The present work makes a brief introduction to QND (Quantum non demolition measurement) measurements and its characteristics. In addition, a qubit coupled to a forced quantum harmonic oscillator which is described theoretically as an example of a QND measurement in a qubit. The formalism developed for this type of coupled quantum systems is developed within the quantum theory of computation. As part of the study of QND measurements, the flow qubits making use of quantum superconducting interferometers (SQUIDs) are introduced. The analysis of this computer schema attempts to introduce the reader to the concepts of quantum computing such as qubit, which is the basic component that allows information to be processed quantumly. The objective of this work is to characterize whether the elaborated measures on the coupled qubit are QND or not. In this sense, the application of the exposed formalism will allow us to glimpse the scope and limitations of coupled qubits in the development and application of quantum computing systems to this day. Additionally, the application of this theory can be applied to QND measurements on superconducting qubits coupled to a quantum harmonic oscillator. All this process is subject to the analysis and methodology provided by the history of science and technology.
The present work makes a brief introduction to QND (Quantum non demolition measurement) measurements and its characteristics. In addition, a qubit coupled to a forced quantum harmonic oscillator which is described theoretically as an example of a QND measurement in a qubit. The formalism developed for this type of coupled quantum systems is developed within the quantum theory of computation. As part of the study of QND measurements, the flow qubits making use of quantum superconducting interferometers (SQUIDs) are introduced. The analysis of this computer schema attempts to introduce the reader to the concepts of quantum computing such as qubit, which is the basic component that allows information to be processed quantumly. The objective of this work is to characterize whether the elaborated measures on the coupled qubit are QND or not. In this sense, the application of the exposed formalism will allow us to glimpse the scope and limitations of coupled qubits in the development and application of quantum computing systems to this day. Additionally, the application of this theory can be applied to QND measurements on superconducting qubits coupled to a quantum harmonic oscillator. All this process is subject to the analysis and methodology provided by the history of science and technology.
El presente trabajo, realiza una breve introducción a las medidas QND (Quantum nondemolition measurement) y sus características. Además, se describe teóricamente un qubit acoplado a un oscilador armónico cuántico forzado como ejemplo de una medición QND en un qubit. El formalismo desarrollado para este tipo de sistemas cuánticos acoplados se desenvuelve dentro de la teoría cuántica de la computación. Como parte del estudio de las mediciones QND, se introducen los qubits de flujo que hacen uso de los interferómetros superconductores cuánticos (SQUIDs). El análisis de este esquema informático intenta introducir al lector en los conceptos de computación cuántica como el quibit que es el componente base que permite procesar información de forma cuántica. El objetivo de este trabajo es caracterizar si las medidas elaboradas sobre el qubit acoplado son o no QND. En este sentido, la aplicación del formalismo expuesto permitirá vislumbrar los alcances y limitaciones de los qubits acoplados en el desarrollo y aplicación de los sistemas cuánticos de la computación hasta el día de hoy. Adicionalmente, la aplicación de esta teoría se puede emplear a mediciones QND sobre qubits superconductores articulados a un oscilador armónico cuántico. Todo este proceso es sujeto al análisis y metodología que nos proporciona la historia de la ciencia y la tecnología. AbstractThe present work makes a brief introduction to QND (Quantum non demolition measurement) measurements and its characteristics. In addition, a qubit coupled to a forced quantum harmonic oscillator which is described theoretically as an example of a QND measurement in a qubit. The formalism developed for this type of coupled quantum systems is developed within the quantum theory of computation. As part of the study of QND measurements, the flow qubits making use of quantum superconducting interferometers (SQUIDs) are introduced. The analysis of this computer schema attempts to introduce the reader to the concepts of quantum computing such as qubit, which is the basic component that allows information to be processed quantumly. The objective of this work is to characterize whether the elaborated measures on the coupled qubit are QND or not. In this sense, the application of the exposed formalism will allow us to glimpse the scope and limitations of coupled qubits in the development and application of quantum computing systems to this day. Additionally, the application of this theory can be applied to QND measurements on superconducting qubits coupled to a quantum harmonic oscillator. All this process is subject to the analysis and methodology provided by the history of science and technology.
