You are previewing Quantum Computing for Computer Architects, Second Edition, 2nd Edition.
O'Reilly logo
Quantum Computing for Computer Architects, Second Edition, 2nd Edition

Book Description

Quantum computers can (in theory) solve certain problems far faster than a classical computer running any known classical algorithm. While existing technologies for building quantum computers are in their infancy, it is not too early to consider their scalability and reliability in the context of the design of large-scale quantum computers. To architect such systems, one must understand what it takes to design and model a balanced, fault-tolerant quantum computer architecture. The goal of this lecture is to provide architectural abstractions for the design of a quantum computer and to explore the systems-level challenges in achieving scalable, fault-tolerant quantum computation. In this lecture, we provide an engineering-oriented introduction to quantum computation with an overview of the theory behind key quantum algorithms. Next, we look at architectural case studies based upon experimental data and future projections for quantum computation implemented using trapped ions. While we focus here on architectures targeted for realization using trapped ions, the techniques for quantum computer architecture design, quantum fault-tolerance, and compilation described in this lecture are applicable to many other physical technologies that may be viable candidates for building a large-scale quantum computing system. We also discuss general issues involved with programming a quantum computer as well as a discussion of work on quantum architectures based on quantum teleportation. Finally, we consider some of the open issues remaining in the design of quantum computers. Table of Contents: Introduction / Basic Elements for Quantum Computation / Key Quantum Algorithms / Building Reliable and Scalable Quantum Architectures / Simulation of Quantum Computation / Architectural Elements / Case Study: The Quantum Logic Array Architecture / Programming the Quantum Architecture / Using the QLA for Quantum Simulation: The Transverse Ising Model / Teleportation-Based Quantum Architectures / Concluding Remarks

Table of Contents

  1. Cover
  2. Half title
  3. Synthesis Lectures on Computer Architecture
  4. Copyright
  5. Title
  6. Abstract
  7. Contents
  8. Preface
  9. 1 Introduction
  10. 2 Basic Elements for Quantum Computation
    1. 2.1 Classical vs. Quantum Signal States (bits vs. qubits)
    2. 2.2 Logic Operations and Circuits
    3. 2.3 Quantum Measurement
    4. 2.4 Example: The 3-Qubit Quantum Toffoli Gate
    5. 2.5 Example: Quantum Fourier Transform (QFT)
    6. 2.6 Example: Quantum Teleportation
    7. 2.7 Example: Deutsch’s Quantum Algorithm
    8. 2.8 Quantum Entanglement and EPR Pairs
    9. 2.9 Other Models of Quantum Computation
  11. 3 Key Quantum Algorithms
    1. 3.1 Quantum Integer Factorization
      1. 3.1.1 The Integer Factorization Problem
      2. 3.1.2 A Quantum Integer Factorization Algorithm
      3. 3.1.3 Quantum Integer Factorization: Proof of Classical Part
    2. 3.2 Order Finding
      1. 3.2.1 Order Finding as Quantum Eigenvalue Estimation
      2. 3.2.2 Order Finding: Continued Fractions
    3. 3.3 Quantum Phase Estimation
      1. 3.3.1 Proof Sketch of the Correctness of the Phase Estimation Circuit
    4. 3.4 Eigenvalue Estimation
    5. 3.5 The Hidden Subgroup Problem
    6. 3.6 Grover’s Algorithm for Quantum Search
      1. 3.6.1 Searching with a Quantum Black Box
      2. 3.6.2 Grover’s Algorithm
      3. 3.6.3 Proof Sketch of the Correctness of Grover Iteration
    7. 3.7 Quantum Adiabatic Algorithms
      1. 3.7.1 3-SAT: An example of a Quantum Adiabatic algorithm
  12. 4 Building Reliable and Scalable Quantum Architectures
    1. 4.1 Reliable and realistic implementation technology
      1. 4.1.1 Optical Quantum Computation: Photons as Qubits
      2. 4.1.2 Trapped-Ion Quantum Computation: Ions as Qubits
    2. 4.2 Robust Error Correction and Fault-Tolerant Structures
      1. 4.2.1 Noise Model Assumptions
      2. 4.2.2 Error Correction: Basics and Notation
      3. 4.2.3 Example: The Steane [[7, 1, 3]] Code
      4. 4.2.4 Logical Qubits in Quantum Computation
      5. 4.2.5 Quantum Error Correction and Fault-Tolerance: The Threshold Result
      6. 4.2.6 The Cost of Quantum Error Correction
      7. 4.2.7 Scale-Up in System Size due to Error Correction
      8. 4.2.8 Error Correction Slowdown
    3. 4.3 Quantum Resource Distribution
      1. 4.3.1 Physical Qubit Movement
      2. 4.3.2 Teleportation-Based Communication and Quantum Repeaters
  13. 5 Simulation of Quantum Computation
    1. 5.1 Simulation of Error Propagation
    2. 5.2 Stabilizer Method for Quantum Simulation
  14. 6 Architectural Elements
    1. 6.1 Quantum Processing Elements (PE’s)
    2. 6.2 Quantum Memory Hierarchy
    3. 6.3 Quantum Addressing Scheme for Classical Memory
    4. 6.4 Error Correction and Quantum Architecture Design
      1. 6.4.1 Effects of Ancilla Preparation and Layout
      2. 6.4.2 Optimizing Error Correction along Critical Paths
  15. 7 Case Study: The Quantum Logic Array Architecture
    1. 7.1 QLA Architecture Overview
    2. 7.2 The Logical Qubit Design in the QLA
    3. 7.3 Logical Qubit Interconnect
    4. 7.4 Compressed QLA Architecture: CQLA
      1. 7.4.1 The Gain Product: Architecture Performance Comparison
      2. 7.4.2 Communication Issues: Executing the Toffoli Gate
      3. 7.4.3 Memory Hierarchy in the CQLA Architecture
      4. 7.4.4 Simulating the Cache in the CQLA
    5. 7.5 Qualypso
  16. 8 Programming the Quantum Architecture
    1. 8.1 Physical-Level Instruction Scheduling
    2. 8.2 High-Level Compiler Design
    3. 8.3 Architecture-Independent Circuit Synthesis
    4. 8.4 Mapping Circuits to Architecture
    5. 8.5 Optimization of the Logical Qubit Tiles
      1. 8.5.1 The Fault-Tolerant Threshold Estimates
      2. 8.5.2 Circuit Scheduling and The Fault-Tolerance Constraint
      3. 8.5.3 Threshold Calculations
      4. 8.5.4 Summary Discussion
  17. 9 Using the QLA for Quantum Simulation: The Transverse Ising Model
    1. 9.1 The Transverse Ising Model Overview
    2. 9.2 TIM Quantum Simulation Resource Estimates
      1. 9.2.1 Phase estimation circuit
      2. 9.2.2 Decomposition of the TIM quantum circuit into fault-tolerant gates
    3. 9.3 Mapping the TIM circuit onto the QLA architecture
      1. 9.3.1 Resource estimates for the 1-D TIM problem
  18. 10 Teleportation-Based Quantum Architectures
    1. 10.1 The CNOT Gate and Single-Qubit Gates through Teleportation
    2. 10.2 The Architecture
    3. 10.3 Error Correction through Teleportation
  19. 11 Concluding Remarks
  20. Bibliography
  21. Authors’ Biographies