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arXiv:2310.19881 · Physical Review A

Quantum parton shower with kinematics

C. Bauer, So Chigusa, Masahito Yamazaki

Published Mar 26, 2024• 9 citations
arXivHTMLPDF

Abstract

Parton showers, which can efficiently incorporate quantum interference effects, have been shown to be run efficiently on quantum computers. However, so far these quantum parton showers have not included the full kinematical information required to reconstruct an event, which in classical parton showers requires the use of a veto algorithm. In this work, we show that adding one extra assumption about the discretization of the evolution variable allows one to construct a quantum veto algorithm, which reproduces the full quantum interference in the event, and allows one to include kinematical effects. We finally show that for certain initial states the quantum interference effects generated in this veto algorithm are classically tractable, such that an efficient classical algorithm can be devised.

DOI
10.1103/physreva.109.032432

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Parton showers, which can efficiently incorporate quantum interference effects, have been shown to be run efficiently on quantum computers. However, so far these quantum parton showers have not included the full kinematical information required to reconstruct an event, which in classical parton showers requires the use of a veto algorithm. In this work, we show that adding one extra assumption about the discretization of the evolution variable allows one to construct a quantum veto algorithm, which reproduces the full quantum interference in the event, and allows one to include kinematical effects. We finally show that for certain initial states the quantum interference effects generated in this veto algorithm are classically tractable, such that an efficient classical algorithm can be devised.
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.
We discuss general criteria that could guide us in applying quantum algorithms/computers to problems in high-energy physics. We then discuss the particular example of parton showers with quantum interference. We summarize the basic ideas behind the classical and quantum parton shower Monte Carlo algorithms and highlight the importance of quantum/classical hybrid algorithms. Our finding in quantum parton showers could serve as a useful case study for further exploration of quantum algorithms/computers in high-energy physics.
The efficient simulation of accurate collider data at modern collider experiments will be crucial for the detection of Beyond the Standard Model signatures in the search for new physics. Simulation of collision processes at hadron colliders like the LHC are carried out by Monte Carlo event generators which simulate the evolution from an initial hard scattering event, downwards in energy scales, towards the formation of long lived particles. However, as we enter a new era of higher luminosity experiments, accurate simulations of these pseudo-event generated data will become further computationally intensive with the vast amounts of data to generate. With the rapid development of quantum computing hardware, quantum computation offers itself as an alternative computing paradigm that may be harnessed to provide a natural framework to model several physical processes in high-energy physics, where the inherent quantum features of the device may be exploited to provide speedups or enhance current simulations. In this thesis, we present general and extendable quantum algorithms for two crucial parts of event generation: the calculation of matrix elements for the hard interaction and the QCD parton shower stage. First, a novel algorithm is proposed for the calculation of helicity amplitudes by outlining a proposal of constructing helicity spinors directly on a quantum circuit and manipulating the spinors to compute helicity amplitudes. This was used to calculate multiple helicity amplitudes for simple tree level scattering processes simultaneously as a proof-of-principle demonstration. The second algorithm outlines a proposal for a Monte Carlo-inspired parton shower algorithm which was used to simulate two shower steps of a simplified QCD model. The final algorithm extends the quantum parton shower algorithm onto a quantum walk framework which demonstrates significant scaling improvements, simulating more realistic shower depths. These algorithms utilise the quantum computers’ ability to remain in a quantum state throughout the computation and represents a first step towards a quantum computing algorithm describing full collision events at the LHC.
This paper presents a novel quantum walk approach to simulating parton showers on a quantum computer. We demonstrate that the quantum walk paradigm offers a natural and more efficient approach to simulating parton showers on quantum devices, with the emission probabilities implemented as the coin flip for the walker, and the particle emissions to either gluons or quark pairs corresponding to the movement of the walker in two dimensions. A quantum algorithm is proposed for a simplified, toy model of a 31-step, collinear parton shower, hence significantly increasing the number of steps of the parton shower that can be simulated compared to previous quantum algorithms. Furthermore, it scales efficiently: the number of possible shower steps increases exponentially with the number of qubits, and the circuit depth grows linearly with the number of steps. Reframing the parton shower in the context of a quantum walk therefore brings dramatic improvements, and is a step towards extending the current quantum algorithms to simulate more realistic parton showers.
Abstract High-quality simulated data is crucial for particle physics discoveries. Therefore, parton shower algorithms are a major building block of the data synthesis in event generator programs. However, the core algorithms used to generate parton showers have barely changed since the 1980s. With quantum computers’ rapid and continuous development, dedicated algorithms are required to exploit the potential that quantum computers provide to address problems in high-energy physics. This paper presents a novel approach to synthesising parton showers using the Discrete QCD method. The algorithm benefits from an elegant quantum walk implementation which can be embedded into the classical toolchain. We use the ibm_algiers device to sample parton shower configurations and generate data that we compare against measurements taken at the ALEPH, DELPHI and OPAL experiments. This is the first time a Noisy Intermediate-Scale Quantum (NISQ) device has been used to simulate realistic high-energy particle collision events.
Quantum computing has emerged as a promising framework for addressing computationally demanding problems in collider physics. In recent years, a growing number of quantum algorithms have been proposed for applications ranging from event generation and parton shower simulation to the evaluation of scattering amplitudes, loop and phase-space integration, and optimization problems relevant to experimental analysis. We provide a concise overview of the main ideas behind these developments, with emphasis on the potential advantages of quantum approaches in comparison with classical methods, as well as on the current limitations imposed by noisy intermediate-scale quantum hardware.