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.
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.
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.
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.
Abstract Quantum computers hold the potential to unlock new discoveries in complex quantum systems by enabling the simulation of physical systems that have heretofore been impossible to implement on classical computers due to intractability. A system of particular interest is that of dirty bosons, whose physics highlights the intriguing interplay of disorder and interactions in quantum systems, playing a central role in describing, for instance, ultracold gases in a random potential, doped quantum magnets, and amorphous superconductors. Here, we demonstrate how quantum computers can be used to elucidate the physics of dirty bosons in one and two dimensions. Specifically, we explore the disorder-induced delocalized-to-localized transition using adiabatic state preparation. In one dimension, the quantum circuits can be compressed to small enough depths for execution on currently available quantum computers. In two dimensions, the compression scheme is no longer applicable, thereby requiring the use of large-scale classical state vector simulations to emulate quantum computer performance. In addition, simulating interacting bosons via emulation of a noisy quantum computer allowed us to study the effect of quantum hardware noise on the physical properties of the simulated system. Our results suggest that scaling laws control how noise modifies observables versus its strength, the circuit depth, and the number of qubits. Moreover, we observe that noise impacts the delocalized and localized phases differently. A better understanding of how noise alters the observed properties of the simulated system is essential for leveraging near-term quantum devices for simulation of dirty bosons, and indeed for condensed matter systems in general.
Based on a multi-mode multi-level Jaynes-Cummings model and multi-photon resonance theory, a set of universal two-qubit and three-qubit gates has been realized where dual-rail qubits are encoded in cavities. In this way, the information has been stored in cavities and the off-resonant levels have been eliminated by the theory of an effective two-level Hamiltonian. A further model, namely the spin-J model, has been introduced so that a complete population inversion for levels of interest has been achieved and periodic multilevel multi-photon models have been performed. The combination of the two models has been employed to address two-level, three-level, four-level, and even five-level configurations. Considering the present cavity-QED experiments, several numerical simulations have been designed in order to check the robustness of the logic gates to variations in experimentally important parameters including the coupling constants and the detunings. Finally, based on Liouville's equation, and the wave-function treatments, the impact of decoherence processes on the fidelity of the qubit states in the iSWAP and the Fredkin gates has been studied. This thesis may have applications to quantum information processing, involving logic with simple quantum bits, with the possible application to the building of a quantum computer.
A variety of photon-mediated operations are critical to the realization of scalable quantum information processing platforms and their accurate characterization is essential for the identification of optimal regimes and their experimental realizations. Such light-matter interactions are often studied with a broad variety of analytical and computational methods that are constrained by approximation techniques or by computational scaling. Quantum processors present a new avenue to address these challenges. We consider the case of cavity mediated two-qubit gates. To investigate quantum state transfer between the qubits, we implement simulations with quantum circuits that are able to reliably track the dynamics of the system. Our quantum algorithm, compatible with NISQ (Noisy Intermediate Scale Quantum) era systems, allows us to map out the fidelity of the state transfer operation between qubits as a function of a broad range of system parameters including the respective detunings between the qubits and the cavity, the damping factor of the cavity, and the respective couplings between the qubits and the cavity. The algorithm provides a robust and intuitive solution, alongside a satisfactory agreement with analytical solutions or classical simulation algorithms in their respective regimes of validity. It allows us to identify under-explored regimes of optimal performance, relevant for heterogeneous quantum platforms, where the two-qubit gate can be rather effective between far-detuned qubits that are neither resonant with each other nor with the cavity. Besides its present application, the method introduced in the current paper can be efficiently used in otherwise untractable variations of the model and in various efforts to simulate and optimize photon-mediated two-qubit gates and other relevant operations in quantum information processing.