Collaborative Research: A Unified Approach to Quantum Tomography, Open Systems Control and Quantum Simulation

University Of Arizona, Tucson AZ

Investigators

Abstract

Information technology has been an engine for economic growth largely due to the trend known as Moore's law, whereby the component density and computational power of computer chips doubles approximately every two years. In the not too distant future the building blocks of these circuits is set to reach atomic scale, where the laws of quantum physics will replace the familiar laws of classical physics that govern our everyday world. Surprisingly, theoretical studies have shown that if we can manipulate and control quantum devices as well as we now manipulate and control classical devices, entirely new avenues will open up to process information according to quantum mechanics. As a result, quantum computers will in principle be able to solve some important computational problems exponentially faster than classical computers. It is also thought that a simpler class of devices, commonly referred to as analog quantum simulators, may provide approximate solutions to important problems in chemistry and materials science that are currently intractable. Though a functional quantum computer remains a distant goal, the transformative ideas of quantum computation and simulation hold promise to radically expand the capabilities of computer and information technology and sustain its future growth. This award builds on previous accomplishments by the Principal Investigators in the science and engineering field known as quantum control, which studies how physical devices governed by quantum mechanics can be manipulated and controlled with high precision, even in the presence of inevitable device imperfections and outside disturbances. The first objective of this award is to develop new techniques whereby one can evaluate and verify the operation of quantum devices. This will be done through the use of protocols known as quantum tomography, which determine the state and behavior of a quantum device through a series of carefully chosen measurements. The challenge will be to make these protocols more efficient, i. e., minimizing the number of measurements required, and also more robust, e. g., reliable in the presence of imperfections. The second objective of this award is to realize an analog quantum simulator based on a single atom. This single-atom device will be used to simulate a model system whose behavior is known to be chaotic, i. e., hypersensitive to imperfections and outside disturbances. By quantifying the accuracy of the simulator in the presence of known imperfections, this research will address essential but so far unanswered questions: How far can one trust the predictions of an analog quantum simulator in this challenging but common scenario? And can its accuracy and reliability be improved through state-of-the-art techniques for quantum control? The answer to these questions is relevant for large, federally funded research programs in analog quantum simulation at top research institutions across the US. State-of-the-art quantum control is approaching the thresholds for fault-tolerant operation on a few physical platforms and is steadily improving on many others. As a result, researchers are now pursuing architectures for rudimentary digital quantum computation and analog quantum simulation (AQS). To continue on this path towards useful quantum information processing (QIP), there is an urgent need for more sophisticated tools in the areas of quantum control and quantum tomography, and especially for protocols that are resistant to real-world errors and imperfections. Furthermore, the quantum information community is heavily invested in AQS under the assumption that errors are less critical than in a digital quantum computer. This makes it imperative to study the tolerance of AQS to errors, even in the absence of decoherence, and the prospects of robust control in the context of complex dynamics such as quantum chaos. This award will focus on quantum control and measurement, and their application in quantum tomography and analog quantum simulation. The work will build on well established ideas from optimal control and measurement theory, bringing these to bear on a unique experimental testbed: electron-nuclear spins of cold 133Cs atoms in their electronic ground state. This system provides long coherence times, can be manipulated with radio-frequency, microwave, and optical fields, is accessible to measurement though Stern-Gerlach analysis, and has a 16-dimensional Hilbert space, large enough to explore non-trivial tasks of QIP. With its proven capability to apply high-fidelity unitary maps and perform high-fidelity orthogonal measurements, the testbed provides the building blocks needed for QIP at levels of increasing complexity. The planned research is a mixture of theory and experiment, and will address topics in quantum measurement and tomography. In addition, analog quantum simulation, studying the quantum simulation of a spin-15/2 Quantum Kicked Top (QKT) and the use of the QKT paradigm to explore robust quantum simulation in the presence of chaos will be explored. Because the methodologies of robust control and tomography are independent of any particular platform, results from this award will serve as a benchmark for what can be achieved, and a template for similar advances elsewhere in laboratories working with different physical systems. This will help facilitate progress in the broader field of QIP.