Light-matter coupled Hamiltonians are central to cavity materials engineering and polaritonic chemistry, but are challenging to simulate with classical hardware due to the scaling of the Hilbert space with the number of quantum photon modes and matter complexity. Leveraging the fact that quantum computers naturally represent photonic modes efficiently, we present a novel approach to simulate quantum-electrodynamical (QED) systems on near-term quantum hardware. After developing the bosonic and mixed operators in the Qiskit Nature framework, we employ them to simulate a first-order Trotterized Hamiltonian for a spontaneous-emission problem of a two-level system in an optical cavity. We find that using a standing-waves photonic basis approach leads to fidelity issues due to hardware connectivity constraints and two-qubits gates errors. Hence, we propose using a localized photonic basis approach that enforces nearest-neighbor couplings, thanks to which we can map the Hamiltonian as a 1D qubit chain. We significantly reduce the noise and, by applying the zero-noise extrapolation error mitigation technique, we recover the accurate quantum dynamics. Finally, we also show that this approach is resilient when relaxing the 1D qubit chain approximation.
Light-matter coupled Hamiltonians are central to cavity materials engineering and polaritonic chemistry, but are challenging to simulate with classical hardware due to the scaling of the Hilbert space with the number of quantum photon modes and matter complexity. Leveraging the fact that quantum computers naturally represent photonic modes efficiently, we present a novel approach to simulate quantum-electrodynamical (QED) systems on near-term quantum hardware. After developing the bosonic and mixed operators in the Qiskit Nature framework, we employ them to simulate a first-order Trotterized Hamiltonian for a spontaneous-emission problem of a two-level system in an optical cavity. We find that using a standing-waves photonic basis approach leads to fidelity issues due to hardware connectivity constraints and two-qubits gates errors. Hence, we propose using a localized photonic basis approach that enforces nearest-neighbor couplings, thanks to which we can map the Hamiltonian as a 1D qubit chain. We significantly reduce the noise and, by applying the zero-noise extrapolation error mitigation technique, we recover the accurate quantum dynamics. Finally, we also show that this approach is resilient when relaxing the 1D qubit chain approximation.
In this work, we provide an overview of how well-established concepts in the fields of quantum chemistry and material sciences have to be adapted when the quantum nature of light becomes important in correlated matter-photon problems. We analyze model systems in optical cavities, where the matter-photon interaction is considered from the weak- to the strong-coupling limit and for individual photon modes as well as for the multimode case. We identify fundamental changes in Born-Oppenheimer surfaces, spectroscopic quantities, conical intersections, and efficiency for quantum control. We conclude by applying our recently developed quantum-electrodynamical density-functional theory to spontaneous emission and show how a straightforward approximation accurately describes the correlated electron-photon dynamics. This work paves the way to describe matter-photon interactions from first principles and addresses the emergence of new states of matter in chemistry and material science.
We investigate the application of quantum computers to the investigation of effects in cavity quantum electrodynamics (“cavity QED”), which are relevant for areas like materials properties, multiphoton effects such as superradiance or systems with strong field-matter coupling. To study these systems, we introduce a boson-to-qubit mapping to facilitate a multi-photon, multi-atom case study, based on the inverse Holstein-Primakoff transformation. In the multi-photon regime, boson operators are expressed via higher-spin operators which are subsequently mapped on a circuit using Pauli operators. We use a Newton series expansion to enable rigorous treatment of the square root operator. With this encoding, we perform simulations of a phase transition in a pair of coupled cavities that permit photon hopping using 6 qubits. We map the spin and boson systems to separate qubit registers and use first-order Trotterization to time-propagate the wavefunction. The order parameter, the observable for the phase transition, is calculated by measuring the number operator and its square. We find that the simulation matches benchmark classical calculations and the phase transition is well resolved with a relatively small amount of shots, indicating that our encoding properly represents the physics of the system, and the simulation can be performed with a modest amount of quantum resources on hardware.
