Quantum optics seminar
Imaginary time evolution and ground state preparation using unitary multi-copy protocols
Dr. Tal Schwartzman
ITAMP, Harvard and Smithsonian
Abstract
Zoom link: https://us02web.zoom.us/j/82462188805?pwd=V9IOoGkn2Q6nBltj2BsyFNaUie6plQ.1
Abstract:
Preparing low-energy states is one of the central challenges in quantum computation and quantum simulation. One useful idea is imaginary time evolution, which replaces real-time dynamics with imaginary-time dynamics and exponentially suppresses higher-energy eigenstates. In this talk, I will describe deterministic unitary protocols that approximate this process using multiple copies of the system, real-time evolution under the system Hamiltonian, and controlled-SWAP operations (or more general SWAP-generated unitaries).
I will focus on two circuit architectures. The first is a tree construction, which comes with provable convergence guarantees but uses many copies of the system. The second is a more compact “hedge” construction, which is motivated by the same idea but uses far fewer copies and appears to perform comparably well in numerical tests. I will also discuss how mid-circuit post-selection can speed up convergence.
Finally, I will show how one can trade circuit volume for post-circuit shot complexity, and briefly discuss possible platform implementations. Overall, these protocols provide low-energy state preparation methods that could be useful on near-term quantum devices.
Abstract:
Preparing low-energy states is one of the central challenges in quantum computation and quantum simulation. One useful idea is imaginary time evolution, which replaces real-time dynamics with imaginary-time dynamics and exponentially suppresses higher-energy eigenstates. In this talk, I will describe deterministic unitary protocols that approximate this process using multiple copies of the system, real-time evolution under the system Hamiltonian, and controlled-SWAP operations (or more general SWAP-generated unitaries).
I will focus on two circuit architectures. The first is a tree construction, which comes with provable convergence guarantees but uses many copies of the system. The second is a more compact “hedge” construction, which is motivated by the same idea but uses far fewer copies and appears to perform comparably well in numerical tests. I will also discuss how mid-circuit post-selection can speed up convergence.
Finally, I will show how one can trade circuit volume for post-circuit shot complexity, and briefly discuss possible platform implementations. Overall, these protocols provide low-energy state preparation methods that could be useful on near-term quantum devices.