The State of Quantum Computing 2025: Foundations, Advanced Materials, and the Road to Scalable Quantum Technologies

Published by Marcos Elias on

Abstract

This whitepaper presents a comprehensive overview of the current state of quantum computing, integrating foundational theory, hardware architectures, advanced materials, and emerging pathways toward scalable quantum technologies.

It begins by establishing the fundamental principles of quantum information, including qubits, superposition, entanglement, and quantum interference, contrasting them with classical computational paradigms. The document then explores the exponential scaling of multi-qubit systems, quantum gates, and algorithmic frameworks such as Shor’s and Grover’s algorithms, alongside key complexity classes including BQP.

Beyond theoretical foundations, the work examines the physical realization of quantum systems across multiple architectures — including superconducting circuits, photonic systems, trapped ions, and topological platforms — as well as the critical role of quantum error correction in enabling reliable computation at scale.

A central contribution of the document lies in its exploration of advanced quantum materials, particularly magic-angle graphene and topological systems, highlighting how quantum geometry, flat-band superconductivity, and strongly correlated states are reshaping the design of next-generation quantum devices.

The whitepaper also addresses recent industry milestones and global developments, outlining the convergence of research, engineering, and investment that is driving the transition from experimental systems toward practical quantum advantage. It concludes by identifying key challenges and future directions, including modular architectures, quantum interconnects, and hybrid quantum-classical systems.

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Marcos Elias

I am the founder of the Rāmānujan Institute for the Development of Prodigious Young Mathematicians, which aims to foster the education and growth of children and young people aged 2 to 16 who demonstrate exceptional mathematical abilities. Our institute is dedicated to providing an advanced and challenging curriculum that not only prepares students for prestigious competitions, such as the International Mathematical Olympiad (IMO), but also supports their overall development. We focus on nurturing mathematical talent while ensuring that our students develop the skills necessary for success in academic and professional environments. Through mentorship programs and a commitment to inclusivity, we strive to create a community where young mathematicians can thrive and make significant contributions to the field. I am also Marcos Eduardo Elias, an engineer and mathematician. My academic journey began with a Bachelor’s degree in Mechatronic Engineering from the Polytechnic School of the University of São Paulo (USP). My education culminated in a Doctorate in Mathematics from St. Petersburg State University, specializing in Real, Complex, and Functional Analysis. I have held teaching positions at institutions such as Ibmec, Insper, and FGV-SP. I am also a member of the Brazilian Mathematical Society. In the financial sector, I founded several institutions, including GAS Investimentos (later Vinci Partners), Empiricus Research, Turing High Frequency Trading, Modena Capital and Guiar Investments. In the financial markets, I am known as the Volatility Hunter, and - in the last 30 years, I have been relentlessly searching for highly asymmetric upside risk (I am on the right side of the barbell). I have been contributing to the MIT Sloan Management Review, primarily on topics related to risk management. My current research interests include real, complex, and functional analysis, linear algebra for quantum algorithmics, Feigenbaum-Coullet-Tresser universality, stochastic calculus, and Grothendieck's Standard Conjectures on Algebraic Cycles.

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