Results obtained in the first reporting period advance our understanding of the potential of near- and intermediate-term quantum devices. Contributions encompass theoretical characterizations of their computational power, their resilience to noise and design imperfections, and an improved quantification of the difficulty of simulating, i.e. emulating their behavior by classical means. Advances with more direct practical relevance include novel protocols for fault-tolerantly generating long-range entanglement, the introduction of efficient decoders for quantum low-density parity check codes, new resource-efficient fault-tolerance constructions incorporating locality considerations, and novel methods for device characterization and validation derived from recent developments in quantum learning.
In the area of quantum complexity theory, a main finding is a new unconditional separation between similarly defined classical- and quantum circuit classes: It was shown that 3D-local, noisy constant-depth are computationally superior to constant-depth classical circuits with unbounded fan-in AND, OR and NOT gates. The corresponding quantum advantage proposal sheds new light on quantum gate teleportation, showing that this basic primitive has significant complexity-theoretic relevance.
New algorithms developed so far include hybrid (classical-quantum) algorithms for combinatorial optimization with improved guarantees on approximation ratios. These are obtained by combining a greedy algorithm with quantum approximate optimization. Furthermore, classical algorithms were developed to enable simulation of non-Gaussian dynamics. This extends the toolbox for studying many-body dynamics, providing new numerical methods to evaluate quantum computing proposals.
