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Building large-scale quantum computers is a highly complex and challenging task that requires advancements in various fields, including quantum physics, materials science, engineering, and error correction. While there is ongoing research and progress in this area, there is no definitive "fastest" way to build large-scale quantum computers. However, I can provide an overview of some key approaches and technologies that are being explored:

  1. Gate-Based Quantum Computers: This approach focuses on developing quantum computers based on gate operations, where qubits are manipulated through sequences of quantum gates to perform computations. Gate-based quantum computers require a large number of qubits, high-fidelity qubit operations, and error correction techniques to mitigate noise and errors.

  2. Superconducting Qubits: Superconducting qubits are one of the most promising candidates for building quantum computers. These qubits are implemented using superconducting circuits that can be manipulated and measured to perform quantum operations. Improvements in qubit coherence, gate fidelity, and scalability are key areas of research in superconducting qubit technology.

  3. Trapped Ion Qubits: Trapped ion qubits use individual ions trapped and manipulated using electromagnetic fields. These qubits have long coherence times and high gate fidelities, making them attractive for quantum computing. Researchers are exploring techniques to scale up trapped ion systems and improve their performance.

  4. Topological Quantum Computing: Topological quantum computing is a theoretical approach that relies on using anyons, exotic particles that can exist in two dimensions. These anyons are manipulated to perform quantum operations, and their inherent topological properties make the system highly resistant to errors. However, building practical topological quantum computers is still a significant challenge.

  5. Quantum Annealing: Quantum annealing is a different paradigm that aims to solve optimization problems using quantum effects. Quantum annealers, such as those developed by D-Wave Systems, are designed to find low-energy states of a problem by evolving a quantum system to a state that encodes the solution. While quantum annealing is not a general-purpose quantum computing model, it has potential applications in specific optimization problems.

It's important to note that building large-scale fault-tolerant quantum computers capable of outperforming classical computers is a complex engineering task that requires overcoming numerous technical challenges, such as improving qubit coherence, minimizing errors, and implementing error correction codes. It will likely require further scientific breakthroughs, technological advancements, and iterative improvements to realize large-scale quantum computers.

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