A Theory Relating Quantum and Stochastic Networked Systems

We developed a mathematical theory pinpointing the similarities and differences among stochastic and quantum complex and network systems, resulting in a large project summarized in a research book [Quantum Techniques for Stochastic Mechanics by John C. Baez, Jacob Biamonte arXiv:1209.3632 (2016)]. The results included Petri nets, chemical reaction networks, electrical networks and their corresponding quantum generalizations.

Universal Adiabatic Quantum Computing

Developed results considered foundational to the field of adiabatic quantum computing. Including the well regarded proof that the tunable sparse two-body model has a QMA-complete (quantum analogy of the complexity class, randomized NP) ground state energy problem [Phys. Rev. A 78, 012352 (2008)] – establishing the contemporary experimental target.

A Quantum Generalization of Community Detection

Determining community structure is a central topic in the study of complex and networked systems. We extended the concept of community detection from classical to quantum systems—a crucial missing component of a theory of complex networks based on quantum mechanics [Physical Review X 4, 041012 (2014)].

Tensor Network States and Graphical Reasoning

We connected the formal graphical language and techniques from category theory with the tensor network states and algorithms found in modern quantum theory – coined ‘categorical tensor network states’ [AIP Advances 1, 042172 (2011)]. We built on this to merge tensor networks with invariant theory and employed this tool to understand the space of states expressible by tensor network families [J. Phys A: Math. Theo. 46, 475301 (20

Explaining Quantum vs. Stochastic Walks on Complex Networks

We developed the first analytical results explaining quantum evolutions on complex networks which recovers the classical result as a limit [Phys. Rev. X 3, 041007 (2013)].

Controlling Quantum Transport on Complex Networks

We introduced chiral quantum walks as a means to control quantum evolutions on complex graphs/networks by controlling time-reversal symmetry breaking and characterized the subtle interplay of this effect with the global topological structure of the underlying network [Scientific Reports 3, 2361 (2013); Physical Review A 93, 042302 (2016)].

Quantum Simulation of Molecular Energies

We developed quantum computing algorithms to simulate molecular energies [Nature Chemistry 2, 106 (2009); Molecular Physics 109, 735 (2011)]. Such quantum algorithms purport to require the fewest quantum resources to surpass classical computers.