Principles of Superconducting Quantum Computers
1. Auflage
Erschienen am 19. April 2022
384 Seiten
978-1-119-75074-1 (ISBN)
Beschreibung
Explore the intersection of computer science, physics, and electrical and computer engineering with this discussion of the engineering of quantum computers
In Principles of Superconducting Quantum Computers, a pair of distinguished researchers delivers a comprehensive and insightful discussion of the building of quantum computing hardware and systems. Bridging the gaps between computer science, physics, and electrical and computer engineering, the book focuses on the engineering topics of devices, circuits, control, and error correction.
Using data from actual quantum computers, the authors illustrate critical concepts from quantum computing. Questions and problems at the end of each chapter assist students with learning and retention, while the text offers descriptions of fundamentals concepts ranging from the physics of gates to quantum error correction techniques.
The authors provide efficient implementations of classical computations, and the book comes complete with a solutions manual and demonstrations of many of the concepts discussed within. It also includes:
* A thorough introduction to qubits, gates, and circuits, including unitary transformations, single qubit gates, and controlled (two qubit) gates
* Comprehensive explorations of the physics of single qubit gates, including the requirements for a quantum computer, rotations, two-state systems, and Rabi oscillations
* Practical discussions of the physics of two qubit gates, including tunable qubits, SWAP gates, controlled-NOT gates, and fixed frequency qubits
* In-depth examinations of superconducting quantum computer systems, including the need for cryogenic temperatures, transmission lines, S parameters, and more
Ideal for senior-level undergraduate and graduate students in electrical and computer engineering programs, Principles of Superconducting Quantum Computers also deserves a place in the libraries of practicing engineers seeking a better understanding of quantum computer systems.
In Principles of Superconducting Quantum Computers, a pair of distinguished researchers delivers a comprehensive and insightful discussion of the building of quantum computing hardware and systems. Bridging the gaps between computer science, physics, and electrical and computer engineering, the book focuses on the engineering topics of devices, circuits, control, and error correction.
Using data from actual quantum computers, the authors illustrate critical concepts from quantum computing. Questions and problems at the end of each chapter assist students with learning and retention, while the text offers descriptions of fundamentals concepts ranging from the physics of gates to quantum error correction techniques.
The authors provide efficient implementations of classical computations, and the book comes complete with a solutions manual and demonstrations of many of the concepts discussed within. It also includes:
* A thorough introduction to qubits, gates, and circuits, including unitary transformations, single qubit gates, and controlled (two qubit) gates
* Comprehensive explorations of the physics of single qubit gates, including the requirements for a quantum computer, rotations, two-state systems, and Rabi oscillations
* Practical discussions of the physics of two qubit gates, including tunable qubits, SWAP gates, controlled-NOT gates, and fixed frequency qubits
* In-depth examinations of superconducting quantum computer systems, including the need for cryogenic temperatures, transmission lines, S parameters, and more
Ideal for senior-level undergraduate and graduate students in electrical and computer engineering programs, Principles of Superconducting Quantum Computers also deserves a place in the libraries of practicing engineers seeking a better understanding of quantum computer systems.
Weitere Details
Weitere Ausgaben
Personen
Daniel D. Stancil, PhD, is the Alcoa Distinguished Professor and Head of Electrical and Computer Engineering at North Carolina State University. In addition to quantum computing, his research interests include spin waves, and microwave and optical devices and systems.
Gregory T. Byrd, PhD, is Professor and Associate Head of Electrical and Computer Engineering at North Carolina State University. His research focuses on both classical and quantum computer architecture and systems.
Gregory T. Byrd, PhD, is Professor and Associate Head of Electrical and Computer Engineering at North Carolina State University. His research focuses on both classical and quantum computer architecture and systems.
Inhalt
List of Figures
- 1.1 Interpretation of classical versus quantum NOT gates. (a) Classical NOT Circuit diagram. The horizontal direction represents space, i.e., the input and output of the circuit are physically accessible from different points in the circuit, and they can be measured simultaneously. (b) Quantum X gate circuit (quantum version of the NOT gate). The horizontal direction represents time, i.e., the input and output of the circuit represent the state of the same qubit after performing the X gate operation. The lower part of the Figure shows an alternate symbol for the quantum NOT gate.
