EAGER-QAC-QCH: NSF-BSF: Quantum Computation as a Non-Equilibrium Dynamical Many-Body System

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Non-technical Summary This award is made on an EAGER proposal invited through the Quantum Algorithm Challenge Dear Colleague Letter. It supports research and education to study new concepts for how quantum mechanical states can be prepared and manipulated to perform computation which includes protocols or algorithms required to use a quantum computer to solve a problem. Quantum computing hardware has significantly advanced over the past few years. Both Google and IBM have recently demonstrated devices with about 50 fully controlled superconducting qubits with high fidelity and long coherence times. The number of qubits may be expected to increase even further, but the number of independent external controls presents a crucial bottleneck in scaling up the modern quantum computing architecture. This means that near-term quantum computers are not going to operate the way classical processors do. The PI aims to develop specific operating protocols, which will allow already existing quantum devices to perform particular optimization tasks, which are exponentially hard for conventional classical algorithms. The latter suffer from being trapped into sub-optimal solutions for extremely long times. Quantum tunneling allows for simultaneous exploration of multiple potentially optimal configurations, and ultimately enables finding the true unique optimum. This project is aimed to investigate theoretical limits for efficiency of these quantum algorithms. Practical demonstration schemes will be conceptualized and possibly implemented on existing prototypical quantum devices. NSF funds will provide training for a graduate student research assistant and (partially) a postdoctoral fellow. Both will be trained in the theoretical apparatus underlying construction of algorithms for quantum computation. The results of the project will be incorporated in graduate classes at the University of Minnesota as well as at regular summer schools, which the PI co-organizes through the Fine Theoretical Physics Institute. Part of the project will be conducted in close cooperation with Prof. Yuval Gefen of the Weizmann Institute, who will be funded separately by BSF. The BSF part will provide training for another postdoctoral fellow. Technical Summary This award is made on an EAGER proposal invited through the Quantum Algorithm Challenge Dear Colleague Letter. It supports research and education to study new concepts for how quantum mechanical states can be prepared and manipulated to perform computation which includes protocols or algorithms required to use a quantum computer to solve a problem. The PI will consider quantum approximate optimization algorithms (QAOA) and quantum image recognition schemes. Both are based on the idea of an information processing engine, which repeatedly performs a particular cycle. The cycle involves coupling and decoupling of the active quantum system, which can be modeled by a Sherrington-Kirkpatrick spin glass encoded with a desired optimization problem, with the information bath. A qubit realization of the Sachdev-Ye-Kitaev (SYK) model will be explored as a model for the information bath. The SYK system, being a holographic dual of a black hole, possesses a finite entropy down to the exponentially small temperature. This allows quantum tunneling among multiple local minima of the spin glass. The quantum measurement operation, performed in the end of each cycle, provides a progressively improving set of candidate optimal spin configurations. A goal of the project is to evaluate the probability of finding the true optimum within such a set. Another goal is to optimize the cycle to determine theoretical bounds for efficiency of the information engine. The NSF-BSF part of the project will deal with a theoretical description in terms of the reduced density matrix of the working substance. We expect to find a Lindblad-like evolution equation. It will allow for an efficient analysis of computation schemes using existing powerful field-theoretical and computational techniques.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.