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arXiv:2310.13742

Simulating Scattering of Composite Particles

Michael Kreshchuk, James P. Vary, Love, Peter J.

Published Oct 20, 2023• 0 citations
arXivHTMLPDF

Abstract

We develop a non-perturbative approach to simulating scattering on classical and quantum computers, in which the initial and final states contain a fixed number of composite particles. The construction is designed to mimic a particle collision, wherein two composite particles are brought in contact. The initial states are assembled via consecutive application of operators creating eigenstates of the interacting theory from vacuum. These operators are defined with the aid of the Møller wave operator, which can be constructed using such methods as adiabatic state preparation or double commutator flow equation. The approach is well-suited for studying strongly coupled systems in both relativistic and non-relativistic settings. For relativistic systems, we employ the language of light-front quantization, which has been previously used for studying the properties of individual bound states, as well as for simulating their scattering in external fields, and is now adopted to the studies of scattering of bound state systems. For simulations on classical computers, we describe an algorithm for calculating exact (in the sense of a given discretized theory) scattering probabilities, which has cost (memory and time) exponential in momentum grid size. Such calculations may be interesting in their own right and can be used for benchmarking results of a quantum simulation algorithm, which is the main application of the developed framework. We illustrate our ideas with an application to the $ϕ^4$ theory in $1+1\rm D$.

