Quantum Enhanced Algorithms

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 in Stochastic Mechanics by John C. Baez, Jacob Biamonte, World Scientific Publishing, 276 pages (2018)]. The results included Petri nets, chemical reaction networks, electrical networks and their corresponding quantum generalizations.

Universal Adiabatic Quantum Computing

In 2007 we proved that a tunable 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

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

Tensor Network States and Quantum Algorithms

We developed ‘categorical tensor network states’ [AIP Advances 1, 042172 (2011)] and 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 (2011)].

Explaining Quantum vs. Stochastic Walks on Scale-Free Networks

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

Chiral Quantum Walks

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.

Quantum Machine Learning

The field of quantum machine learning explores how to devise and implement quantum software that could enable machine learning that is faster than that of classical computers. Read more:   Biamonte et. al, Nature 549, 195-202 (2017)