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International Journal of Quantum Information

PROTECTED COMPUTATIONAL SUBSPACES OF COUPLED SUPERCONDUCTING QUBITS

Andrea Mastellone, Antonio D’Arrigo, Elisabetta Paladino, G. Falci

Published Jul 1, 2008• 3 citations
Publisher

Abstract

We discuss the effect of low-frequency noise on interacting superconducting qubits in a fixed coupling scheme. By properly choosing operating conditions, within the adiabatic framework the systems develops two decoupled subspaces. The subspace where a SWAP operation takes place turns out to be resilient to low frequency fluctuations. The possibility to encode a single qubit in a protected two-physical-qubit system subspace is briefly discussed.

DOI
10.1142/s0219749908003906

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We discuss the effect of low-frequency noise on interacting superconducting qubits in a fixed coupling scheme. By properly choosing operating conditions, within the adiabatic framework the systems develops two decoupled subspaces. The subspace where a SWAP operation takes place turns out to be resilient to low frequency fluctuations. The possibility to encode a single qubit in a protected two-physical-qubit system subspace is briefly discussed.
We study the effects of correlated low-frequency noise sources acting on a two-qubit gate in a fixed coupling scheme. A decoherence model for the spatial and cross-talk correlations is introduced. The efficiency inside the SWAP subspace is analyzed by combining analytic results based on the adiabatic approximation and numerical simulations. Results critically depend on amplitude of the low-frequency noise with respect to the qubits' coupling strength. Correlations between noise sources induce different qualitative behavior depending on the values of the above parameters. The possibility to reduce dephasing due to correlated low-frequency noise by a recalibration protocol is discussed.
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.
Decoherence-free subspaces protect quantum information from the effects of noise that is correlated across the physical qubits used to implement them. Given the ability to impose suitable Hamiltonians upon such a multi-qubit system, one can also implement a set of logical gates which enables universal computation on this information without compromising this protection. Real physical systems, however, seldom come with the correct Hamiltonians built-in, let alone the ability to turn them off and on at will. In the course of our development of quantum information processing devices based on liquid-state NMR, we have found the task of operating on quantum information encoded in decoherence-free subspaces rather more challenging than is commonly assumed. This contribution presents an overview of these challenges and the methods we have developed for overcoming them in practice. These methods promise to be broadly applicable to many of the physical systems proposed for the implementation of quantum information processing devices.
Recent advances have significantly enhanced the coherence times of superconducting qubits. However, high-fidelity storage of multiqubit quantum states in large-scale circuits is still limited by factors such as the flux noise and crosstalk. We propose an X-iSwap decoupling sequence combining single-qubit ${X}_{\ensuremath{\pi}}$ gates and two-qubit iSwap gates to effectively mitigate dephasing from the low-frequency flux noise and eliminate crosstalk between qubits. Numerical simulations of noisy random evolution show excellent agreement with the theoretical models. In quantum memory applications, our method substantially extends the decay time of two-qubit fidelity and eliminates fidelity oscillations caused by the ZZ crosstalk. Compared to the traditional decoupling methods based on single-qubit gates, the X-iSwap sequence exhibits superior robustness against small system errors, which holds promise for widespread application in two-qubit systems and large-scale quantum processors for tasks such as long-term quantum memory and entanglement protection.
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.