Our group seeks to develop efficient modeling approaches to accelerate the design process of quantum electromagnetic technologies that will be used in building quantum computers, quantum sensors, and quantum communication systems. We aim to do this by developing novel mathematical models for quantum systems whose solutions can directly benefit from the latest research in robust and efficient computational electromagnetics (CEM) methods. The CEM methods we develop to analyze quantum systems of interest also provide unique capabilities for modeling challenging classical electromagnetics applications that involve multiscale, multiphysics, time-varying, and nonlinear features. We leverage the numerical methods we develop for these classical electromagnetics applications whenever possible.
Spontaneous Emission Rate Modeling of Transmon Qubits
Transmon qubits are one of the leading candidates being pursued to achieve various forms of quantum computation. These qubits consist of superconducting Josephson junctions that are embedded in planar microwave circuitry, such as coplanar waveguides. Generally, the transmon qubit will be coupled to a number of microwave resonators in order to control the qubit, read out its state, and drive qubit-qubit interactions. This requires a careful balance between providing control of the qubit and protecting its fragile quantum state. One of the primary mechanisms that can destroy the qubit's state is by spontaneously emitting its excitation into the many microwave transmission lines around the qubit. Hence, modeling the spontaneous emission rate for practical qubit implementations can provide valuable information about the performance limitations of a device before fabrication.
However, the commonly used theoretical models for analyzing transmon qubits are not conducive to rigorously determining the spontaneous emission rate of practical devices. Further, the detailed numerical electromagnetic analysis of realistic devices can also be challenging due to the strongly multiscale nature of these devices; which have important features sizes that range from sub-micrometer to multiple centimeters in length. We are approaching this problem by developing a more general theoretical model for the interaction of a transmon qubit with electromagnetic fields. With this generalized model, we can show that the spontaneous emission rate of the transmon qubit can be computed using completely classical computational electromagnetics methods. We are now leveraging potential-based time domain integral equation solvers we developed that are well-suited to analyzing multiscale devices to compute the spontaneous emission rate of practical devices.
Full-Wave Modeling of the Emission of Single Photon Sources
The development of efficient and deterministic single photon sources remains a challenge for implementing scalable quantum information processing systems. In addition to having high efficiency, one of the most sought after properties of singe photon sources is for them to produce highly indistinguishable photons. This is required so that photons produced by different sources can coherently interfere with each other, producing the uniquely quantum effects that are necessary for many quantum processing algorithms to be effective. A number of studies have looked at the fundamental bounds on the indistinguishability of single photons produced by various hardware platforms. However, these studies neglect the loss of indistinguishability that can occur due to manufacturing tolerances and different photon propagation environments experienced by photons produced by different sources.
To provide a more complete description of the indistinguishability a single photon source can achieve in a practical geometry, we are developing a full-wave modeling process to rigorously compute the spatial and temporal dependence of the emission of a single photon source. This allows us to more completely account for the specific layout of a single photon source and the electromagnetic propagation environment the photon is emitted into. Our approach is generally applicable to microwave or optical frequency single photon sources. We have begun testing this numerical modeling approach by analyzing a microwave single photon source that consists of a transmon qubit embedded in a coplanar waveguide cavity resonator. Our model has shown promising results that match expectations for device performance based on the experimental results achieved for a similarly designed device.
Modeled transmon-based single photon source.
Multiscale Computational Electromagnetics Methods
A surprising number of emerging quantum electromagnetic applications can be analyzed using completely classical CEM techniques. However, using these classical tools to model quantum applications requires the CEM method to perform increasingly broadband analyses of multiscale and subwavelength structures with complicated geometric features. This kind of analysis has long been a challenge for traditional CEM techniques that typically are not well-suited to modeling multiscale structures.
We have recently developed novel time domain integral equation solvers formulated in terms of the magnetic vector and electric scalar potentials. Our work has shown that potential-based methods can greatly outperform traditional approaches that describe the physics in terms of electric and magnetic fields when analyzing multiscale geometries. We are continuing to mature these techniques by making them applicable to a wider range of materials and by developing efficient preconditioners that can be used in accelerating the solution of practical multiscale systems. We are also engaged in extending these concepts to other methods, such as differential equation solvers like the finite element method.
Results from a multiscale time domain integral equation method. Arrows show the solved for current on the geometry and the coloring is proportional to the charge density on the geometry.