During the first reporting period, the FoQaCiA consortium published a total of 43 papers and preprints featuring work on all four scientific work packages. The primary focus is on theory, but there were also some experimental tests of the ideas developed by the project, using integrated photonic chips and ion traps. On a more applied side, the FoQaCiA project released 7 open software packages with code to reproduce some published results and to enable further work on these topics by the wider community.
WP1 investigates the interplay between nonclassicality criteria and causality in pinpointing the source of quantum advantage in different tasks. On this topic, the project published numerous studies. We have proved fundamental results on nonlocality and contextuality, developed unified theoretical frameworks for causality and contextuality and took the first steps in applying them to analyse quantum advantage in various computational setpus. We also implemented new experimental tests of coherence, dimension, and contextuality, and we published a paper on a practical measurement-based scheme for hybrid quantum/classical computation using d-level systems instead of qubits.
WP2 focuses on new techniques for classical simulation of quantum computation. We have explored emerging features of classical simulation using extensions of the stabilizer formalism, in particular the so-called Λ polytopes, which can represent positively a wider range of states and dynamics than usual stabilizer subtheory. We also published two open source software packages embodying newly derived stabilizer techniques for simulation of qubits and qudits, one other piece of software for optimising sum-over-Clifford decompositions to improve stabiliser-rank or stabiliser-extent simulations, and two further software packages developing related ideas for cryptographic applications.
WP3 studies some discrete structures arising in quantum circuits and error correction, in particular quantum measurements known as symmetric informationally-complete (SIC) POVMs, and techniques for obtaining exact circuit synthesis for operations on d-level quantum systems (qudits). In this first reporting period, we have developed and released code to work with general Clifford and Heisenberg groups of unitaries, and tackled the problem of qutrit circuit synthesis, with ongoing work on qudit circuit synthesis for d>3, and improving some already obtained results on SIC-POVMs for certain dimensions.
In WP4 we work with optimization of techniques useful for fault-tolerance of future, larger-scale quantum computers, which often rely on a technique known as magic state injection and distillation. We have characterized certain qutrit gates which admit a magic state injection circuit of half the usual size, and are currently developing work capable of delivering the same advantage for qudits. We have done some preliminary work devising topological rules for manipulating entangled resource states for quantum computation in the form of 3D graph states, which in the future will enable us to explore this computationally. We are also unveiling connections between the foundational notion of contextuality and both 3D cluster states and the resource theory magic states.
