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International Journal of Modern Physics A

Simulating quantum field theories on near-term quantum devices

Simon Williams

Published Jun 12, 2025• 3 citations
Publisher

Abstract

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.

DOI
10.1142/s0217751x25300108

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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
Matter under extreme conditions behaves as a non-equilibrium, strongly-interacting quantum system. Such systems are in the non-perturbative regime of quantum chromodynamics (QCD), where their time evolution is classically intractable. Quantum computing offers a promising alternative, but present-day devices are limited in qubit count and circuit depth, so efficient formulations and algorithms are key to scaling toward experimentally relevant QCD simulations. A scalable framework is established for simulating energy loss and hadronization in 1+1-dimensional SU(2) lattice gauge theory, in which a heavy quark traverses a lattice of light quarks. Classical lattice QCD methods are translated into physics-informed circuits to prepare the interacting ground state. The evolution is run on IBM's quantum processor ibm_pittsburgh, where the charge distribution and energy loss are measured. A further study develops the quantum simulation of the fully gauge-fixed SU(2) Hamiltonian in a mixed basis, a formulation that is expected to remain efficient at all gauge couplings. Digitizing the continuous gauge fields with as few as three qubits per plaquette reproduces low-energy observables with 10−310^{-3}10−3 precision. Scaling to larger systems is limited by resource overhead, which motivates truncations that preserve the relevant observables. Sequency Hierarchy Truncation (SeqHT) exploits the hierarchy in basis-operator contributions. Demonstrated on the adiabatic preparation of the λφ4λφ^4λφ4 ground state on ibm_sherbrooke, SeqHT reduces circuit depth by ~30%, suppressing hardware noise in the extracted observables. All simulations in this dissertation are validated on quantum hardware against classical benchmarks. These studies advance quantum simulations of real-time QCD dynamics.
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.
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.
We delve into the use of photonic quantum computing to simulate quantum mechanics and extend its application towards quantum field theory. We develop and prove a method that leverages this form of continuous-variable quantum computing (CVQC) to reproduce the time evolution of quantum-mechanical states under arbitrary Hamiltonians, and we demonstrate the method's remarkable efficacy with various potentials. Our method centers on constructing an , a specially prepared quantum state that induces the desired time evolution on the target state. This is achieved by introducing a non-Gaussian operation using a measurement-based quantum computing approach, enhanced by machine learning. Furthermore, we propose a framework in which these methods can be extended to encode field theories in CVQC without discretizing the field values, thus preserving the continuous nature of the fields. This opens new avenues for quantum computing applications in quantum field theory. Published by the American Physical Society 2024
Quantum field theory (QFT) simulations are a potentially important application for noisy intermediate scale quantum (NISQ) computers. The ability of a quantum computer to emulate a QFT therefore constitutes a natural application-centric benchmark. Foundational quantum algorithms to simulate QFT processes rely on fault-tolerant computational resources, but to be useful on NISQ machines, error-resilient algorithms are required. Here we outline and implement a hybrid algorithm to calculate the lowest energy levels of the paradigmatic 1+11+11+1--dimensional ${\ensuremath{\phi}}^{4}$ interacting scalar QFT. We calculate energy splittings and compare results with experimental values obtained on currently available quantum hardware. We show that the accuracy of mass-renormalization calculations represents a useful metric with which near-term hardware may be benchmarked. We also discuss the prospects of scaling the algorithm to full simulation of interacting QFTs on future hardware.