Quantum Theory from Principles, Quantum Software from Diagrams

Inclusion-Exclusion Principle for Open Quantum Systems with Bosonic Bath

We present two fast algorithms which apply inclusion-exclusion principle to sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo (dQMC) and inchworm Monte Carlo method, respectively. In the case of inchworm Monte Carlo, the proposed fast algorithm gives an extension to the work ["Inclusion-exclusion principle for many-body diagrammatics", Phys. Rev. B, 98:115152, 2018] from fermionic to bosonic systems. We prove that the proposed fast algorithms reduce the computational complexity from double factorial to exponential. Numerical experiments are carried out to verify the theore…

Inclusion-Exclusion Principle for Many-Body Diagrammatics

Recent successes in Monte Carlo methods for simulating fermionic quantum impurity models have been based on diagrammatic resummation techniques, but are restricted by the need to sum over factorially large classes of diagrams individually. We present a fast algorithm for summing over the diagrams appearing in Inchworm hybridization expansions. The method relies on the inclusion-exclusion principle to reduce the scaling from factorial to exponential. We analyze the growth rate and compare with related algorithms for expansions in the many-body interaction. An implementation demonstrates that fo…

Software science view on quantum circuit algorithms

We show that, on the abstraction level of quantum circuit diagrams, quantum circuit algorithms belong to the species of interactive sequential algorithms that we studied in earlier work. This observation leads to a natural specification language for quantum circuit algorithms.

Rewriting Context-free Families of String Diagrams

String diagrams provide a convenient graphical framework which may be used for equational reasoning about morphisms of monoidal categories. However, unlike term rewriting, rewriting string diagrams results in shorter equational proofs, because the string diagrammatic representation allows us to formally establish equalities modulo any rewrite steps which follow from the monoidal structure. Manipulating string diagrams by hand is a time-consuming and error-prone process, especially for large string diagrams. This can be ameliorated by using software proof assistants, such as Quantomatic. Howeve…

添加或移除杨图方框的信道的最小输出熵，以及每个置换对称性的泡利原理

Minimal output entropy for the channels that add or remove a box of a Young diagram, and a Pauli principle for every permutation symmetry

研究杨图相差一个方框的四个协变量子信道，证明相干态最小化输出熵并给出显式结果，应用于置换对称粒子的单粒子谱界，推广了泡利原理。