Quantum Complexity
A universal quantum simulator needs unlimited access to a so-called universal set of gates. Universal gates, however, are expensive and noisy and therefore a resource that must be used sparingly with current technology. Understanding how starting from economical designs one can achieve more universal quantum simulators with sparse resources is of fundamental importance in both the construction of realistic quantum computers and in the theoretical understanding of quantum complexity, quantum chaos, and even black hole physics. Advancing our understanding of quantum simulators and quantum computers is one of the main goals of the country’s current endeavor in both fundamental and applied science. Being at the forefront of the upcoming quantum information industrial revolution will bring enormous benefits for the economy, in particular creating new opportunities for people from disadvantageous backgrounds and provide an impulse for the advancement of scientific education at all levels.
How universal a quantum circuit is can be captured by how well it reproduces some average properties of quantum evolutions. In this project, the group aims at studying how by doping circuits made of non-universal Clifford gates by means of non-Clifford gates one can drive transitions in quantum complexity and achieve more universal coverage of the ensemble of quantum circuits. They study the transitions in quantum complexity by entanglement complexity, out-of-time-order correlation functions, unitary t-designs, and the behavior of such circuits under an entanglement cooling protocol. Moreover, they plan to apply techniques of machine learning by a deep neural network to both detect the transitions in quantum complexity and to optimize the circuit architecture given the density of non-Clifford gates.
Quantum Matter
Quantum matter describes physical systems specified by two characteristics. The first characteristic is that salient properties of these systems are emergent properties of a quantum many-body system. Here we are using these notions in the same way P. Anderson did in his famous paper More is different. Anderson does not use the word “emergent”, but he posits that the properties of complex systems cannot be reconstructed from simple fundamental laws. This is what we mean by emergent. The second characteristic of Quantum Matter is that it describes those systems whose emergent properties are intrinsically quantum. A good example is superconductivity, whose properties are explained by a macroscopic quantum wave-function. The quantum fluctuations and the coherence of this wave-function are fundamental to explain superconductivity. In past twenty years, there has been a flourishing of contexts where our definition applies. The subject of quantum matters includes as subjects of interest Topological phases of matter, Critical phases of matter and exotic quantum critical points, State-of-the-art numerical and analytic approaches to the many-body problem, application of modern information and complexity theory to quantum many-body physics, quantum error correction, CFT, and bulk locality in holography and beyond, non-equilibrium phenomena, quantum chaos, scrambling, and complexity in quantum matter and holography.
Quantum Chaos and Black Holes
The onset of chaos is at the root of the explanation of thermalization in closed quantum many-body systems, where the time evolution is supposed to be unitary.
Although the precise definition of quantum chaos remains elusive, one can usefully refer to quantum chaos as a bundle of features comprising information scrambling, complex entanglement, universal behavior of out-of-time-order correlation functions (OTOCs) and quantum dynamics modeled by random unitary operators. Information scrambling is the quantum analogue of the butterfly effect, signaling that local disturbances are spread around through operator growth. This phenomenon is aptly detected by the norm of commutators, or, equivalently by the OTOC.
In the context of black hole physics, one wonders whether information is destroyed by a black hole or can be recovered from Hawking radiation as the black hole evaporates. A black hole thermalizes information quickly spreading it rapidly across the system and scrambling it, though through unitary dynamics. We study information recovery protocols from the Hawking radiation by quantum machine learning algorithms based on measures of entanglement complexity.