different Josephson junctions that are connected by a superconducting loop. Our scheme can be applied to explore the coupling between two-level system fluctuators and superconducting resonators as well as the coherent properties of the fluctuators.
We propose an encoding scheme to fight against ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$-type local collective noise. In our scheme, a logical qubit consists of two charge qubits coupled by a variable capacitance, and different logical qubits are coupled by a common inductance. A logical qubit provides a decoherence-free subspace (DFS) immune to the ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$-type collective noise. We show how to realize universal quantum computation in the DFS. Any two logical qubits can be selectively and controllably coupled by adjusting fluxes through the common inductance and superconducting-quantum-interference-device loops, which makes it possible to scale our scheme up to a large number of logical qubits. Finally, we show how to prepare a logical qubit in the DFS.
Decoherence is inevitable when manipulating quantum systems. It decreases the quality of quantum manipulations and thus is one of the main obstacles for large-scale quantum computation, where high-fidelity quantum gates are needed. Generally, the longer a gate operation is, the more decoherence-induced gate infidelity will be. Therefore, how to shorten the gate time becomes an urgent problem to be solved. To this end, time-optimal control based on solving the quantum brachistochrone equation is a straightforward solution. Here, based on time-optimal control, we propose a scheme to realize universal quantum gates on superconducting qubits in a two-dimensional square lattice configuration, and the two-qubit gate fidelity approaches 99.999.9%99.9. Meanwhile, we can further accelerate the ZZZ-axis gate considerably by adjusting the detuning of the external driving. Finally, in order to reduce the influence of the dephasing error, decoherence-free subspace encoding is also incorporated in our physical implementation. Therefore, we present a fast quantum scheme which is promising for large-scale quantum computation.
A central task towards building a practical quantum computer is to protect individual qubits from decoherence while retaining the ability to perform high-fidelity entangling gates involving arbitrary two qubits. Here we propose and demonstrate a dephasing-insensitive procedure for storing and processing quantum information in an all-to-all connected superconducting circuit involving multiple frequency-tunable qubits, each of which can be controllably coupled to any other through a central bus resonator. Although it is generally believed that the extra frequency tunability enhances the control freedom but induces more dephasing impact for superconducting qubits, our results show that any individual qubit can be dynamically decoupled from dephasing noise by applying a weak continuous and resonant driving field whose phase is reversed in the middle of the pulse. More importantly, we demonstrate a new method for realizing a two-qubit phase gate with inherent dynamical decoupling via the combination of continuous driving and qubit-qubit swapping coupling. We find that the weak continuous driving fields not only enable the conditional dynamics essential for quantum information processing, but also protect both qubits from dephasing during the gate operation.