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.
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.
Abstract : A key step in the construction of quantum computing technologies is the identification and elimination of unwanted sources of noise and its resulting quantum decoherence. In solid state devices, one important source of noise is the fluctuating electric and magnetic fields that come from the device elements themselves. The ultimate source of these fluctuations is the random electric currents that are strongest in the metallic electrodes and leads. This random motion has both thermal and quantum components, though in most devices presently under investigation, the thermal part dominates. In the past, this important physical effect has generally been modeled by picturing the device using an equivalent RC circuit and applying the Nyquist theorem to this circuit. This approach has limitations, since it depends on global quantities, rather than on the detailed geometry and the local electromagnetic properties of the components. Our aim in this research project was to compute the effect from first principles. We considered the underlying physical law (quantum electrodynamics) governing the devices in question. Given the position- and frequency-dependent dielectric function, the electromagnetic noise spectrum can be calculated, and the decohering effect can be deduced. Semiconducting quantum dot and superconducting flux qubits were investigated.
High-fidelity quantum gate operations are essential for achieving scalable quantum circuits. In spin qubit quantum computing systems, metallic gates and antennas that are necessary for qubit operation, initialization, and readout, also cause detrimental effects by enhancing fluctuations of electromagnetic fields. Therefore, evanescent wave Johnson noise (EWJN) caused by near-field thermal and vacuum fluctuations becomes an important unmitigated noise, which induces the decoherence of spin qubits and limits the quantum gate operation fidelity. Here, we first develop a macroscopic quantum electrodynamics theory of EWJN to account for the dynamics of two spin qubits interacting with metallic circuitry. Then we propose a numerical technique based on volume integral equations to quantify EWJN strength in the vicinity of nanofabricated metallic gates with arbitrary geometry. We study the limits to two-spin-qubit gate fidelity from EWJN-induced relaxation processes in two experimentally relevant quantum computing platforms: (a) the silicon quantum dot system and (b) nitrogen-vacancy centers in diamond. Finally, we introduce a Lindbladian engineering method to optimize the control pulse sequence design and show its enhanced performance over Hamiltonian engineering in mitigating the influence of thermal and vacuum fluctuations. Our work leverages advances in computational electromagnetics, fluctuational electrodynamics, and open quantum systems to suppress the effects of near-field thermal and vacuum fluctuations and reach the limits of two-spin-qubit gate fidelity.
This thesis discusses a series of experimental and theoretical studies on fast control and decoherence in superconducting quantum circuits. These two subjects are complementary aspects of the problem of improving the gate fidelities in quantum information processing devices based on superconducting circuits. \n \nIn the first part of this thesis, we present experiments on fast control of a superconducting flux qubit using strong driving. We explore driving with short pulses and a driving strength significantly exceeding the transition frequency. The observed dynamics is described in terms of quasienergies and quasienergy states, in agreement with Floquet theory. We observe the role of pulse shaping in the dynamics, as determined by non-adiabatic transitions between Floquet states. In addition, based on adiabatic perturbation theory in the Floquet picture, we propose a control scheme for fast and high-fidelity single-qubit operations with strong driving. These results pave the way to quantum control with a fidelity beyond the threshold of fault-tolerant quantum computation. \n \nIn the second part of this thesis, we discuss experimental methods and present the characterization of decoherence in superconducting resonators and superconducting qubits. Firstly, we present an analysis method on the measurements of photon loss in superconducting resonators. We use this method to characterize the microwave loss of aluminum oxide, an important material in superconducting circuits. The power and temperature dependence of the measured loss is consistent with loss due to two-level defects in amorphous materials. Secondly, we present experimental results on decoherence and noise spectroscopy of a superconducting flux qubit. Using the qubit as a noise spectrometer, we perform detailed measurements on the power spectral density of the flux noise in superconducting circuits over a wide range of frequencies, from 10^-3 to 10^8 Hz, and over a temperature range from 35 to 130 mK. We also present measurements of frequency and temperature dependence of the qubit energy relaxation.
A high degree of quantum coherence is a crucial requirement for the implementation of quantum logic devices. Solid state nanodevices seem particularly promising from the point of view of integrability and flexibility in the design. However decoherence is a serious limitation, due to the presence of many types low energy excitations in the ``internal'' environment and of ``external'' sources due to the control circuitery. Here we study both kind of dephasing in a special implementation, the charge Josephson qubit, however many of our results are applicable to a large class of solid state qubits. This is the case of 1/f noise for which we introduce and study a model of an environment of bistable fluctuatiors. External sources of noise are analized in terms of a suitable harmonic oscillator environment and the explicit mapping on the spin boson model is presented. We perform a detailed investigation of various computation procedures (single shot measurements, repeated measurements) and discuss the problem of the information needed to characterize the effect of the environment. For a fluctuator environment with 1/f spectrum memory effects turn out to be important. Although in general information beyond the power spectrum is needed, in many situations this results in the knowledge of only one more microscopic parameter of the environment. This allows to determine which degrees of freedom of the environment are effective sources of decoherence in each different physical situation considered.
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 f approximately as 1/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/f in a large frequency range. This paper reviews the current state of the theory of decoherence due to degrees of freedom producing 1/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/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.
In this thesis work, the quantum behavior of a superconducting circuit implementing a quantum bit or qubit is studied. With the use of resonant microwave pulses the full manipulation of the quantum state of this system is demonstrated: any rotation of the state vector around the Bloch sphere can be achieved and by using particular NMR inspired sequences of microwave pulses, the robustness of an operation against particular types of errors, like slow fluctuations of the transition frequency of the qubit, can be improved. The phenomenon of decoherence which drives the system from a quantum behavior to a classical one, has been characterized in the free evolution regime. By properly tuning the working point in the external parameter space, the qubit can be decoupled to first order from the fluctuations of its environment, thus enhancing coherence. In these optimal conditions, low frequency charge noise probably of microscopic origin appears to be the limiting source of decoherence for our system. The study of decoherence during driven evolution demonstrated that by suppressing the effect of those fluctuations of the environment slower than that of the driving field, the coherence of the qubit can be improved. Finally a new non-dissipative readout method based on microwave reflectometry has been set up, which improves the sensitivity and could in principle lead to a non-demolition measurement of the qubit state.