Related papers: On QBF Proofs and Preprocessing
We present qlbm, a Python software package designed to facilitate the development, simulation, and analysis of Quantum Lattice Boltzmann Methods (QBMs). qlbm is a modular framework that introduces a quantum component abstraction hierarchy…
A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al.,…
The analysis of formal models that include quantitative aspects such as timing or probabilistic choices is performed by quantitative verification tools. Broad and mature tool support is available for computing basic properties such as…
Quantum error correction (QEC) is fundamental for suppressing noise in quantum hardware and enabling fault-tolerant quantum computation. In this paper, we propose an efficient verification framework for QEC programs. We define an assertion…
Predictive coding, once used in only a small fraction of legal and business matters, is now widely deployed to quickly cull through increasingly vast amounts of data and reduce the need for costly and inefficient human document review.…
Training Neural Networks (NNs) to serve as Barrier Functions (BFs) is a popular way to improve the safety of autonomous dynamical systems. Despite significant practical success, these methods are not generally guaranteed to produce true BFs…
In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…
Computational security in cryptography has a risk that computational assumptions underlying the security are broken in the future. One solution is to construct information-theoretically-secure protocols, but many cryptographic primitives…
Quantum computing is fast evolving as a technology due to recent advances in hardware, software, as well as the development of promising applications. To use this technology for solving specific problems, a suitable quantum algorithm has to…
We show that interactive protocols between a prover and a verifier, a well-known tool of complexity theory, can be used in practice to certify the correctness of automated reasoning tools. Theoretically, interactive protocols exist for all…
Verifying the correctness of Bayesian computation is challenging. This is especially true for complex models that are common in practice, as these require sophisticated model implementations and algorithms. In this paper we introduce…
We consider numerical certification of approximate solutions to a system of polynomial equations with more equations than unknowns by first certifying solutions to a square subsystem. We give several approaches that certifiably select which…
The Coq Platform is a continuously developed distribution of the Coq proof assistant together with commonly used libraries, plugins, and external tools useful in Coq-based formal verification projects. The Coq Platform enables reproducing…
Quantum signal processing (QSP) provides a representation of scalar polynomials of degree $d$ as products of matrices in $\mathrm{SU}(2)$, parameterized by $(d+1)$ real numbers known as phase factors. QSP is the mathematical foundation of…
Numerically solving partial differential equations is a ubiquitous computational task with broad applications in many fields of science. Quantum computers can potentially provide high-degree polynomial speed-ups for solving PDEs, however…
With experimental quantum computing technologies now in their infancy, the search for efficient means of testing the correctness of these quantum computations is becoming more pressing. An approach to the verification of quantum computation…
In this paper we consider quantum interactive proof systems, i.e., interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. It is proved that every language in PSPACE has a…
The quantum Fourier transform (QFT) has emerged as the primary tool in quantum algorithms which achieve exponential advantage over classical computation and lies at the heart of the solution to the abelian hidden subgroup problem, of which…
Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…
Safety is a critical property for control systems in medicine, transportation, manufacturing, and other applications, and can be defined as ensuring positive invariance of a predefined safe set. This paper investigates the problems of…