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.
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.
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.
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 gauge field theory in (1+1)D and the pure gauge theory in (2+1)D. In this work, we investigate various options for simulating the fermionic Z2 gauge field theory in (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 scalable quantum simulation framework for real-time dynamics of the multi-flavor Gross-Neveu model in 1+1 dimensions. Using superconducting quantum processors at utility scale, we develop a hardware-efficient Trotterization whose per-step circuit depth scales with fermion flavor number rather than total system size, enabling simulations beyond 100 qubits. A central contribution of this work is the Localized Diagonal Operator Approximation (LDOA), which systematically reduces the overhead associated with quartic interactions. We formulate diagonal unitary synthesis as a structured least-squares problem in phase space and obtain analytic solutions via the Moore-Penrose pseudoinverse. This formulation provides a principled and quantitatively controlled approximation: in the small Trotter-step regime, the unitary error is directly linked to the phase reconstruction error and vanishes asymptotically as the Trotter step size decreases. This establishes a clear mathematical foundation for the LDOA while significantly reducing two-qubit gate counts and circuit depth, and is broadly applicable to diagonal quantum operators with long-range structure, making it particularly well suited for quantum hardware with limited qubit connectivity. Using these techniques, we run large-scale simulations on IBM superconducting processors and study real-time observables, including density-density correlators. We benchmark against exact diagonalization and tensor network-based methods, finding strong agreement across system sizes. These results show that combining hardware-aware circuit design with rigorous approximations enables practical near-term simulation of interacting fermionic field theories and provides a scalable pathway toward more complex quantum field theory simulations.
Approximation based on perturbation theory is the foundation for most of the quantitative predictions of quantum mechanics, whether in quantum many-body physics, chemistry, quantum field theory, or other domains. Quantum computing provides an alternative to the perturbation paradigm, yet state-of-the-art quantum processors with tens of noisy qubits are of limited practical utility. Here, we introduce perturbative quantum simulation, which combines the complementary strengths of the two approaches, enabling the solution of large practical quantum problems using limited noisy intermediate-scale quantum hardware. The use of a quantum processor eliminates the need to identify a solvable unperturbed Hamiltonian, while the introduction of perturbative coupling permits the quantum processor to simulate systems larger than the available number of physical qubits. We present an explicit perturbative expansion that mimics the Dyson series expansion and involves only local unitary operations, and show its optimality over other expansions under certain conditions. We numerically benchmark the method for interacting bosons, fermions, and quantum spins in different topologies, and study different physical phenomena, such as information propagation, charge-spin separation, and magnetism, on systems of up to 48 qubits only using an 8+1 qubit quantum hardware. We demonstrate our scheme on the IBM quantum cloud, verifying its noise robustness and illustrating its potential for benchmarking large quantum processors with smaller ones.
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
Abstract Quantum simulation represents the most promising quantum application to demonstrate quantum advantage on near-term noisy intermediate-scale quantum (NISQ) computers, yet available quantum simulation algorithms are prone to errors and thus difficult to realize with limited circuit depth on nowadays quantum devices. Herein, we propose a novel scheme to utilize intrinsic gate errors of NISQ devices to enable controllable simulation of open quantum system dynamics without ancillary qubits or explicit bath engineering, thus turning unwanted quantum noises into useful quantum resources. Specifically, we simulate the energy transfer process in a photosynthetic dimer system on IBM-Q cloud. By employing tailored decoherence-inducing gates, we show that quantum dissipative dynamics can be simulated efficiently across coherent-to-incoherent regimes with results comparable to those of the numerically exact classical method. Moreover, we demonstrate a calibration routine that enables consistent and predictive simulations of open-quantum system dynamics in the intermediate coupling regime. This work provides a new direction for quantum advantage in the NISQ era.