- 1.2 NAND circuit diagram.
- 1.3 Circuit representation of Eq. (1.31). In a quantum circuit diagram, the operation goes from left to right, while the matrix expression is shown going from right to left. The final box is a measurement in the standard basis, resulting in a classical bit.
- 1.4 Symbol for a CNOT gate, and its effect on basis states.
- 1.5 Circuit for creating an entangled state known as a Bell State. When the two qubits are measured, they will either both be 0, or they will both be 1.
- 1.6 Result of executing the circuit 1024 times on a quantum simulator, compared with executing the circuit 1024 times on a real IBM quantum computer.
- 1.7 Hypothetical cloning operator, that creates an exact and independent copy of unknown quantum state |a?. The text will show that such an operator cannot be implemented.
- 1.8 Conceptual illustration of the Deutsch Problem.
- 1.9 Reversible circuit for calculating f(x).
- 1.10 Implementations of black-box function Uf for Deutsch's problem. Top output is |y?f(x)?, and bottom output is |x?.
- 1.11 Implementation of Deutsch's algorithm. The dashed box is equivalent to U in Figure 1.8.
- 1.12 System diagram for a superconducting quantum computer.
- 2.1 Rotation of a vector of length r CCW around the z axis.
- 2.2 Illustration of how two consecutive rotations can be replaced with a single equivalent rotation.
- 2.3 Representation of a single qubit state on the Bloch Sphere (created in part using [2]).
- 2.4 Precession of spin vector for a particle with positive charge in a z-directed magnetic field.
- 2.5 Solutions to the coupled mode equations for ?=0 and ?/?=3. For the case of Rabi oscillations, |?t|=ORt/2.
- 2.6 Rotations enabling measurement of the projections of the state vector along the x and y axes. (a) The Hadamard gate corresponds to rotation of the state vector around an axis in the x-z plane making a 45o angle with the z axis. This rotates the x component to z axis. (b) z rotation of -90o followed by a Hadamard rotation to estimate the projection along y.
- 2.7 (a) Bloch sphere representation of a mixed state, and (b) the result of applying a Hadamard gate (H) to the mixed state. Plots generated using Qiskit [2].
- 3.1 Common symbols for the SWAP, iSWAP, and iSWAP two-qubit gates.
- 3.2 Operations needed to convert a iSWAP´ gate to a CNOT.
- 3.3 Controlled-U gate. If the control qubit is |1?, the U gate is applied to the target qubit. Otherwise, the gate is not applied.
- 3.4 Implementation of controlled-U gate using Eq. (3.39).
- 4.1 Ladder line used for radio frequency transmission.
- 4.2 Equivalent circuit for a transmission line. (a) Lumped elements can be used so long as the distance ?z is small compared to the distance traveled during a period of the signal. (b) Single section along the line for analysis.
- 4.3 A transmission line terminated with a load impedance. Note that two coordinate systems have their origins at the load location: the coordinate z increases to the right, and the coordinate l increases to the left.
- 4.4 Voltage standing wave pattern along a transmission line with a mismatched load.
- 4.5 Impedance looking into a terminated transmission line of length l.
- 4.6 A real impedance can be matched to a lossless transmission line using a quarter wavelength line whose impedance is the geometric mean of the load and line to be matched. This is referred to as a quarter wave matching transformer.
- 4.7 Some commonly-used types of transmission lines. Since there are multiple ways to drive the coplanar guide, the most common source connection is explicitly shown. All of the dielectric materials are assumed to be nonmagnetic for our purposes.
- 4.8 Incoming and outgoing wave amplitudes used in the definitions of S parameters.
- 4.9 Definition of voltages and currents for the ABCD transmission matrix.
- 4.10 Definitions for constructing the ABCD matrix of a section of transmission line.
- 4.11 Circuit for an attenuator.
