many years, the fields of quantum mechanics and computer science formed distinct academic communities. Modern quantum theory developed in the 1920s to explain the waveparticle duality observed at atomic scales, and digital computers emerged in the following decades to replace human computers for tedious calculations. Both disciplines had practical applications during World War II; computers played a major role in wartime cryptography, and quantum physics was essential for the nuclear physics used in the Manhattan Project. As physicists applied quantum mechanical models to computational problems and swapped digital bits for qubits, the fields of quantum mechanics and computer science began to converge. In 1980, Paul Benioff introduced the quantum Turing machine, which uses quantum theory to describe a simplified computer. When digital computers became faster, physicists faced an exponential increase in overhead when simulating quantum dynamics, prompting Yuri Manin and Richard Feynman to independently suggest that hardware based on quantum phenomena might be more efficient for computer simulation. In a 1984 paper, Charles Bennett and Gilles Brassard applied quantum theory to cryptography protocols and demonstrated that quantum key distribution could enhance information security. Quantum algorithms then emerged for solving oracle problems, such as Deutsch's algorithm in 1985, the BernsteinVazirani algorithm in 1993, and Simon's algorithm in 1994. These algorithms did not solve practical problems, but demonstrated mathematically that one could gain more information by querying a black box in superposition, sometimes referred to as quantum parallelism. Peter Shor built on these results with his 1994 algorithms for breaking the widely-used RSA and DiffieHellman encryption protocols, which drew significant attention to the field of quantum computing. In 1996, Grover's algorithm established a quantum speedup for the widely-applicable unstructured search problem. The same year, Seth Lloyd proved that quantum computers could simulate quantum systems without the exponential overhead present in classical simulations, validating Feynman's 1982 conjecture. Over the years, experimentalists have constructed small-scale quantum computers using trapped ions and superconductors. In 1998, a two-qubit quantum computer demonstrated the feasibility of the technology, and subsequent experiments have increased the number of qubits and reduced error rates. In 2019, Google AI and NASA announced that they had achieved quantum supremacy with a 54-qubit machine, performing a computation that is impossible for any classical computer. However, the validity of this claim is still being actively researched. The threshold theorem shows how increasing the number of qubits can mitigate errors, yet fully fault-tolerant quantum computing remains