In this paper, we aim to broaden the spectrum of possible applications of quantum computers and use their capabilities to investigate effects in cavity quantum electrodynamics (cavity QED). Interesting application examples are material properties, multiphoton effects such as superradiance, systems with strong field-matter coupling, and others. For QED applications, experimental studies are challenging, and classical simulations are often expensive. Therefore, exploring the capabilities of quantum computers is of interest. Below we present a methodology for simulating a phase transition in a pair of coupled cavities that permit photon hopping. We map the spin and boson systems to separate parts of the register and use first-order Trotterization to time-propagate the wave function. The order parameter, the observable for the phase transition, is calculated by measuring the number operator and its square. We introduce a boson-to-qubit mapping to facilitate a multiphoton, multiatom case study. Our mapping scheme is based on the inverse Holstein-Primakoff transformation. In the multiphoton regime, boson operators are expressed via higher-spin operators which are subsequently mapped on a circuit using Pauli operators. We use a Newton series expansion to enable rigorous treatment of the square root operator. We reproduce the results of classical simulations of a phase transition with a noiseless six-qubit simulation. We find that the simulation can be performed with a modest amount of quantum resources. Finally, we perform simulations on noisy emulators and find that mitigation techniques are essential to distinguish signal from noise.
The recent advent of quantum algorithms for noisy quantum devices offers a new route toward simulating strong light–matter interactions of molecules in optical cavities for polaritonic chemistry. In this work, we introduce a general framework for simulating electron–photon-coupled systems on small, noisy quantum devices. This method is based on the variational quantum eigensolver (VQE) with the polaritonic unitary coupled cluster (PUCC) ansatz. To achieve chemical accuracy, we exploit various symmetries in qubit reduction methods, such as electron–photon parity, and use recently developed error mitigation schemes, such as the reference zero-noise extrapolation method. We explore the robustness of the VQE-PUCC approach across a diverse set of regimes for the bond length, cavity frequency, and coupling strength of the H 2 molecule in an optical cavity. To quantify the performance, we measure two properties: ground-state energy, fundamentally relevant to chemical reactivity, and photon number, an experimentally accessible general indicator of electron–photon correlation.
Open quantum systems are central to quantum optics, condensed matter, and chemistry, yet their simulation remains challenging for both classical and near-term quantum hardware. In this work we implement and execute utility-scale quantum circuits that accurately reproduce the dissipative dynamics of interacting qubits. We consider a one-dimensional chain of many qubits weakly coupled to a common Markovian bath. The Markovian time evolution of the system is implemented through Trotterized evolution with the introduction of ancilla-assisted dissipative channels, including single-qubit and two-qubit dissipators to capture collective decay. Mid-circuit measurements, conditional gates, and hardware-aware transpilation significantly reduce circuit depth. We further implement a biased Clifford data regression (biased CDR), an error mitigation strategy that outperforms the uniform Cliffordization baseline and a variety of zero-noise extrapolation protocols. We execute large-scale quantum experiments of the dynamics of chains comprising up to 86 emitters on the IBM System Two \texttt{ibm\_basquecountry}. In order to do so, we use 129 total qubits (including ancillas), with the largest circuits contain about 8000 two-qubit gates. To validate these experiments we develop a classical Monte Carlo-Time-Evolving Block-Decimation (MC-TEBD) tensor-network method that incorporates reset operations through stochastic pure-state trajectories, obtaining very good agreement. The approach presented here opens a practical route for utility-scale quantum simulation of dissipative dynamics, enabled by dynamic circuits, targeted error mitigation, and tensor-network validation, and enables to tackle complex dynamics of systems such as quantum emitters in dissipative optical cavities.
Abstract In digital quantum simulation of fermionic models with qubits, non-local maps for encoding are often encountered. Such maps require linear or logarithmic overhead in circuit depth which could render the simulation useless, for a given decoherence time. Here we show how one can use a cavity–QED system to perform digital quantum simulation of fermionic models. In particular, we show that highly nonlocal Jordan–Wigner or Bravyi–Kitaev transformations can be efficiently implemented through a hardware approach. The key idea is using ancilla cavity modes, which are dispersively coupled to a qubit string, to collectively manipulate and measure qubit states. Our scheme reduces the circuit depth in each Trotter step of the Jordan–Wigner encoding by a factor ofN2, comparing to the scheme for a device with only local connectivity, whereNis the number of orbitals for a generic two-body Hamiltonian. Additional analysis for the Fermi–Hubbard model on anN × Nsquare lattice results in a similar reduction. We also discuss a detailed implementation of our scheme with superconducting qubits and cavities.