- 4.12 Circulator Circuit diagrams. In actual devices, the three ports are symmetrically placed at 120º angles, as represented on the left. However, in drawing circuit diagrams, it is often convenient to show the ports at right angles, as shown in the center. As shown on the right, you can make an isolator by connecting one of the ports to a matched load.
- 4.13 Wilkinson power divider.
- 4.14 Quadrature hybrid 4-port network. For clarity each transmission line is represented by a single line, with the return conductors understood (e.g., an implied ground plane) [24].
- 4.15 Even and odd mode analysis of a quadrature hybrid coupler. All impedances are shown normalized to Zc [24].
- 4.16 Commonly-used symbol for a quadrature hybrid. A signal applied to port 1 is evenly split into quadrature signals at ports 2 and 3.
- 4.17 Mixer Circuit diagrams. In an ideal mixer, the signal at the output terminal is the product of the signals applied to the two input ports.
- 4.18 (a) Circuit to shape a microwave pulse. (b) Example of creating a pulse with a Gaussian pulse shape.
- 4.19 (a) Circuit to recover the cosine (in-phase, or I) and sine (quadrature, or Q) components of an RF signal. (b) The amplitude and phase plotted on the IQ plane. (c) Raw I-Q signals measured on ibm-q-armonk, a 1 qubit demonstration processor on the IBM Q Network. The means for each state are indicated by the large markers.
- 4.20 Low-pass filter circuits.
- 4.21 Frequency response of the T network low-pass filter.
- 4.22 Circuit illustrating thermal noise power from a resistor at temperature T. (a) Resistor at temperature T coupled to a load through a lossless bandpass filter with bandwidth B. (b) Equivalent circuit explicitly showing a noise voltage source that depends on temperature.
- 4.23 Quantum noise as a function of temperature normalized to the photon energy. Solid line is the exact expression (4.161), while the dashed line is the Rayleigh-Jeans approximation (4.160).
- 4.24 Noise added by a circuit with power gain G. For an amplifier, G>1, while for an attenuator G<1.
- 4.25 Thermal noise from a passive element such as an attenuator at temperature T. (a) Power applied to port 2 is partially reflected and partially transmitted to the output, with the balance dissipated as heat. The power dissipated is visualized as being conveyed to a fictitious port 3 connected to a thermal reservoir at temperature T. (b) The total power out has a contribution from the input as well as the thermal reservoir attached to the fictitious port 3.
- 4.26 Noise in a system of cascaded components.
- 4.27 Layered structure of different semiconductor materials used to separate the donor impurities from the donor electrons to achieve minimal scattering. Structures of different materials like this are referred to as heterostructures. Owing to the different band structure of AlGaAs and GaAs, donor electrons from the heavily-doped AlGaAs layer become trapped on the GaAs side of the interface between intrinsic GaAs and AlGaAs, forming a "2D electron gas." This concentration of electrons is depicted by the shaded region. A heterostructure similar to this is a key feature of HEMTs.
- 5.1 Resonator circuits.
- 5.2 Equivalent circuits for capacitively-coupled lumped-element resonator.
- 5.3 Capacitively-coupled transmission line resonator.
- 5.4 Near the nth resonant frequency of the transmission line, the capacitively-coupled transmission line resonator can be modeled as a capacitively-coupled lumped-element resonator.
- 5.5 Equivalent circuits used to calculate the insertion loss and return loss of a capacitively-coupled transmission line resonator.
- 5.6 Characteristics of capacitively-coupled transmission line resonator. Note the significantly different frequency scales on the horizontal axis as well as the different vertical scales for |S11|. Parameters used are Ln = 0.453µH/m, Zc=RL=50O, f0 = 5 GHz, Qint = 2.3, ×105, and l = 11.04 mm. These values are comparable to experimentally-measured parameters. Based on [26].
- 5.7 Two LC resonant circuits coupled by a capacitor.
- 5.8 Coupling between lossless LC resonators for Cg/CACB = 0.05.
- 5.9 Tire swings suspended...
