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arXiv:1105.0333 · New Journal of Physics

Decoherence times of universal two-qubit gates in the presence of broad-band noise

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

Published Sep 28, 2011• 31 citations
arXivHTMLPDF

Abstract

The controlled generation of entangled states of two quantum bits is a fundamental step toward the implementation of a quantum information processor. In nano-devices this operation is counteracted by the solid-state environment, characterized by a broadband and non-monotonic power spectrum, often 1/ f , at low frequencies. For single-qubit gates, incoherent processes due to fluctuations acting on different time scales result in peculiar short- and long-time behavior. Markovian noise gives rise to exponential decay with relaxation and decoherence times, T 1 and T 2 , simply related to the symmetry of the qubit–environment coupling Hamiltonian. Noise with the 1/ f power spectrum at low frequencies is instead responsible for defocusing processes and algebraic short-time behavior. In this paper, we identify the relevant decoherence times of an entangling operation due to the different decoherence channels originating from solid-state noise. Entanglement is quantified by concurrence, which we evaluate in an analytic form employing a multi-stage approach. The 'optimal' operating conditions of reduced sensitivity to noise sources are identified. We apply this analysis to a superconducting gate for experimental noise spectra.

DOI
10.1088/1367-2630/13/9/093037

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The controlled generation of entangled states of two quantum bits is a fundamental step toward the implementation of a quantum information processor. In nano-devices this operation is counteracted by the solid-state environment, characterized by a broadband and non-monotonic power spectrum, often 1/ f , at low frequencies. For single-qubit gates, incoherent processes due to fluctuations acting on different time scales result in peculiar short- and long-time behavior. Markovian noise gives rise to exponential decay with relaxation and decoherence times, T 1 and T 2 , simply related to the symmetry of the qubit–environment coupling Hamiltonian. Noise with the 1/ f power spectrum at low frequencies is instead responsible for defocusing processes and algebraic short-time behavior. In this paper, we identify the relevant decoherence times of an entangling operation due to the different decoherence channels originating from solid-state noise. Entanglement is quantified by concurrence, which we evaluate in an analytic form employing a multi-stage approach. The 'optimal' operating conditions of reduced sensitivity to noise sources are identified. We apply this analysis to a superconducting gate for experimental noise spectra.
The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the qubits. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, the noise that the quantum device demonstrates has a 1/ f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review, the current state of the theory of the decoherence due to the qubit interaction with the fluctuators is discussed. The effect of such an environment on two different protocols of the qubit manipulations, free induction and echo signal, is described. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently, the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function alone. We describe the effect of the fluctuators using the so-called spin-fluctuator model. Being quite realistic, this model allows one to exactly evaluate the qubit dynamics in the presence of one fluctuator. This solution is found, and its features, including non-Gaussian effects, are analyzed in detail. We extend this consideration to systems of large numbers of fluctuators, which interact with the qubit and lead to the 1/ f noise. We discuss existing experiments on the Josephson qubit manipulation and try to identify non-Gaussian behavior.
The efficiency of the future devices for quantum information processing is limited mostly by the finite decoherence rates of the individual qubits and quantum gates. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources obtained by engineering. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, quantum devices are affected by noise decreasing with frequency fff approximately as 1/f1/f1/f. According to the present point of view, such noise is due to material- and device-specific microscopic degrees of freedom interacting with quantum variables of the nanodevice. The simplest picture is that the environment that destroys the phase coherence of the device can be thought of as a system of two-state fluctuators, which experience random hops between their states. If the hopping times are distributed in an exponentially broad domain, the resulting fluctuations have a spectrum close to 1/f1/f1/f in a large frequency range. This paper reviews the current state of the theory of decoherence due to degrees of freedom producing 1/f1/f1/f noise. Basic mechanisms of such noises in various nanodevices are discussed and several models describing the interaction of the noise sources with quantum devices are reviewed. The main focus of the review is to analyze how the 1/f1/f1/f noise destroys their coherent operation. The start is from individual qubits concentrating mostly on the devices based on superconductor circuits and then some special issues related to more complicated architectures are discussed. Finally, several strategies for minimizing the noise-induced decoherence are considered.
Broadband noise represents a severe limitation towards the implementation of a solid-state quantum information processor. Considering common spectral forms, we propose a classification of noise sources based on the effects produced instead of on their microscopic origin. We illustrate a multi-stage approach to broadband noise which systematically includes only the relevant information on the environment, out of the huge parametrization needed for a microscopic description. We apply this technique to a solid-state two-qubit gate in a fixed coupling implementation scheme.
Abstract. The efficiency of the future devices for quantum information processing is limited mostly by the finite decoherence rates of the qubits. Recently a substantial progress was achieved in enhancing the time, which a solid-state qubit demonstrates a coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions the material-inherent sources of noise start to play a crucial role. In most cases the noise that quantum device demonstrate has 1/f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review we discuss the current state of the theory of the decoherence due to the qubit interaction with the fluctuators. We describe the effect of such an environment on different protocols of the qubit manipulations- free induction and echo signal. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function only.
Understanding error mechanisms in two-qubit gate operations is essential for building high-fidelity quantum processors. While prior studies predominantly treat dephasing noise as either Markovian or predominantly low-frequency, realistic qubit environments exhibit structured, frequency-dependent spectra. Here we demonstrate that noise at frequencies matching the dressed-state energy splitting--set by the inter-qubit coupling strength g--induces a distinct relaxation channel that degrades gate performance. Through combined theoretical analysis and experimental verification on superconducting qubits with engineered noise spectra, we show that two-qubit gate errors scale predictably with the noise power spectral density at frequency 2g, extending the concept of T1ρT_{1ρ}T1ρ​ relaxation to interacting systems. This frequency-selective relaxation mechanism, universal across platforms, enriches our understanding of decoherence pathways during gate operations. The same mechanism sets coherence limits for dual-rail or singlet-triplet encodings.
We present a general route to reduce inhomogeneous broadening in nanodevices due to 1/f1/f1/f noise. We apply this method to a universal two-qubit gate and demonstrate that for selected optimal couplings, a high-efficient gate can be implemented even in the presence of 1/f1/f1/f noise. Entanglement degradation due to interplay of 1/f1/f1/f and quantum noise is quantified via the concurrence. A charge-phase $\sqrt{\text{i}\ensuremath{-}\text{SWAP}}$ gate for spectra extrapolated from single-qubit experiments is analyzed.