Related papers: Picturing Counting Reductions with the ZH-Calculus
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
Loop quantum gravity (LQG) attempts to unify general relativity with quantum physics to offer a complete description of the universe by quantising spacetime geometry, but the numerical calculations we encounter are extraordinarily…
Let $X$ be a smooth projective hypersurface over a finite field $k$ of characteristic $p$. We address the problem of practically computing the zeta function $Z(X,T)$ of $X$ (equivalently, the point counts $\#X(\mathbb{F}_q)$, where $q =…
In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.
Diagrammatic representations of quantum algorithms and circuits offer novel approaches to their design and analysis. In this work, we describe extensions of the ZX-calculus especially suitable for parameterized quantum circuits, in…
Path sums are a convenient symbolic formalism for quantum operations with applications to the simulation, optimization, and verification of quantum protocols. Unlike quantum circuits, path sums are not limited to unitary operations, but can…
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…
ZW-calculus is a useful graphical language for pure qubit quantum computing. It is via the translation of the completeness of ZW-calculus that the first proof of completeness of ZX-calculus was obtained. A d-level generalisation of qubit…
ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain…
Towards better understanding of gate elimination, the only method known that can prove complexity lower bounds for explicit functions against unrestricted Boolean circuits, this work contributes: (1) formalizing circuit simplifications as a…
PolySAT is a word-level decision procedure supporting bit-precise SMT reasoning over polynomial arithmetic with large bit-vector operations. The PolySAT calculus extends conflict-driven clause learning modulo theories with two key…
In order for quantum computations to be done as efficiently as possible it is important to optimise the number of gates used in the underlying quantum circuits. In this paper we find that many gate optimisation problems for approximately…
The poset cover problem seeks a minimum set of partial orders whose linear extensions cover a given set of linear orders. Recognizing its NP-completeness, we devised a non-trivial reduction to the Boolean satisfiability problem using a…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
We study the fine-grained complexity of evaluating Boolean Conjunctive Queries and their generalization to sum-of-product problems over an arbitrary semiring. For these problems, we present a general semiring-oblivious reduction from the…
In this work, we develop a graphical calculus for multi-qudit computations with generalized Clifford algebras, building off the algebraic framework developed in our prior work. We build our graphical calculus out of a fixed set of graphical…
While the circuit model of quantum computation defines its logical depth or "computational time" in terms of temporal gate sequences, the measurement-based model could allow totally different temporal ordering and parallelization of logical…
We present fully polynomial-time (deterministic or randomised) approximation schemes for Holant problems, defined by a non-negative constraint function satisfying a generalised second order recurrence modulo a couple of exceptional cases.…
We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is…
Quantum computing is an emerging computational paradigm with the potential to outperform classical computers in solving a variety of problems. To achieve this, quantum programs are typically represented as quantum circuits, which must be…