Quantum Digital Twins
Daniel Appelö (Lead PI), Virginia Tech
Mohammad Motamed (Co-PI), University of New Mexico
Co-Investigators:
Yingda Cheng, Virginia Tech
May 2, 2024

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 with 10–100s of qubits and resonators.
The final aim is to demonstrate and disseminate the QuBiC-enhanced QDTs by hardening
developed algorithms and methods into existing open-source software products.