El presente trabajo, realiza una breve introducción a las medidas QND (Quantum nondemolition measurement) y sus características. Además, se describe teóricamente un qubit acoplado a un oscilador armónico cuántico forzado como ejemplo de una medición QND en un qubit. El formalismo desarrollado para este tipo de sistemas cuánticos acoplados se desenvuelve dentro de la teoría cuántica de la computación. Como parte del estudio de las mediciones QND, se introducen los qubits de flujo que hacen uso de los interferómetros superconductores cuánticos (SQUIDs). El análisis de este esquema informático intenta introducir al lector en los conceptos de computación cuántica como el quibit que es el componente base que permite procesar información de forma cuántica. El objetivo de este trabajo es caracterizar si las medidas elaboradas sobre el qubit acoplado son o no QND. En este sentido, la aplicación del formalismo expuesto permitirá vislumbrar los alcances y limitaciones de los qubits acoplados en el desarrollo y aplicación de los sistemas cuánticos de la computación hasta el día de hoy. Adicionalmente, la aplicación de esta teoría se puede emplear a mediciones QND sobre qubits superconductores articulados a un oscilador armónico cuántico. Todo este proceso es sujeto al análisis y metodología que nos proporciona la historia de la ciencia y la tecnología. AbstractThe present work makes a brief introduction to QND (Quantum non demolition measurement) measurements and its characteristics. In addition, a qubit coupled to a forced quantum harmonic oscillator which is described theoretically as an example of a QND measurement in a qubit. The formalism developed for this type of coupled quantum systems is developed within the quantum theory of computation. As part of the study of QND measurements, the flow qubits making use of quantum superconducting interferometers (SQUIDs) are introduced. The analysis of this computer schema attempts to introduce the reader to the concepts of quantum computing such as qubit, which is the basic component that allows information to be processed quantumly. The objective of this work is to characterize whether the elaborated measures on the coupled qubit are QND or not. In this sense, the application of the exposed formalism will allow us to glimpse the scope and limitations of coupled qubits in the development and application of quantum computing systems to this day. Additionally, the application of this theory can be applied to QND measurements on superconducting qubits coupled to a quantum harmonic oscillator. All this process is subject to the analysis and methodology provided by the history of science and technology.
We theoretically describe the weak measurement of a two-level system (qubit) and quantify the degree to which such a qubit measurement has a quantum nondemolition (QND) character. The qubit is coupled to a harmonic oscillator, which undergoes a projective measurement. Information on the qubit state is extracted from the oscillator measurement outcomes, and the QND character of the measurement is inferred from the result of subsequent measurements of the oscillator. We use the positive operator valued measure (POVM) formalism to describe the qubit measurement. Two mechanisms lead to deviations from a perfect QND measurement: (i) the quantum fluctuations of the oscillator, and (ii) quantum tunneling between the qubit states ∣0⟩ and ∣1⟩ during measurements. Our theory can be applied to QND measurements performed on superconducting qubits coupled to a circuit oscillator.
We present experiments that address the issue of measurement of superconducting qubits. A quantum non‐demolition (QND) type of readout is used to implement a projective measurement, which is an important component of many protocols in quantum information. The state of a persistent current qubit is measured using a driven non‐linear resonator, based on DC‐SQUID whose Josephson inductance is qubit‐state dependent. When properly optimized, the readout is efficient and projective. We discuss the relation between the concept of QND detection and the observed projective character of the measurement.
In a quantum computer, the information carriers, which are bits in ordinary computers, are implemented as devices that exhibit coherent superpositions of physical states and entanglement. Such components, known as quantum bits or qubits, can be realized with various different types of two-state quantum systems. Quantum computers will be built for computational speed, with hoped for applications especially in cryptography and in other tasks where classical computers remain inefficient. Circuit quantum electrodynamics (cQED) is a quantum-computer architecture which employs superconducting electronic components and microwave photon fields as building blocks. Compared to cavity quantum electrodynamics (CQED), where atoms are trapped in physical cavities, cQED is more attractive in that its qubits are tunable and conveniently integrable with the electronics already in use. This architecture has shown some of the most promising qubit designs, despite their coherence times reaching tens of microseconds, are still below the state of the art with spin qubits, which reach milliseconds. Coherence times are historically the most relevant parameters describing the fitness of a qubit, although these days not necessarily the limiting factor. This thesis presents a comprehensive set of theoretical and experimental methods for measuring the characteristic parameters of superconducting qubits. We especially study transmission-line-shunted plasma oscillation qubits, or transmons, and presents experimental results for a single sample. Transmon capacitively couples a superconducting quantum interference device (SQUID) with a coplanar waveguide (CPW) resonator, often with added frequency tunability utilizing an external magnet. The number of superconducting charge carriers tunnelled through a junction in the SQUID are used as qubit degrees of freedom. Readout of the qubit state is carried out by measuring transmission through the CPW. A cryogenic setup is employed with measurement and driving pulses delivered from microwave sources. Steady-state spectroscopy is employed to determine the resonance frequencies of the qubit and the resonator, qubit-resonator coupling constants, and the energy parameters of the qubit. Pulse-modulated measurements are employed to determine the coherence times of the qubit. The related analysis- and simulation programs and scripts are collected togithub.com/patomaki.
Summary form only given. The present techniques allow one to perform continuous or discrete quantum measurements at or even beyond the standard "quantum noise" level, even on single quantum objects. In this context, Kip Thorne and Vladimir Braginsky introduced in the seventies the concept of "Quantum Non Demolition (QND) measurement", which was initially meant to be applied to mechanical harmonic oscillators designed for detecting gravitational waves, the so-called "Weber's bars". But the QND ideas encountered a real success in quantum optics, where quantum fluctuations are readily accessible, and can also be circumvented. We review the state of the art of QND measurements, in this broad sense of sub-shot-noise optical information processing. Most of the initial objectives of QND measurements have now been successfully reached through proof-of-principle experiments. The domain is now opening on future perspectives related to quantum information processing (e.g. quantum cryptography), either with "discrete" or "continuous" quantum variables. In this context the close relationship between QND measurements and controlled-NOT (CNOT) gates are discussed and illustrated.