Related papers: Formally verified 32- and 64-bit integer division …
As basic elements of the quantum computer - quantum bits (qubits) we offer semiconductor quantum dots containing one electron each and consisting each of two tunnel-connected parts. The numerical solution of a Schroedinger equation with the…
We propose a new library to model and verify hardware circuits in the Coq proof assistant. This library allows one to easily build circuits by following the usual pen-and-paper diagrams. We define a deep-embedding: we use a (dependently…
Cody & Waite argument reduction technique works perfectly for reasonably large arguments but as the input grows there are no bit left to approximate the constant with enough accuracy. Under mild assumptions, we show that the result computed…
Quantum algorithms to solve practical problems in quantum chemistry, materials science, and matrix inversion often involve a significant amount of arithmetic operations which act on a superposition of inputs. These have to be compiled to a…
With disks and networks providing gigabytes per second, parsing decimal numbers from strings becomes a bottleneck. We consider the problem of parsing decimal numbers to the nearest binary floating-point value. The general problem requires…
The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…
As quantum computing moves toward fault-tolerant architectures, quantum error correction (QEC) decoder performance is increasingly critical for scalability. Understanding the impact of transitioning from floating-point software to…
Compilation optimizes quantum algorithms performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers,…
Most software domains rely on compilers to translate high-level code to multiple different machine languages, with performance not too much worse than what developers would have the patience to write directly in assembly language. However,…
In this paper, the authors propose the idea of a combined integer and floating point multiplier(CIFM) for FPGAs. The authors propose the replacement of existing 18x18 dedicated multipliers in FPGAs with dedicated 24x24 multipliers designed…
Formal proof checkers such as Coq are capable of validating proofs of correction of algorithms for finite field arithmetics but they require extensive training from potential users. The delayed solution of a triangular system over a finite…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
With qubit measurement and control fidelities above the threshold of fault-tolerance, much attention is moving towards the daunting task of scaling up the number of physical qubits to the large numbers needed for fault tolerant quantum…
I present two new methods for exactly summing a set of floating-point numbers, and then correctly rounding to the nearest floating-point number. Higher accuracy than simple summation (rounding after each addition) is important in many…
As quantum devices continue to scale, distributed quantum computing emerges as a promising strategy for executing large-scale tasks across modular quantum processors. A central challenge in this paradigm is verifying the correctness of…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
A scalable and programmable quantum computer holds the potential to solve computationally intensive tasks that classical computers cannot accomplish within a reasonable time frame, achieving quantum advantage. However, the vulnerability of…
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…
Various physical constraints limit the number of qubits that can be implemented in a single quantum processor, and thus it is necessary to connect multiple quantum processors via quantum interconnects. While several compiler implementations…
We present a novel right-to-left long division algorithm based on the Montgomery modular multiply, consisting of separate highly efficient loops with simply carry structure for computing first the remainder (x mod q) and then the quotient…