Quantum Information and Computation for Chemistry -- Contributors to Volume 154 -- Foreword -- Preface to The Series -- Contents -- Introduction to Quantum Information and Computation for Chemistry -- I. Introduction -- A. Qubits and Gates -- B. Circuits and Algorithms -- C. Teleportation -- II. Quantum Simulation -- A. Introduction -- B. Phase Estimation Algorithm -- 1. General Formulation -- 2. Implementation of Unitary Transformation U -- 3. Group Leaders Optimization Algorithm -- 4. Numerical Example -- 5. Simulation of the Water Molecule -- III. Algorithm for Solving Linear Systems Ax = b -- A. General Formulation -- B. Numerical Example -- IV. Adiabatic Quantum Computing -- A. Hamiltonians of n-Particle Systems -- B. The Model of Adiabatic Computation -- C. Hamiltonian Gadgets -- V. Topological Quantum Computing -- A. Anyons -- B. Non-Abelian Braid Groups -- C. Topological Phase of Matter -- D. Quantum Computation Using Anyons -- VI. Entanglement -- VII. Decoherence -- VIII. Major Challenges and Opportunities -- References -- Back to The Future: A Roadmap for Quantum Simulation from Vintage Quantum Chemistry -- I. Introduction -- II. Quantum Computing -- A. Phase Estimation -- B. Time Evolution and the Cartan Decomposition -- III. Quantum Chemistry: The CI Method -- A. Second Quantization: Direct Mapping -- B. FCI: Compact Mapping -- IV. A Selection of Historical Calculations in Quantum Chemistry -- A. The 1930s and 1940s -- B. The 1950s -- C. The 1960s -- V. Boys's 1950 Calculation for Be -- VI. Conclusions -- References -- Introduction to Quantum Algorithms for Physics and Chemistry -- I. Introduction -- A. Quantum Computational Complexity and Chemistry -- 1. An Exponential Wall for Many-Body Problems -- 2. Computational Complexity of Quantum Simulation -- B. Basic Quantum Algorithms for Digital Quantum Simulation.

1. Quantum Fourier Transform -- 2. Phase Estimation Algorithm -- II. Digital Quantum Simulation -- A. Overview -- B. Simulation of Time Evolution -- 1. Suzuki-Trotter Formulas -- 2. First-Quantized Representation -- 3. Second-Quantized Representation -- 4. Open-System Dynamics -- C. State Preparation -- 1. Preparing Ground States -- 2. Preparing Thermal States Using Quantum Metropolis -- 3. Preparing Thermal States with Perturbative Updates -- D. Algorithmic Quantum Cooling -- 1. Basic Idea of the Quantum Cooling Method -- 2. Connection with Heat-Bath Algorithmic Cooling -- III. Special Topics -- A. Adiabatic Nondestructive Measurements -- B. TDDFT and Quantum Simulation -- IV. Conclusion and Outlook -- References -- Quantum Computing Approach to Nonrelativistic and Relativistic Molecular Energy Calculations -- I. Overview -- II. Quantum Computing Background -- A. Quantum Fourier Transform -- B. Semiclassical Approach to Quantum Fourier Transform -- C. Phase Estimation Algorithm -- D. Iterative Phase Estimation Algorithm -- III. Quantum Full Configuration Interaction Method -- A. Mapping of Quantum Chemical Wave Functions onto Quantum Register -- B. Initial States for the Algorithm -- 1. Adiabatic State Preparation -- C. Controlled "Time Propagation" -- 1. Decomposition of Unitary Propagator to Elementary Quantum Gates -- IV. Application to Nonrelativistic Molecular Hamiltonians -- A. Example of CH2 Molecule -- V. Extension to Relativistic Molecular Hamiltonians -- A. Example of SbH Molecule -- VI. Conclusions -- References -- Density Functional Theory and Quantum Computation -- I. Introduction -- II. Qubit/Fermion Transformation -- III. NP-Complete Problem MAXCUT -- IV. GS-DFT -- V. TD-DFT -- VI. Minimum Gap -- VII. Discussion -- References -- Quantum Algorithms for Continuous Problems and Their Applications -- I. Introduction.

