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arXiv:1008.2554 · Physical Review B

Effect of an Ohmic environment on an optimally controlled flux-biased phase qubit

Amrit Poudel, Maxim Vavilov

Published Oct 28, 2010• 4 citations
arXivHTMLPDF

Abstract

We analyze the effect of environment on the gate operation of flux-biased phase qubits. We employ the master equation for a reduced density matrix of the qubit system coupled to an Ohmic environment, described by the Caldeira-Leggett model. Numerically solving this equation, we evaluate the gate error as a function of gate time, temperature, and environmental coupling strength for experimentally determined qubit parameters. The analysis is presented for single-quadrature microwave (control) pulses as well as for two-quadrature pulses, which lower the gate error significantly for idealized systems in the absence of environment. Our results indicate that two-quadrature pulses with fixed and variable driving frequency have similar performance, which outweighs the performance of single-quadrature pulses, in the presence of environment.

DOI
10.1103/physrevb.82.144528

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We analyze the effect of environment on the gate operation of flux-biased phase qubits. We employ the master equation for a reduced density matrix of the qubit system coupled to an Ohmic environment, described by the Caldeira-Leggett model. Numerically solving this equation, we evaluate the gate error as a function of gate time, temperature, and environmental coupling strength for experimentally determined qubit parameters. The analysis is presented for single-quadrature microwave (control) pulses as well as for two-quadrature pulses, which lower the gate error significantly for idealized systems in the absence of environment. Our results indicate that two-quadrature pulses with fixed and variable driving frequency have similar performance, which outweighs the performance of single-quadrature pulses, in the presence of environment.
Abstract : This thesis addresses the origin and effect of noise and fluctuations in quantum devices that find applications in quantum information processing. In the first half of the thesis, we consider a phenomenological model of the noise and study its effect on the fidelity of quantum measurements and operations that are essential for quantum computing. We focus primarily on quantum gate operations in phase qubits, detection of microwave photons and the measurement of the Berry curvature. Specifically, we examine the effect of the Ohmic noise on optimally controlled flux-biased phase qubits for one- and two-quadrature microwave pulses and demonstrate that twoquadrature pulses with fixed driving frequency are as robust as variable driving frequency, in the presence of environment. Next, we present a model to analyze the quantum efficiency of a microwave photon detector based on a current-biased Josephson junction and study the effect of decoherence on the detection efficiency of the detector. We also present alternative set-ups for microwave photon detection and provide a systematic method to compute the power absorbed by the detector. We then consider the effect of decoherence on the Berry curvature measurement, which employs a novel non-adiabatic protocol, and show that the curvature is immune to decoherence. In the second half of the thesis, we go beyond the phenomenological models of the noises and perform a detailed study of the microscopic description of the Johnson noise. Here we focus primarily on quantum dot devices. We present a formalism to compute relaxation rates in charge and spin qubits due to evanescent wave Johnson noise (EWJN) from the metallic gates that are in proximity to quantum dots. The EWJN is analyzed for the metallic gates that are characterized by both local and nonlocal dielectric response functions.
We study decoherence effects in qubits coupled to environments that exhibit resonant frequencies in their spectral function. We model the coupling of the qubit to its environment via the Caldeira-Leggett formulation of quantum dissipation/coherence, and study the simplest example of decoherence effects in circuits with resonances such as a dc superconducting quantum interference device (SQUID) phase qubit in the presence of an isolation circuit. Using the dc SQUID phase qubit as an example, we obtain two quite general results. First, when the frequency of the qubit is at least two times larger than the resonance frequency of the environmental spectral density (the isolation circuit in the case of a dc SQUID phase qubit), we find that the decoherence time of the qubit is a few orders of magnitude larger than that of the typical Ohmic regime, where the frequency of the qubit is much smaller than the resonance frequency of the spectral density. Second, we show that, when the qubit frequency is nearly the same as the resonant frequency of the environmental spectral density, an oscillatory non-Markovian decay emerges, as the qubit and its environment self-generate Rabi oscillations of characteristic time scales shorter than the decoherence time.
