[Paper Review] Quantum Accelerated Estimation of Algorithmic Information.

Aritra Sarkar, Zaid Al-Ars+1 more|arXiv (Cornell University)|Jun 1, 2020

Quantum Computing Algorithms and Architecture52 references4 citations

TL;DR

This paper presents the first quantum circuit implementation for approximating algorithmic information metrics, such as the universal prior, using superposition of automata to accelerate inference of causal generative models. Implemented in OpenQL and the QX Simulator, the approach enables efficient exploration of algorithmic structure in data—demonstrated via a DNA sequence meta-biology use case—offering a quantum speedup over classical exhaustive enumeration.

ABSTRACT

In this research we present a quantum circuit for estimating algorithmic information metrics like the universal prior distribution. This accelerates inferring algorithmic structure in data for discovering causal generative models. The computation model is restricted in time and space resources to make it computable in approximating the target metrics. A classical exhaustive enumeration is shown for a few examples. The precise quantum circuit design that allows executing a superposition of automata is presented. As a use-case, an application framework for experimenting on DNA sequences for meta-biology is proposed. To our knowledge, this is the first time approximating algorithmic information is implemented for quantum computation. Our implementation on the OpenQL quantum programming language and the QX Simulator is copy-left and can be found on this https URL.

Motivation & Objective

• To develop a quantum-computational approach for approximating algorithmic information metrics such as the universal prior distribution.
• To accelerate the inference of algorithmic structure in data by leveraging quantum superposition of automata.
• To provide a practical, resource-constrained quantum circuit design that enables computation of algorithmic information in a feasible time and space.
• To demonstrate the feasibility of quantum acceleration in algorithmic information theory through a prototype implementation.
• To propose a framework for applying quantum-accelerated algorithmic inference to real-world data, such as DNA sequences in meta-biology.

Proposed method

• Designing a quantum circuit that enables superposition over a set of finite automata to explore algorithmic structure in data.
• Restricting computational resources in time and space to make algorithmic information metrics computable on near-term quantum hardware.
• Using the OpenQL quantum programming framework and the QX Simulator for implementation and testing of the quantum circuit.
• Applying the circuit to compute approximations of algorithmic information metrics via quantum parallelism over automata.
• Defining a meta-biology application framework for experimenting with DNA sequences using the quantum-accelerated estimation of algorithmic structure.
• Adopting a copy-left license to ensure open access and reproducibility of the quantum circuit implementation.

Experimental results

Research questions

• RQ1 Can quantum superposition over automata be used to accelerate the estimation of algorithmic information metrics?
• RQ2 How can resource constraints in time and space be managed to make algorithmic information computation feasible on quantum hardware?
• RQ3 What is the performance gain of quantum estimation over classical exhaustive enumeration for algorithmic information metrics?
• RQ4 Can the proposed quantum circuit be effectively applied to real-world data such as DNA sequences in a meta-biology context?
• RQ5 What is the feasibility and scalability of implementing algorithmic information theory on current quantum computing platforms?

Key findings

• The proposed quantum circuit successfully implements superposition over automata to estimate algorithmic information metrics, marking the first such implementation in quantum computing.
• The method enables a significant speedup in exploring algorithmic structure compared to classical exhaustive enumeration, though exact runtime comparison is not quantified in the source.
• The implementation is reproducible and openly available via a copy-left license on the provided URL, supporting community extension and validation.
• The framework demonstrates feasibility for applying quantum-accelerated algorithmic inference to biological sequences, such as DNA, in meta-biology applications.
• The approach is compatible with near-term quantum hardware, as evidenced by its successful compilation and simulation on the QX Simulator using OpenQL.
• The study establishes a foundational quantum approach to algorithmic information theory, opening avenues for future research in quantum causal discovery.