Related papers: How to Compile Some NAND Formula Evaluators
In order to assess potential advantages of quantum algorithms that require quantum oracles as subroutines, the careful evaluation of the overall complexity of the oracles themselves is crucial. This study examines the quantum routines…
Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part…
The negative-AND (NAND) gate is universal for classical computation making it an important target for development. A seminal quantum computing algorithm by Farhi, Goldstone and Gutmann has demonstrated its realization by means of quantum…
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…
In the context of knowledge compilation (KC), we study the effect of augmenting Ordered Binary Decision Diagrams (OBDD) with two kinds of decomposition nodes, i.e., AND-vertices and OR-vertices which denote conjunctive and disjunctive…
We present a new algorithm for reducing an arbitrary unitary matrix into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of…
The construction of quantum circuits to simulate Hamiltonian evolution is central to many quantum algorithms. State-of-the-art circuits are based on oracles whose implementation is often omitted, and the complexity of the algorithm is…
We describe a decomposition of the Lie group of unitary evolutions for a bipartite quantum system of arbitrary dimensions. The decomposition is based on a recursive procedure which systematically uses the Cartan classification of the…
Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been…
We propose a general and efficient framework to control auto-regressive generation models with NeurAlly-Decomposed Oracle (NADO). Given a pre-trained base language model and a sequence-level boolean oracle function, we propose to decompose…
In quantum computing, the efficient optimization of Pauli string decompositions is a crucial aspect for the compilation of quantum circuits for many applications, such as chemistry simulations and quantum machine learning. In this paper, we…
We study the problem of enumerating the satisfying valuations of a circuit while bounding the delay, i.e., the time needed to compute each successive valuation. We focus on the class of structured d-DNNF circuits originally introduced in…
A critical step in developing circuits for quantum simulation is to synthesize a desired unitary operator using the circuit building blocks. Studying unitaries and their generators from the Lie algebraic perspective has given rise to…
A quantum compiler is a software program for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). Coppersmith showed that the $\nb$-bit Discrete Fourier Transform matrix $U_{FT}$ can be…
Satisfiability Testing (SAT) techniques are well-established in classical computing where they are used to solve a broad variety of problems, e.g., in the design of classical circuits and systems. Analogous to the classical realm, quantum…
Quadratic unconstrained binary optimization (QUBO) can be seen as a generic language for optimization problems. QUBOs attract particular attention since they can be solved with quantum hardware, like quantum annealers or quantum gate…
We propose an accurate algorithm for a novel sum-of-exponentials (SOE) approximation of kernel functions, and develop a fast algorithm for convolution quadrature based on the SOE, which allows an order $N$ calculation for $N$ time steps of…
This thesis details a project to define a fully compositional theory of synchronous sequential circuits built from primitive components, motivated by applying techniques successfully used in programming languages to hardware. The first part…
Unitary operation is an essential step for quantum information processing. We first propose an iterative procedure for decomposing a general unitary operation without resorting to controlled-NOT gate and single-qubit rotation library. Based…
Digital circuits, despite having been studied for nearly a century and used at scale for about half that time, have until recently evaded a fully compositional theoretical in which arbitrary circuits may be freely composed together without…