Quantum Digital Twins

D. Appelo, Virginia Polytechnic Institute and State University (Principal Investigator)
M. Motamed, University of New Mexico (Co-Investigator)
Y. Cheng, Virginia Polytechnic Institute and State University (Co-Investigator)

The proposed research will develop and deploy Quantum Digital Twins (QDT), hardware emulators that are individual digital clones of existing quantum devises. The QDT framework we propose will provide the foundational glue that binds currently available software tools, data, and hardware. We consider general hardware descriptions whose properties can be modeled by the Lindblad quantum master equation but note that other models are allowed by our QDT framework. 

A key feature of our QDTs is the bi-directional interaction between virtual and physical siblings. In a calibration phase, a QDT’s performance is monitored and improved in a cost-efficient way by optimal experimental design. When calibrated, the QDT can be used to test any software on the quantum software stack that uses the hardware the QDT emulates. The QDTs will be realized by robust optimal transport-driven Bayesian techniques and novel, scalable numerical methods. The QDT emulators integrate the physics of quantum hardware, described by Schrödinger’s and Lindblad’s equations, using high-order accurate and structure-preserving numerical techniques. They also address the inherent complexity and incompleteness of these descriptions, known as model inadequacy, by employing robust Bayesian techniques that handle the inherent uncertainty and noise in the quantum hardware. 

The research program proposes to address the limitations of traditional approaches through four specific aims. The first aim is to design, analyze, and implement QDTs and algorithms using a Quantum Bi-directional Communication (QuBiC) approach. This approach first focuses on characterization tasks, employing optimal design of experiments, real quantum measurements, and statistical techniques driven by optimal transport. The second aim is to use the QuBiC approach for the optimal control tasks during the calibration phase of the QDT. This will be achieved through new arbitrary order accurate Hermite interpolation-based methods for time evolution and discrete adjoint computations, which will enable large speedups for problems of medium size. The third aim is to develop low-rank methods for Lindblad’s quantum master equations to emulate large composite open systems. The final aim is to demonstrate and disseminate the QuBiC-enhanced QDTs by hardening developed algorithms and methods into existing open-source software products. 

Our research has the potential to influence quantum computing methods for addressing scientific challenges relevant to the DOE. Our work can provide valuable intuition regarding the utility of specific quantum computing hardware. Additionally, the insights gained from this study can guide the design and training of general digital twins, thereby broadening their applicability to applications of relevance to the DOE.