Related papers: Certified Quantum Computation in Isabelle/HOL
This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization…
The precise control of complex quantum systems promises numerous technological applications including digital quantum computing. The complexity of such devices renders the certification of their correct functioning a challenge. To address…
Large language models (LLM), such as Google's Minerva and OpenAI's GPT families, are becoming increasingly capable of solving mathematical quantitative reasoning problems. However, they still make unjustified logical and computational…
We provide simple equational principles for deriving rely-guarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution…
The Variational Quantum Eigensolver (VQE) is a promising quantum algorithm for applications in chemistry within the Noisy Intermediate-Scale Quantum (NISQ) era. The ability for a quantum computer to simulate electronic structures with high…
This whitepaper surveys the current landscape and short- to mid-term prospects for quantum-enabled optimization and machine learning use cases in industrial settings. Grounded in the QCHALLenge program, it synthesizes hardware trajectories…
In this paper we present an efficient approach to implementing model checking in the Higher Order Logic (HOL) of Isabelle. This is a non-trivial task since model checking is restricted to finite state sets. By restricting our scope to…
The holographic principle and its realization in the AdS/CFT correspondence led to unexpected connections between general relativity and quantum information. This set the stage for studying aspects of quantum gravity models, which are…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
We demonstrate the feasibility of quantum computing for large-scale, realistic chemical systems through the development of a new interface using a quantum circuit simulator and CP2K, a highly efficient first-principles calculation software.…
A protocol-independent secrecy theorem is established and applied to several non-trivial protocols. In particular, it is applied to protocols proposed for protecting the computation results of free-roaming mobile agents doing comparison…
In this paper, the application of quantum computing (QC) in solving gate insulator Poisson equation is studied, through QC simulator and hardware in IBM. Various gate insulator stacks with and without fixed charges are studied. It is found…
Fault-tolerant quantum computations require alternating quantum and classical computations, where the classical computations prove vital in detecting and correcting errors in the quantum computation. Recently, interest in using these…
This paper describes a formal theory of smooth vector fields, Lie groups and the Lie algebra of a Lie group in the theorem prover Isabelle. Lie groups are abstract structures that are composable, invertible and differentiable. They are…
Simulating quantum dynamics is expected to be performed more easily on a quantum computer than on a classical computer. However, the currently available quantum devices lack the capability to implement fault-tolerant quantum algorithms for…
We present Monte Carlo wavefunction simulations for quantum computations employing an exchange-coupled array of quantum dots. Employing a combination of experimentally and theoretically available parameters, we find that gate fidelities…
We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being non-universal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses.…
Oracle quantum programs are a fundamental class of quantum programs that serve as a critical bridge between quantum computing and classical computing. Many important quantum algorithms are built upon oracle quantum programs, making it…
Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed.…
We formalise the pi-calculus using the nominal datatype package, based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics…