Quantum algorithm to compute particle collisions

Torsten V. Zache

James Scoville

An algorithm is presented to simulate fluid dynamics on a three qubit type II quantum computer: a lattice of small quantum computers that communicate classical information. The algorithm presented is called a three qubit factorized quantum lattice gas algorithm. It is modeled after classical lattice gas algorithms which move virtual particles along an imaginary lattice and change the particles' momentums using collision rules when they meet at a lattice node. Instead of moving particles, the quantum algorithm presented here moves probabilities, which interact via a unitary collision operator. Probabilities are determined using ensemble measurement and are moved with classical communications channels. The lattice node spacing is defined to be a microscopic scale length. A mesoscopic governing equation for the lattice is derived for the most general three qubit collision operator which preserves particle number. In the continuum limit of the lattice, a governing macroscopic partial differential equation-the diffusion equation-is derived for a particular collision operator using a Chapman-Enskog expansion. A numerical simulation of the algorithm is carried out on a conventional desktop computer and compared to the analytic solution of the diffusion equation. The simulation agrees very well with the known solution.

Annie Y. Wei, Preksha Naik, Aram W. Harrow +1 more

Identifying jets formed in high-energy particle collisions requires solving optimization problems over potentially large numbers of final-state particles. In this work, we consider the possibility of using quantum computers to speed up jet clustering algorithms. Focusing on the case of electron-positron collisions, we consider a well-known event shape called thrust whose optimum corresponds to the most jetlike separating plane among a set of particles, thereby defining two hemisphere jets. We show how to formulate thrust both as a quantum annealing problem and as a Grover search problem. A key component of our analysis is the consideration of realistic models for interfacing classical data with a quantum algorithm. With a sequential computing model, we show how to speed up the well-known $O({N}^{3})$ classical algorithm to an $O({N}^{2})$ quantum algorithm, including the $O(N)$ overhead of loading classical data from $N$ final-state particles. Along the way, we also identify a way to speed up the classical algorithm to $O({N}^{2}\mathrm{log}N)$ using a sorting strategy inspired by the siscone jet algorithm, which has no natural quantum counterpart. With a parallel computing model, we achieve $O(N\mathrm{log}N)$ scaling in both the classical and quantum cases. Finally, we consider the generalization of these quantum methods to other jet algorithms more closely related to those used for proton-proton collisions at the Large Hadron Collider.

Alexander Miessen, Pauline J. Ollitrault, Francesco Tacchino +1 more

Kazumasa Ueno, Hiroaki Miura

Quantum computing may help reduce computational costs of simulating large and nonlinear systems, but research into the use of quantum computers in atmospheric and oceanic sciences is still at an early stage. This study explores the use of quantum computing for calculating the collision-coalescence process that dominates the size growth of liquid particles in cloud microphysics. Inspired by the quantum algorithms developed in the field of financial engineering, we propose a new algorithm based on a master equation that describes the time evolution of the droplet mass distribution. Our algorithm uses the quantum amplitudes to encode the probability distribution of droplet mass and calculates the expected number of droplets via the quantum amplitude estimation. The key contribution is an encoding strategy that maps the multivariate collision-coalescence problem onto a quantum computation by recording only the transition history rather than the full mass distributions at every time step. This approach reduces the per-step qubit cost from $O(\sqrt{N})$ to $O(\log N)$, where $N$ is the number of mass bins. Our resource analysis shows that the number of T gates (T-count) scales as $\widetilde{O}(N^2)$ per mass bin in $N$, for a fixed number of time steps and a given target accuracy, where the $\widetilde{O}$ notation suppresses polylogarithmic factors in $N$. This is a substantial improvement over classical master-equation methods, whose cost grows super-polynomially with $N$ as the number of possible states increases. Our results suggest that the collision-coalescence process is one of the promising targets of quantum computing in the field of atmospheric science.

Khadeejah Bepari, Sarah Alam Malik, Michael Spannowsky +1 more

The interpretation of measurements of high-energy particle collisions relies heavily on the performance of full event generators, which include the calculation of the hard process and the subsequent parton shower step. With the continuous improvement of quantum devices, dedicated algorithms are needed to exploit the potential quantum that computers can provide. We propose general and extendable algorithms for quantum gate computers to facilitate calculations of helicity amplitudes and the parton shower process. The helicity amplitude calculation exploits the equivalence between spinors and qubits and the unique features of a quantum computer to compute the helicities of each particle involved simultaneously, thus fully utilizing the quantum nature of the computation. This advantage over classical computers is further exploited by the simultaneous computation of s- and t-channel amplitudes for a $2\ensuremath{\rightarrow}2$ process. The parton shower algorithm simulates collinear emission for a two-step, discrete parton shower. In contrast to classical implementations, the quantum algorithm constructs a wave function with a superposition of all shower histories for the whole parton shower process, thus removing the need to explicitly keep track of individual shower histories. Both algorithms utilize the quantum computers ability to remain in a quantum state throughout the computation and represent a first step towards a quantum computing algorithm describing the full collision event at the LHC.