DOI
10.48550/arxiv.2310.13742

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We develop a non-perturbative approach to simulating scattering on classical and quantum computers, in which the initial and final states contain a fixed number of composite particles. The construction is designed to mimic a particle collision, wherein two composite particles are brought in contact. The initial states are assembled via consecutive application of operators creating eigenstates of the interacting theory from vacuum. These operators are defined with the aid of the Møller wave operator, which can be constructed using such methods as adiabatic state preparation or double commutator flow equation. The approach is well-suited for studying strongly coupled systems in both relativistic and non-relativistic settings. For relativistic systems, we employ the language of light-front quantization, which has been previously used for studying the properties of individual bound states, as well as for simulating their scattering in external fields, and is now adopted to the studies of scattering of bound state systems. For simulations on classical computers, we describe an algorithm for calculating exact (in the sense of a given discretized theory) scattering probabilities, which has cost (memory and time) exponential in momentum grid size. Such calculations may be interesting in their own right and can be used for benchmarking results of a quantum simulation algorithm, which is the main application of the developed framework. We illustrate our ideas with an application to the ϕ4ϕ^4ϕ4 theory in 1+1D1+1\rm D1+1D.
The last few years have seen rapid development of applications of quantum computation to quantum field theory. The first algorithms for quantum simulation of scattering have been proposed in the context of scalar and fermionic theories, requiring thousands of logical qubits. These algorithms are not suitable to simulate scattering of incoming bound states, as the initial-state preparation relies typically on adiabatically transforming wavepackets of the free theory into wavepackets of the interacting theory. In this paper we present a strategy to excite wavepackets of the interacting theory directly from the vacuum of the interacting theory, allowing the preparation of states of composite particles. This is the first step towards digital quantum simulation of scattering of bound states. The approach is based on the Haag-Ruelle scattering theory, which provides a way to construct creation and annihilation operators of a theory in a full, nonperturbative framework. We provide a quantum algorithm requiring a number of ancillary qubits that is logarithmic in the size of the wavepackets, and with a success probability vanishing at most like a polynomial in the lattice parameters and the energy of the wavepacket. The gate complexity for a single iteration of the circuit is equivalent to that of a time evolution for a fixed time. Furthermore, we propose a complete protocol for scattering simulation using this algorithm. We study its efficiency and find improvements with respect to previous algorithms in the literature. Published by the American Physical Society 2024
Quantum simulation holds promise of enabling a complete description of high-energy scattering processes rooted in gauge theories of the Standard Model. A first step in such simulations is preparation of interacting hadronic wave packets. To create the wave packets, one typically resorts to adiabatic evolution to bridge between wave packets in the free theory and those in the interacting theory, rendering the simulation resource intensive. In this work, we construct a wave-packet creation operator directly in the interacting theory to circumvent adiabatic evolution, taking advantage of resource-efficient schemes for ground-state preparation, such as variational quantum eigensolvers. By means of an ansatz for bound mesonic excitations in confining gauge theories, which is subsequently optimized using classical or quantum methods, we show that interacting mesonic wave packets can be created efficiently and accurately using digital quantum algorithms that we develop. Specifically, we obtain high-fidelity mesonic wave packets in the Z 2 and U ( 1 ) lattice gauge theories coupled to fermionic matter in 1+1 dimensions. Our method is applicable to both perturbative and non-perturbative regimes of couplings. The wave-packet creation circuit for the case of the Z 2 lattice gauge theory is built and implemented on the Quantinuum H1-1 trapped-ion quantum computer using 13 qubits and up to 308 entangling gates. The fidelities agree well with classical benchmark calculations after employing a simple symmetry-based noise-mitigation technique. This work serves as a step toward quantum computing scattering processes in quantum chromodynamics.
One of the most ambitious goals of quantum simulation of quantum field theory is the description of scattering in real time, which would allow not only for computation of scattering amplitudes, but also for studying the collision process step by step. The initial state of such simulation is made of typically two wave packets of stable particles moving on top of the vacuum, whose preparation is difficult. Here we extend a previous work to create wave packets of a general kind of particle from the vacuum in lattice gauge theories in various dimensions, including three-dimensional QCD for the first time. The conceptual foundation of this approach is the Haag-Ruelle scattering theory, and the only theoretical limitation is given by the presence of massless particles. In the context of digital quantum computation, the wave packet creation from the vacuum is implemented with the technique known as LCU (linear combination of unitaries). The preparation is performed successfully upon measuring an ancillary register with a certain probability, which vanishes polynomially in the lattice spacing, the wave-packet energy, and the momentum narrowness.
Simulations of collisions of fundamental particles on a quantum computer are expected to have an exponential advantage over classical methods and promise to enhance searches for new physics. Furthermore, scattering in scalar field theory has been shown to be BQP-complete, making it a representative problem for which quantum computation is efficient. As a step toward large-scale quantum simulations of collision processes, scattering of wavepackets in one-dimensional scalar field theory is simulated using 120 qubits of IBM's Heron superconducting quantum computer ibm_fez. Variational circuits compressing vacuum preparation, wavepacket initialization, and time evolution are determined using classical resources. By leveraging physical properties of states in the theory, such as symmetries and locality, the variational quantum algorithm constructs scalable circuits that can be used to simulate arbitrarily-large system sizes. A new strategy is introduced to mitigate errors in quantum simulations, which enables the extraction of meaningful results from circuits with up to 4924 two-qubit gates and two-qubit gate depths of 103. The effect of interactions is clearly seen, and is found to be in agreement with classical Matrix Product State simulations. The developments that will be necessary to simulate high-energy inelastic collisions on a quantum computer are discussed.
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive ϕ4\phi^4ϕ4 theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling.
Simulating the real-time dynamics of particle collisions is a promising application of quantum simulators, because classical methods such as tensor networks struggle to capture the highly entangled states generated in high-energy scattering. Realizing such simulations requires both the preparation of incoming wave packets and the detection of the outgoing scattering products. In this work, we propose protocols that address both challenges on programmable analog and digital quantum simulation platforms. Our state-preparation scheme uses a weakly coupled auxiliary qubit - or, more generally, a customized local quench - to inject a single quasiparticle with well-defined momentum. Because it relies only on conservation of energy, this scheme requires no fine-tuning or prior knowledge about particle eigenstates, making it robust against errors in calibration and implementation. The momenta of scattering products are then extracted, using only local measurements, from the interference pattern that arises when particles are reflected at the system's boundary. We validate our protocols through numerical simulations, first in a simple single-particle model and subsequently in two interacting many-body systems: a Rydberg atom chain and an Ising chain in a mixed field. We demonstrate how high-energy regimes, necessary to access inelastic scattering processes, can be reached through an adiabatic ramp, and how the wave packet shape can be optimized by spatially modulating the Hamiltonian. Finally, we show how the protocol can be generalized to systems with more than one spatial dimension. Our proposal provides a versatile approach to the quantum simulation of scattering phenomena, and is compatible with several quantum simulation platforms that are already experimentally available.