Quantum Information and Computation for Chemistry, Volume 154

Sabre Kais, Aaron R. Dinner, Stuart A. Rice

• Publisher: Wiley
• Year: 2014
• Print ISBN:
  9781118495667
• Edition: 1
• eBook ISBN:
  9781118742600
• Topic: Physical Sciences
• Subtopic: Chemistry
• Index: Chemistry

Examines the intersection of quantum information and chemical physics

The Advances in Chemical Physics series is dedicated to reviewing new and emerging topics as well as the latest developments in traditional areas of study in the field of chemical physics. Each volume features detailed comprehensive analyses coupled with individual points of view that integrate the many disciplines of science that are needed for a full understanding of chemical physics.

This volume of the series explores the latest research findings, applications, and new research paths from the quantum information science community. It examines topics in quantum computation and quantum information that are related to or intersect with key topics in chemical physics. The reviews address both what chemistry can contribute to quantum information and what quantum information can contribute to the study of chemical systems, surveying both theoretical and experimental quantum information research within the field of chemical physics.

With contributions from an international team of leading experts, Volume 154 offers seventeen detailed reviews, including:

• Introduction to quantum information and computation for chemistry
• Quantum computing approach to non-relativistic and relativistic molecular energy calculations
• Quantum algorithms for continuous problems and their applications
• Photonic toolbox for quantum simulation
• Vibrational energy and information transfer through molecular chains
• Tensor networks for entanglement evolution

Reviews published in Advances in Chemical Physics are typically longer than those published in journals, providing the space needed for readers to fully grasp the topic: the fundamentals as well as the latest discoveries, applications, and emerging avenues of research. Extensive cross-referencing enables readers to explore the primary research studies underlying each topic.

Review of Decoherence-Free Subspaces, Noiseless Subsystems, and Dynamical Decoupling

Daniel A. Lidar

Departments of Electrical Engineering, Chemistry, and Physics, and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, CA 90089, USA

I. Introduction

II. Decoherence-Free Subspaces

A. A Classical Example

B. Collective Dephasing DFS

C. Decoherence-Free Subspaces in the Kraus OSR

D. Hamiltonian DFS

E. Deutsch's Algorithm

F. Deutsch's Algorithm with Decoherence

III. Collective Dephasing

A. The Model

B. The DFS

C. Universal Encoded Quantum Computation

IV. Collective Decoherence and Decoherence-Free Subspaces

A. One Physical Qubit

B. Two Physical Qubits

C. Three Physical Qubits

D. Generalization to N Physical Qubits

E. Higher Dimensions and Encoding Rate

F. Logical Operations on the DFS of Four Qubits

V. Noiseless/Decoherence-Free Subsystems

A. Representation Theory of Matrix Algebras

B. Computation Over a NS

C. Example: Collective Decoherence Revisited

1. General Structure

2. The Three-Qubit Code for Collective Decoherence

3. Computation Over the Three-Qubit Code

VI. Dynamical Decoupling

A. Decoupling Single-Qubit Pure Dephasing

1. The Ideal Pulse Case

2. The Real Pulse Case

B. Decoupling Single-Qubit General Decoherence

VII. Dynamical Decoupling as Symmetrization

VIII. Combining Dynamical Decoupling with DFS

A. Dephasing on Two Qubits: A Hybrid DFS–DD Approach

B. General Decoherence on Two Qubits: A Hybrid DFS–DD Approach

IX. Concatenated Dynamical Decoupling: Removing Errors of Higher Order in Time

X. Dynamical Decoupling and Representation Theory

A. Information Storage and Computation Under DD

B. Examples

1. Example 1:

2. Example 2:

3. Example 3:

4. Example 4: Linear System–Bath Coupling

XI. Conclusions

References

I. Introduction

The protection of quantum information is a central task in quantum information processing [1]. Decoherence and noise are obstacles that must be overcome and managed before large-scale quantum computers can be built. This chapter provides an introduction to th...

Table of contents

• Cover
• Editorial Board
• Title Page
• Copyright
• Contributors to Volume 154
• Foreword
• Preface to the Series
• Introduction to Quantum Information and Computation for Chemistry
• Back to the Future: A Roadmap for Quantum Simulation from Vintage Quantum Chemistry
• Introduction to Quantum Algorithms for Physics and Chemistry
• Quantum Computing Approach to Nonrelativistic and Relativistic Molecular Energy Calculations
• Density Functional Theory and Quantum Computation
• Quantum Algorithms for Continuous Problems and Their Applications
• Analytic Time Evolution, Random Phase Approximation, and Green Functions for Matrix Product States
• Few-Qubit Magnetic Resonance Quantum Information Processors: Simulating Chemistry and Physics
• Photonic Toolbox for Quantum Simulation
• Progress in Compensating Pulse Sequences for Quantum Computation
• Review of Decoherence-Free Subspaces, Noiseless Subsystems, and Dynamical Decoupling
• Functional Subsystems and Strong Correlation in Photosynthetic Light Harvesting
• Vibrational Energy Transfer Through Molecular Chains: An Approach Toward Scalable Information Processing
• Ultracold Molecules: Their Formation and Application to Quantum Computing
• Dynamics of Entanglement in One-and Two-Dimensional Spin Systems
• From Topological Quantum Field Theory to Topological Materials
• Tensor Networks for Entanglement Evolution
• Author Index
• Subject Index