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.
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.
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.
Quantum simulation of many-body systems offers a powerful approach to exploring collective quantum dynamics beyond classical computational reach. Although spin and fermionic models have been extensively simulated on digital quantum computers, the simulation of bosonic systems on programmable quantum processors is often hindered by the intrinsically large Hilbert space of bosonic modes. In this work, we study the digital quantum simulation of bosonic modes using the Holstein-Primakoff (HP) transformation and implement this protocol on a cloud-based superconducting quantum processor. Two representative models are realized on quantum hardware: (i) the driven harmonic oscillator and (ii) the Jaynes-Cummings model. Using data obtained from the quantum simulations, we systematically examine the interplay between algorithmic and hardware-induced errors to identify optimal simulation parameters. The dominant algorithmic errors arise from the finite number of qubits used in the HP mapping and the finite number of Trotter steps in the time evolution, while hardware errors mainly originate from gate infidelity, decoherence, and readout errors. This study advances the digital quantum simulation of many-body systems involving bosonic degrees of freedom on currently available cloud quantum processors and provides a framework that can be extended to more complex spin-boson and multimode cavity models.
Dicke model describes a collective interaction between the two-level atoms and the light cavity and has been predicted to show a peculiar quantum phase transition, which is a second-order phase transition from a normal phase (in a weak-coupling strength) to a superradiant phase (in a strong-coupling strength). The model plays an important role in illustrating the quantum ground-state properties of many-body macroscopic quantum states. In the experiment, Dicke quantum phase transition in an open system could be formed by a Bose-Einstein condensate coupled to a high-finesse optical cavity. This experiment on the Bose-Einstein condensate trapped in the optical cavity have opened new frontiers, which could combine the cold atoms with quantum optics and makes it possible to enter into the strongly coupled regime of cavity quantum electrodynamics. In strong coupled regime, the atoms exchange the photons many times before spontaneous emission and cavity losses set in. It has become a hot research topic in recent years and plays an important role in many fields of modern physics, such as condensed matter physics, nuclear physics, etc. It can be applied to the manipulation of the geometric phase and entanglement in quantum information and computing. Quantum phase transition has been widely studied for the Dicke model as a typical example. Many different research methods about the mean-field approximation have been used to analyze the ground state properties of the Dicke model. In this paper, we study the ground state properties of two-component Bose-Einstein condensate in a single-mode cavity. Meanwhile, the associated quantum phase transition is described by the spin-coherent-state variational method, whose advantage is that the ground state energy and wave function can be obtained without the thermodynamic limit. By taking the average in the boson coherent state, we obtain an equivalent effective pesudospin Hamiltonian, which will be diagonalized by using the spin coherent state. Finally, we can obtain the energy functional, which is the basics of the variation to obtain the numerical solution of photon number and the expression of the atomic number and the ground state energy. This paper presents a rich phase diagram, which can be manipulated by changing the atom-field coupling imbalance between two components and the atom-field frequency detuning. While in the single-mode Dicke model there exist only the normal phase and the superradiation phase. When the frequency of one component atom is zero or the frequency of the two component atoms are equal in optical cavity, the system returns to the standard Dicke model, in which there occurs the second-order phase transition from the normal phase to the superradiant phase by adjusting the atom-field coupling. In conclusion, we discover that the stimulated radiation comes from the collective state of atomic population inversion, which does not exist in the single-mode Dicke model. Meanwhile, the new stimulated-radiation state S and S, which can only be produced by one component of the atom, are observed in the two-component Bose-Einstein condensates in the single-mode optical cavity. By adjusting the atom-field coupling imbalance and the atom-field frequency detuning (the blue or red detuning), the order of the superradiation state and the stimulated-radiation states can be exchanged between the two components of the atom.
By modelling the coupling of multiple superconducting qubits to a single cavity in the circuit-quantum electrodynamics (QED) framework we find that it should be possible to observe superradiance and phase multistability using currently available technology. Owing to the exceptionally large couplings present in circuit QED, we predict that superradiant microwave pulses should be observable with only a very small number of qubits (just three or four), in the presence of energy relaxation and non-uniform qubit–field coupling strengths. This paves the way for circuit-QED implementations of superradiant state readout and decoherence free subspace state encoding in subradiant states. The system considered here also exhibits phase multistability when driven with large field amplitudes, and this effect may have applications for collective qubit readout and for quantum feedback protocols.
Since the photon box gedanken experiments of several of the founding fathers of modern physics, considerable progress has been made in differentiating the quantum and classical worlds. In this pursuit, the cavity as an open quantum system has been indispensable. From the quantization of the atom and field within a superconducting cavity, a unique realm of EPR type entanglement has emerged. In this way, dynamical evolution of the system in the strong coupling regime is intimately tied with the coupling of an atom with a single resonant or non-resonant mode within the cavity. More specifically, the cavity can be prepared so that the atom is detected in a desired state. Here, the essentials of the strong coupling regime of Cavity Quantum Electrodynamics (QED) are reviewed for cavities tuned with a single atomic transition. A brief introduction of the systems is followed by an approach of the more striking effects, leading towards Ramsey Interferometry and Quantum Non-Demolition measurements as means for quantum gate protocol. Because the integrity of the atom and photon states is important for the advancement of quantum computation, a brief discussion of the decoherence problems is also presented. This document is meant to introduce the topic in a way that makes it easily accessible to those working in closely related areas of physics, and to highlight key applications and some basic questions concerning decoherence and the measurement problem.