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arXiv:2505.03878

Real-Time Scattering on Quantum Computers via Hamiltonian Truncation

James Ingoldby, Michael Spannowsky, Timur Sypchenko, Simon Williams, Matthew Wingate A

Published May 6, 2025• 0 citations
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Abstract

We present a quantum computational framework using Hamiltonian Truncation (HT) for simulating real-time scattering processes in $(1+1)$-dimensional scalar $ϕ^4$ theory. Unlike traditional lattice discretisation methods, HT approximates the quantum field theory Hilbert space by truncating the energy eigenbasis of a solvable reference Hamiltonian, significantly reducing the number of required qubits. Our approach involves preparing initial states as wavepackets through adiabatic evolution from the free-field theory to the interacting regime. We experimentally demonstrate this state preparation procedure on an IonQ trapped-ion quantum device and validate it through quantum simulations, capturing key phenomena such as wavepacket dynamics, interference effects, and particle production post-collision. Detailed resource comparisons highlight the advantages of HT over lattice approaches in terms of qubit efficiency, although we observe challenges associated with circuit depth scaling. Our findings suggest that Hamiltonian Truncation offers a promising strategy for quantum simulations of quantum field theories, particularly as quantum hardware and algorithms continue to improve.

DOI
10.48550/arxiv.2505.03878

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We present a quantum computational framework using Hamiltonian Truncation (HT) for simulating real-time scattering processes in (1+1)(1+1)(1+1)-dimensional scalar ϕ4ϕ^4ϕ4 theory. Unlike traditional lattice discretisation methods, HT approximates the quantum field theory Hilbert space by truncating the energy eigenbasis of a solvable reference Hamiltonian, significantly reducing the number of required qubits. Our approach involves preparing initial states as wavepackets through adiabatic evolution from the free-field theory to the interacting regime. We experimentally demonstrate this state preparation procedure on an IonQ trapped-ion quantum device and validate it through quantum simulations, capturing key phenomena such as wavepacket dynamics, interference effects, and particle production post-collision. Detailed resource comparisons highlight the advantages of HT over lattice approaches in terms of qubit efficiency, although we observe challenges associated with circuit depth scaling. Our findings suggest that Hamiltonian Truncation offers a promising strategy for quantum simulations of quantum field theories, particularly as quantum hardware and algorithms continue to improve.
Quantum computing offers a paradigm shift in efficiently simulating quantum field theories (QFTs). In this review, we outline two new techniques for the simulation of QFTs on quantum devices. The first technique employs Hamiltonian Truncation (HT) for nonperturbative real-time QFT simulations on Noisy Intermediate-Scale Quantum (NISQ) devices. As a use case, we apply the HT approach to the Schwinger model. For the observables studied, HT avoids complex state preparation, reducing circuit depth and making the algorithm well suited for NISQ devices. Validated on the ibm_brisbane quantum computer with results showing good agreement with numerical simulations, HT presents an efficient alternative to lattice models. The second approach introduces a continuous-variable quantum computing (CVQC) framework for simulating the real-time dynamics of QFTs, where quantum field values are encoded directly into photonic qumodes. By avoiding the overhead of field digitization, CVQC enables scalable simulations using significantly fewer quantum resources than traditional qubit-based approaches. Classical emulation of the qumode lattice successfully reproduces scattering processes in [Formula: see text]-dimensional [Formula: see text] theory. Together, these methods demonstrate viable paths toward near-term quantum simulations of interacting field theories, offering complementary strategies to address challenges in nonperturbative studies in high-energy physics.
Quantum computers can efficiently simulate highly entangled quantum systems, offering a solution to challenges facing classical simulation of quantum field theories (QFTs). This paper presents an alternative to traditional methods for simulating the real-time evolution in QFTs by leveraging Hamiltonian truncation (HT). As a use case, we study the Schwinger model, systematically reducing the complexity of the Hamiltonian via HT while preserving essential physical properties. For the observables studied in this paper, the HT approach converges quickly with the number of qubits, allowing for the interesting physics processes to be captured without needing many qubits. Identifying the truncated free Hamiltonian’s eigenbasis with the quantum device’s computational basis avoids the need for complicated and costly state preparation routines, reducing the algorithm’s overall circuit depth and required coherence time. As a result, the HT approach to simulating QFTs on a quantum device is well suited to noisy-intermediate scale quantum devices, which have a limited number of qubits and short coherence times. We validate our approach by running simulations on a noisy-intermediate scale quantum device, showcasing strong agreement with theoretical predictions. We highlight the potential of HT for simulating QFTs on quantum hardware. Published by the American Physical Society 2024
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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
We propose a framework for simulating the real-time dynamics of quantum field theories using continuous-variable quantum computing (CVQC). Focusing on ( 1 + 1 )-dimensional φ 4 scalar field theory, the approach employs the Hamiltonian formalism to map the theory onto a spatial lattice, with fields represented as quantum harmonic oscillators. Using measurement-based quantum computing, we implement non-Gaussian operations for CQVC platforms. The study introduces methods for preparing initial states with specific momenta and simulating their evolution under the φ 4 Hamiltonian. Key quantum objects, such as two-point correlation functions, validate the framework against analytical solutions. Scattering simulations further illustrate how mass and coupling strength influence field dynamics and energy redistribution. Thus, we demonstrate CVQC's scalability for larger lattice systems and its potential for simulating more complex field theories.
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.