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Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Variational wave functions and their overlap with the ground state.
Christophe Mora1, Xavier Waintal
1Laboratoire Pierre Aigrain, Département de Physique, Ecole Normale Supérieure, 24 rue Lhomond, F-75005 Paris, France.
Physical Review Letters
|August 7, 2007
Summary
A new formula quantifies variational wave function quality by calculating overlap with the ground state. This overlap, derived from imaginary time quantum dynamics, simplifies quality assessment in quantum Monte Carlo simulations.
Area of Science:
- Quantum mechanics
- Computational physics
Background:
- Assessing variational wave function quality is crucial for accurate quantum simulations.
- Overlap with the true ground state is an intrinsic measure of wave function quality.
Purpose of the Study:
- To derive a general formula for computing the overlap between a variational wave function and the system's ground state.
- To establish a connection between this overlap and accessible quantum dynamics in imaginary time.
Main Methods:
- Derivation of a general formula relating overlap to imaginary time dynamics.
- Utilizing the energy as a function of imaginary time (E(tau)) curve.
- Application to quantum Monte Carlo (QMC) simulations.
Main Results:
- The overlap is directly proportional to the area under the E(tau) curve.
- Overlap calculation becomes a byproduct of standard QMC simulations.
- Fast convergence in QMC simulations is equivalent to high overlap with the ground state.
Conclusions:
- The derived formula provides an intrinsic and practical measure of variational wave function quality.
- This method enhances the efficiency and interpretability of quantum Monte Carlo simulations.
- A good variational wave function in QMC is one that closely approximates the true ground state.
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