Po-Wei Huang

Rare events, though infrequent, can have significant impacts across various domains. We present a quantum algorithm for efficiently sampling rare events from stochastic processes. Our algorithm constructs quantum sample states that superpose only rare events, defined as those occurring with probability below a threshold \(\Delta\). The algorithm consists of three key steps: (1) constructing an amplitude block encoding from the quantum sample state of the original process, (2) implementing quantum singular value transformation of a polynomial approximation of a thresholding function, and (3) performing measurement and post-selection. For sufficiently large sequence lengths, we prove that our algorithm achieves a quadratic speedup over classical methods, requiring only \(\Theta(1/\sqrt{\Delta})\) queries to prepare an even superposition over rare events, compared to the classical \(\mathcal{O}(1/\Delta)\) complexity. We demonstrate our algorithm's effectiveness through numerical simulations on the Dyson-Ising chain, showing successful identification and amplification of rare events while suppressing non-rare events.

Amplitude estimation, in its original form, is formulated as phase estimation upon the amplification walk operator. Since its introduction, subsequent improvements made to the algorithm have removed the use of phase estimation and introduced low-depth variants that trade speedup factors with circuit depth. In this paper, we formalize amplitude estimation as a phase difference estimation problem solvable by ancilla-free phase estimation, and provide two algorithms for both near-Heisenberg-limited and low-depth circuit guarantees inspired by development in early fault-tolerant statistical phase estimation. Our algorithms provide a simpler classical post-processing procedure compared to prior work for both near-Heisenberg-limited and low-depth regimes. Numerical results show that our near-Heisenberg-limited algorithm performs on par with prior work, and our low-depth version supports the query-depth tradeoff in terms of runtime speedups.

Accurately computing the free energies of biological processes is a cornerstone of computer-aided drug design, but it is a daunting task. The need to sample vast conformational spaces and account for entropic contributions makes the estimation of binding free energies very expensive. While classical methods, such as thermodynamic integration and alchemical free energy calculations, have significantly contributed to reducing computational costs, they still face limitations in terms of efficiency and scalability. We tackle this through a quantum algorithm for the estimation of free energy differences by adapting the existing Liouvillian approach and introducing several key algorithmic improvements. We directly implement the Liouvillian operator and provide an efficient description of electronic forces acting on both nuclear and electronic particles on the quantum ground state potential energy surface. This leads to super-polynomial runtime scaling improvements in the precision of our Liouvillian simulation approach and quadratic improvements in the scaling with the number of particles relative to prior quantum algorithms. Second, our algorithm calculates free energy differences via a fully quantum implementation of thermodynamic integration and alchemy, thereby foregoing expensive entropy estimation subroutines used in prior works. Our results open new avenues towards the application of quantum computers in drug discovery.