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IEEE International Conference on Quantum Computing and Engineering (QCE)

Simulating Quantum Field Theories on Gate-Based Quantum Computers

Gayathree M. Vinod, Anil Shaji

Published Sep 15, 2024• 0 citations
Publisher

Abstract

This poster is based on the recently published work titled 'Simulating Quantum Field Theories on Gate-based Quantum Computers', published in the IEEE Transactions on Quantum Engineering journal (pp. 1–14, vol. 5, 2024, DOI: 10.1109/TQE.2024.3385372). This work involves the non-perturbative simulation of the Yukawa model in 1+1 space-time dimensions on an IBM quantum computer, using the light-front formulation to control the resource requirement and complexity of the simulation. Qubit operators for the bosonic excitations were also created and were used along with the fermionic ones already available, to simulate the theory involving all of these particles. With the restriction on the number of logical qubits available on the existent gate-based Noisy Intermediate-Scale Quantum (NISQ) devices” the trotterization approximation is also used.

DOI
10.1109/qce60285.2024.10400

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This poster is based on the recently published work titled 'Simulating Quantum Field Theories on Gate-based Quantum Computers', published in the IEEE Transactions on Quantum Engineering journal (pp. 1–14, vol. 5, 2024, DOI: 10.1109/TQE.2024.3385372). This work involves the non-perturbative simulation of the Yukawa model in 1+1 space-time dimensions on an IBM quantum computer, using the light-front formulation to control the resource requirement and complexity of the simulation. Qubit operators for the bosonic excitations were also created and were used along with the fermionic ones already available, to simulate the theory involving all of these particles. With the restriction on the number of logical qubits available on the existent gate-based Noisy Intermediate-Scale Quantum (NISQ) devices” the trotterization approximation is also used.
We implement a simulation of a quantum field theory in 1+1 space-time dimensions on a gate-based quantum computer using the light front formulation of the theory. The non-perturbative simulation of the Yukawa model field theory is verified on IBM's simulator and is also demonstrated on a small-scale IBM circuit-based quantum processor, on the cloud, using IBM Qiskit. The light front formulation allows for controlling the resource requirement and complexity of the computation with commensurate trade-offs in accuracy and detail by modulating a single parameter, namely the harmonic resolution. Qubit operators for the bosonic excitations were also created and were used along with the fermionic ones already available, to simulate the theory involving all of these particles. With the restriction on the number of logical qubits available on the existent gate-based Noisy Intermediate-Scale Quantum (NISQ) devices, the trotterization approximation is also used. We show that experimentally relevant quantities like cross sections for various processes, survival probabilities of various states, etc. can be computed. We also explore the inaccuracies introduced by the bounds on achievable harmonic resolution and Trotter steps placed by the limited number of qubits and circuit depth supported by present-day NISQ devices.
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
The quantum simulation of fermionic gauge field theories is one of the anticipated uses of quantum computers in the noisy intermediate-scale quantum (NISQ) era. Recently work has been done to simulate properties of the fermionic Z2{\mathbb{Z}}_{2}Z2​ gauge field theory in (1+1)D(1+1)\mathrm{D}(1+1)D and the pure gauge theory in (2+1)D(2+1)\mathrm{D}(2+1)D. In this work, we investigate various options for simulating the fermionic Z2{\mathbb{Z}}_{2}Z2​ gauge field theory in (2+1)D(2+1)\mathrm{D}(2+1)D. To simulate the theory on a NISQ device it is vital to minimize both the number of qubits used and the circuit depth. In this work we propose ways to optimize both criteria for simulating time dynamics. In particular, we develop a new way to simulate this theory on a quantum computer, with minimal qubit requirements. We provide a quantum circuit for simulating a single first-order Trotter step that minimizes the number of 2-qubit gates needed and gives comparable results to methods requiring more qubits. Furthermore, we investigate variational Trotterization approaches that allow us to further decrease the circuit depth.
We present a novel method for simulating the noisy behavior of quantum computers, which allows to efficiently incorporate environmental effects in the driven evolution implementing the gates acting on the qubits. We show how to modify the noiseless gate executed by the computer to include any Markovian noise, hence resulting in what we will call a noisy gate. We compare our method with the IBM qiskit simulator, and show that it follows more closely both the analytical solution of the Lindblad equation as well as the behavior of a real quantum computer, where we ran algorithms involving up to 18 qubits; as such, our protocol offers a more accurate simulator for NISQ devices. The method is flexible enough to potentially describe any noise, including non-Markovian ones. The noise simulator based on this work is available as a python package at the link, https://pypi.org/project/quantum-gates.
The lecture notes cover the basics of quantum computing methods for quantum field theory applications. No detailed knowledge of either quantum computing or quantum field theory is assumed and we have attempted to keep the material at a pedagogical level. We review the anharmonic oscillator, using which we develop a hands-on treatment of certain interesting QFTs in 1+1D1+1D1+1D: φ4φ^4φ4 theory, Ising field theory, and the Schwinger model. We review quantum computing essentials as well as tensor network techniques. The latter form an essential part for quantum computing benchmarking. Some error modelling on QISKIT is also done in the hope of anticipating runs on NISQ devices. These lecture notes are the expanded version of a one semester course taught by AS during August-November 2025 at the Indian Institute of Science and TA-ed by UB. The programs written for this course are available in a GitHub repository.
A new interactive simulator for Quantum Computation has been developed for simulation of the universal set of quantum gates and for construction of new gates of up to 3 qubits. The simulator also automatically generates an equivalent quantum circuit for any arbitrary unitary transformation on a qubit. Available quantum computer simulators attempt to emulate the various physical realisations of quantum computation, simulate existing quantum algorithms or are aimed at facilitating the development of new algorithms. However, because of the level of advancement and complexity of quantum computation algorithms, these simulators tend to be quite complex, at least from a novice's point of view. As a result of this, beginners are often at a loss when trying to interact with them. The simulator here proposed therefore is aimed at bridging the gap somewhat, making quantum computer simulation more accessible to novices in the field. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 433-446