Presents the approaches to building a quantum computer, the different substrates being used to build a scalable quantum computer, the profound challenges in doing so, and finally, an outlook on how the scientific challenges and economic incentives will shape quantum computing projects.
We are on the verge of a new era in computation, one that operates on the strange and wonderful rules of the quantum world. This article explores the story of quantum computing, a technology that promises to solve problems far beyond the reach of today's fastest supercomputers. We'll journey from the core ideas that make it all possible—concepts like superposition and entanglement—to the incredible machines being built in labs around the world. We'll see how these machines are being programmed and witness the first hints of their power in fields like medicine, materials science, and cybersecurity. Finally, we'll take an honest look at the immense challenges that still lie ahead on the path to building a truly powerful quantum computer. This is a story of human ingenuity pushing the boundaries of science, a tale of the immense potential and practical hurdles of the coming quantum age.
This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for understanding how noise and intrinsic randomness shape quantum computational outcomes in the language of mathematics. By grounding quantum computation in statistical inference, we highlight how mathematical tools such as probabilistic modeling, stochastic analysis, Bayesian inference, and sensitivity analysis, can directly address error propagation and reliability challenges in today's quantum devices. We also connect these methods to key scientific priorities in the field, including scalable uncertainty-aware algorithms and characterization of correlated errors. The purpose is to narrow the conceptual divide between applied mathematics, scientific computing and quantum information sciences, demonstrating how mathematically rooted UQ methodologies can guide validation, error mitigation, and principled algorithm design for emerging quantum technologies, in order to address challenges and opportunities present in modern-day quantum high performance and fault-tolerant quantum computing paradigms.
A quantum machine may solve some complex problems that are intractable for even the most powerful classical computers. By exploiting quantum superposition and entanglement phenomena, quantum algorithms can achieve from polynomial to exponential speed up when compared to their best classical counterparts. A quantum computer will be a part of a heterogeneous, multi-core computer in which a classical processor will interact with several accelerators such as FPGAs, GPUs and also a quantum co-processor. Figure 1 shows the different layers of the quantum computer system stack [1]. Building such a quantum system requires contributions from different fields such as physics, electronics, computer science and computer engineering for addressing the following challenges: i) build scalable quantum chips integrating qubits with long coherence times and high-fidelity operations, ii) develop classical control electronics at possibly cryogenic temperatures and iii) create the microarchitecture as well as the software for quantum computation.
Quantum computing technologies have become a hot topic in academia and industry receiving much attention and financial support from all sides. Building a quantum computer that can be used practically is in itself an outstanding challenge that has become the ‘new race to the moon’. Next to researchers and vendors of future computing technologies, national authorities are showing strong interest in maturing this technology due to its known potential to break many of today’s encryption techniques, which would have significant and potentially disruptive impact on our society. It is, however, quite likely that quantum computing has beneficial impact on many computational disciplines. In this article we describe our vision of future developments in scientific computing that would be enabled by the advent of software-programmable quantum computers. We thereby assume that quantum computers will form part of a hybrid accelerated computing platform like GPUs and co-processor cards do today. In particular, we address the potential of quantum algorithms to bring major breakthroughs in applied mathematics and its applications. Finally, we give several examples that demonstrate the possible impact of quantum-accelerated scientific computing on society.