Researchers have developed novel protocols that could dramatically improve the precision of quantum simulations, allowing them to surpass the limits of classical computers. By employing advanced techniques like superresolution and manifold optimization, the team was able to accurately estimate the Hamiltonian parameters of a superconducting quantum processor, paving the way for highly precise quantum simulations.
Unlocking the Secrets of Quantum Processors
When the researchers at Google AI encountered difficulties in accurately calibrating their sycamore superconducting quantum chip, they turned to Jens Eisert and his team for help. Eisert, a physicist at Freie Universität Berlin, had extensive experience in analog quantum simulation and systems identification methodology.
Initially, Eisert thought the problem would be easy to solve, but he soon realized it was more challenging than expected. The team struggled to recover the correct Hamiltonian frequencies, a critical step in identifying the system’s unknown Hamiltonian. Undeterred, Eisert assembled a talented group of PhD students, Ingo Roth, Dominik Hangleiter, and Jonas Fuksa, to tackle the issue.
After years of hard work and persistence from the experimental lead, Pedram Roushan, the team developed a robust solution. They combined several innovative techniques, including superresolution to enhance the resolution of eigenvalue estimation and manifold optimization to recover the eigenspaces of the Hamiltonian operator.
Overcoming Obstacles in Hamiltonian Learning
The researchers’ initial tests revealed that accurately recovering the Hamiltonian parameters was a significant challenge. Eisert explained, “Even to understand the processes of switching on and off was important, as these processes are not perfect and instantaneous (and not even unitary), so if one tries to fit a Hamiltonian evolution that is in parts not Hamiltonian at all, one gets a mess.”
To address these obstacles, the team introduced a new technique called TensorEsprit, a novel method for implementing superresolution. By combining TensorEsprit with a manifold optimization approach, they were able to robustly identify the Hamiltonian parameters for up to 14 coupled superconducting qubits distributed across two Sycamore processors.
The researchers’ work highlights the importance of accurately characterizing the Hamiltonian of a quantum system, as it is a fundamental prerequisite for achieving precise quantum simulations. As Eisert pointed out, “An old and yet often underappreciated question is that of what a Hamiltonian of a system is. This question is already asked in the basic lectures on quantum mechanics. Because even if it characterizes the system, it is often assumed to be known, an assumption that is often not the case.”
The team’s findings suggest that their proposed techniques could be scalable and robustly applicable to large quantum processors, potentially paving the way for the realization of highly precise quantum simulations that surpass the capabilities of classical computers. This breakthrough could have significant implications for the development of quantum technologies and our understanding of complex quantum systems.
Expanding the Frontiers of Quantum Simulation
The researchers’ work is not limited to superconducting quantum processors; they are also exploring the application of similar ideas derived from tensor networks to quantum systems comprised of cold atoms, which were first introduced by physicist Immanuel Bloch.
As Eisert stated, “I think that this field will become important in the future.” By aiding the characterization of analog quantum simulators, the team’s work could open new avenues for the realization of high-precision quantum simulations, allowing researchers to explore complex quantum systems and materials in unprecedented detail.
The researchers’ future studies will focus on applying their methods to interacting quantum systems, further expanding the frontiers of quantum simulation. By combining advanced techniques like superresolution and manifold optimization, the team has developed a powerful toolkit for unlocking the full potential of quantum processors, paving the way for groundbreaking advancements in quantum technology and our understanding of the quantum world.