We study decoherence effects in qubits coupled to environments that exhibit resonant frequencies in their spectral function. We model the coupling of the qubit to its environment via the Caldeira-Leggett formulation of quantum dissipation/coherence, and study the simplest example of decoherence effects in circuits with resonances such as a dc SQUID phase qubit in the presence of an isolation circuit, which is designed to enhance the coherence time. We emphasize that the spectral density of the environment is strongly dependent on the circuit design, and can be engineered to produce longer decoherence times. We begin with a general discussion of superconducting qubits such as the flux qubit, the Cooper pair box and the phase qubit and show that in these kinds of systems appropriate circuit design can greatly modify the spectral density of the environment and lead to enhancement of decoherence times. In the particular case of the phase qubit, for instance, we show that when the frequency of the qubit is at least two times larger than the resonance frequency of the environmental spectral density, the decoherence time of the qubit is a few orders of magnitude larger than that of the typical ohmic regime, where the frequency of the qubit is much smaller than the resonance frequency of the spectral density. In addition, we demonstrate that the environment does not only affect the decoherence time, but also the frequency of the transition itself, which is shifted from its environment-free value. Second, we show that when the qubit frequency is nearly the same as the resonant frequency of the environmental spectral density, an oscillatory non-Markovian decay emerges, as the qubit and its environment self-generate Rabi oscillations of characteristic time scales shorter than the decoherence time.
Typical for qubit realizations are two performance-limiting shortcomings: the physical system is not a perfect two-level system and it couples to an environment. In this work we investigate the limits of performance of the Josephson charge qubit due to the interplay of leakage into unwanted states and dissipative effects due to environmental noise within optimal control theory. For the example of the Hadamard transformation, we show that external control field-gate bias and magnetic flux, which perform the operation for the ideal qubit perfectly, show different robustness regarding leakage into unwanted states and against dissipation. Proper selection of the temporal evolution of gate bias and magnetic flux leads to performance improvements of typically 20% regarding dissipative effects with a predicted optimal fidelity of typically 98%, presuming perfect initial-state preparation and switching times of the order of 500 ps.
We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a nonideal two level subspace, identified as the qubit, and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model that we use is an rf-SQUID under macroscopic quantum coherence and coupled inductively to a flux noise characterized by an environmental spectrum. The model interaction can generate dipole couplings which can be appreciable between the qubit and the high levels. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system's reduced density matrix. We calculate the relaxation and dephasing times as the spectral parameters of the environment are varied. We observe that, these calculated time scales receive contribution from all available frequencies in the noise spectrum (even well above the system's resonant frequency scales) stressing the dominant role played by the nonresonant transitions. The relaxation and dephasing and the leakage times thus calculated, strongly depend on the appreciably interacting levels determined by the strength of the dipole coupling. Under the influence of these nonresonant and multilevel effects, the validity of the two level approximation is dictated not by the low temperature as conveniently believed, but by these multilevel dipole couplings as well as the availability of the environmental modes.
We study decoherence effects in a dc SQUID phase qubit caused by an isolation circuit with a resonant frequency. The coupling between the SQUID phase qubit and its environment is modeled via the Caldeira-Leggett formulation of quantum dissipation/coherence, where the spectral density of the environment is related to the admittance of the isolation circuit. When the frequency of the qubit is at least two times larger than the resonance frequency of the isolation circuit, we find that the decoherence time of the qubit is two orders of magnitude larger than the typical ohmic regime, where the frequency of the qubit is much smaller than the resonance frequency of the isolation circuit. Lastly, we show that when the qubit frequency is on resonance with the isolation circuit, an oscillatory non-Markovian decay emerges, as the dc SQUID phase qubit and its environment self-generate Rabi oscillations of characteristic time scales shorter than the decoherence time.