Contracted Quantum Eigensolver for the Quantum Simulation of Many-Electron Systems

Explore a 42-minute lecture on the Contracted Quantum Eigensolver (CQE) for quantum simulation of many-electron systems. Delve into this novel hybrid quantum-classical algorithm presented by David Mazziotti from the University of Chicago's Chemistry department at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Learn about the CQE's advantages over variational quantum eigensolvers, its potential for exponential speed-up, and its application in resolving ground-state energies of benzyne isomers using IBM quantum processing units. Discover error-mitigation strategies, the integration of classical 2-RDM methods for total electron correlation, and the application of anti-Hermitian contracted Schrödinger equation (ACSE) and multi-component pair density functional (MC-PDFT) theories. Gain insights into molecular simulations, hardware-efficient onsets, and the accuracy of quantum eigensolvers in this comprehensive exploration of cutting-edge quantum computational methods.

Introduction
Background
Variational Quantum Eigensolver
Contracted Quantum Eigensolver
Example Calculation
Algorithm
Advantages
Comparison to other algorithms
Comparison to AdaptQV
Error Mitigation
LimitPreserving Correction
Representability Conditions
Semidefinite Programming
Relative Energy Comparison
Two Areas of Further Advance
Molecular Simulations
Hardware Efficient Onsots
Cubic Particle Wave Functions
Quantum Eigensolver
Quantum Eigensolver Accuracy
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