北京雁栖湖应用数学研究院

刘正伟

雅各布·比亚蒙特

2021年10月22日 09:30 至 12:15

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

物理学家和计算机科学家，2010年从英国牛津大学博士毕业，之后同时在哈佛大学、牛津大学/新加坡国立大学联合项目任博士后。2012年加入意大利都灵ISI研究所并领导量子科学组。2017年起加入莫斯科Skoltech研究院，从2019年开始担任该机构量子信息实验室主任。长期致力于量子计算机科学和现代量子理论的研究，因奠定了量子机器学习的理论基础而闻名，并贡献了多个普适性证明。此外他在量子张量网络的数学理论发表了多项成果，提供了用图形化的语言重新理解量子物理中的过程的新观念。曾荣获郎格特希金斯奖等多个国际奖项。