II. The Model of Computation -- A. Quantum Queries -- B. Quantum Algorithms -- III. Applications -- A. Integration -- B. Path Integration -- C. Approximation -- D. Ordinary Differential Equations -- E. Partial Differential Equations -- F. Optimization -- G. Gradient Estimation -- H. Simulation -- I. Eigenvalue Estimation -- J. Linear Systems -- References -- Analytic Time Evolution, Random Phase Approximation, and Green Functions for Matrix Product States -- I. Introduction -- II. Stationary States -- III. Time Evolution and Equations of Motion -- IV. Random Phase Approximation -- V. Green Functions and Correlations -- VI. Conclusion -- References -- Few-Qubit Magnetic Resonance Quantum Information Processors: Simulating Chemistry and Physics -- I. Nuclear Magnetic Resonance QIP -- A. Introduction -- B. Quantum Algorithms for Chemistry -- 1. Digital Quantum Simulation -- 2. Adiabatic Quantum Simulation -- C. NMR and the DiVincenzo Criteria -- 1. Scalability with Well-Characterized Qubits: Spin-1/2 Nuclei -- 2. Initialization: The Pseudopure State -- 3. A Universal Set of Quantum Gates: RF Pulses and Spin Coupling -- 4. Measurement: Free Induction Decay -- 5. Noise and Decoherence: T1/T2 versus Coupling Strength -- II. Quantum Control in Magnetic Resonance QIP -- A. Advances in Pulse Engineering -- B. Advances in Dynamical Decoupling -- C. Control in the Electron-Nuclear System -- 1. Indirect Control via the Anisotropic Hyperfine Interaction -- 2. Dynamic Nuclear Polarization and Algorithmic Cooling -- 3. Spin Buses and Parallel Information Transfer -- III. NMR QIP for Chemistry -- A. Recent Experiments in NMR Quantum Simulation -- 1. Simulation of Burgers' Equation -- 2. Simulation of the Fano-Anderson Model -- 3. Simulation of Frustrated Magnetism -- IV. Prospects for Engineered Spin-Based QIPs -- References.

Photonic Toolbox for Quantum Simulation -- I. Introduction -- II. Toolbox of Photonic Quantum Simulator -- A. Entangled Photon-Pair Source -- B. Encoding and Processing Quantum Information on Single Photon -- C. Photon-Photon Interaction via Measurement -- III. Quantum Chemistry on a Photonic Quantum Computer -- IV. Conclusions -- References -- Progress in Compensating Pulse Sequences for Quantum Computation -- I. Introduction -- II. Coherent Control Over Spin Systems -- A. Errors in Quantum Control -- B. NMR Spectroscopy as a Model Control System -- 1. Error Models -- C. Binary Operations on Unitary Operators -- 1. Hilbert-Schmidt Inner Product -- 2. Fidelity -- III. Group Theoretic Techniques for Sequence Design -- A. Lie Groups and Algebras -- 1. The Spinor Rotation Group SU(2) -- B. Baker-Campbell-Hausdorff and Magnus Formulas -- 1. The Magnus Expansion -- 2. A Method for Studying Compensation Sequences -- C. Decompositions and Approximation Methods -- 1. Basic Building Operations -- 2. Euler Decomposition -- 3. Cartan Decomposition -- IV. Composite Pulse Sequences on SU(2) -- A. Solovay-Kitaev Sequences -- 1. Narrowband Behavior -- 2. Broadband Behavior -- 3. Generalization to Arbitrary Gates in SU(2) -- 4. Arbitrarily Accurate SK Sequences -- B. Wimperis/Trotter-Suzuki Sequences -- 1. Narrowband Behavior -- 2. Broadband Behavior -- 3. Passband Behavior -- 4. Arbitrarily Accurate Trotter-Suzuki Sequences -- C. CORPSE -- 1. Arbitrarily Accurate CORPSE -- 2. Concatenated CORPSE: Correcting Simultaneous Errors -- D. Shaped Pulse Sequences -- V. Composite Pulse Sequences on Other Groups -- A. Compensated Two-Qubit Operations -- 1. Cartan Decomposition of Two-Qubit Gates -- 2. Operations Based on the Ising Interaction -- 3. Extension to SU(2n) -- VI. Conclusions and Perspectives -- References.

Review of Decoherence-Free Subspaces, Noiseless Subsystems, and Dynamical Decoupling -- 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: G = (SU(2))N -- 2. Example 2: G = Collective SU(2) -- 3. Example 3: G = Sn -- 4. Example 4: Linear System-Bath Coupling -- XI. Conclusions -- References -- Functional Subsystems and Strong Correlation in Photosynthetic Light Harvesting -- I. Introduction.

II. Effect of Strong Electron Correlation.