Beijing Institute of Mathematical Sciences and Applications

Zheng Wei Liu

Jacob Biamonte

Friday, October 22, 2021 9:30 AM - 12:15 PM

JCY-1

Tencent 953 7541 0477 (2024)

We present a mathematical apparatus to create (program) Hamiltonian ground states relevant for variational quantum computation.  Given a set of vectors, can one deduce an effective non-negative k-body Hamiltonian with a kernel spanning this set?  This can be called the 'parent Hamiltonian’ or ‘quantum kernel problem' and is a core element of the presented theory.  As a interesting example, propositional logic operations can be embedded into the low-energy sector of Ising spins whereas three (and higher) body Ising interaction terms can be mimicked through the minimisation of 2- and 1-body Ising terms with the introduction of strongly coupled slack spins.  Determining the minimal number of required slack spins for a given spanning set of bit vectors remains open as do several other related problems.  To solve the quantum kernel problem more generally, perturbation theory gadgets enable the emulation of interactions not present in a given quantum spin Hamiltonian, e.g. YY interactions can be realized from ZZ, XX.  Such ideas enabled the quantum kernel problem to be solved for the Feynman-Kitaev history state which then enabled proofs that two-body model Hamiltonian's have a QMA-complete ground state energy decision problem.  In variational quantum computation, the expected value of a Hamiltonian is calculated on a quantum co-processor by evaluating a sum of expected values term wise.  The expected value is minimised using classical outer loop optimisation.  We elevate the variational approach to a formal model of quantum computation and prove its universality.  In this setting, we also explain several recent findings related to Hamiltonian minimisation by short quantum circuits, including problem density induced underparameterisation (reachability deficits), analytical results showing that parameters approach limiting values independent of the problem size as well as some

Dr. Biamonte's research career has been dedicated to studying the theoretical aspects of quantum information processing, specifically at the interface between quantum applications and physical hardware constraints. He has held positions as a quantum applications developer at D-Wave Systems Inc. in Vancouver, Canada, and as a Fellow at Harvard University in the Aspuru-Guzik Group. In 2010, Dr. Biamonte obtained his PhD from the University of Oxford. He then worked as a postdoctoral researcher with John Carlos Baez as part of a joint Oxford/Singapore program and as a Lecturer at St Peter's College Oxford before joining the Institute for Scientific Interchange (ISI Foundation) in Torino, Italy as their Quantum Science Group Leader from 2012-2017. In 2017, Dr. Biamonte joined the Skolkovo Institute of Science and Technology as a Tenure Track Associate Professor. He was subsequently promoted to Head of the Laboratory for Quantum Information Processing and then to tenured Full Professor. Dr. Biamonte was the first American-born scientist to have successfully defended a higher Doctorate at the Moscow Institute of Physics and Technology. Unfortunately, his time in Moscow was cut short due to the war against Ukraine. Dr. Biamonte currently holds the Jingdong Foundation Chair at the Yanqi Lake Beijing Institute of Mathematical Sciences and Applications. Dr. Biamonte's research vision is to develop a data-driven approach to quantify emergent and collective effects in quantum information processing. He is also a dedicated educator, teaching applied and engineering mathematics, quantum information theory, and quantum computation.