Scaling quantum computers to handle complex real-world problems involves several key advancements:

1. Improving Qubit Quality: Enhancing the stability and coherence of qubits (the basic units of quantum information) is essential. This involves developing qubits that maintain their quantum state longer and are less prone to errors. Technologies like superconducting qubits, trapped ions, and topological qubits are being explored for this purpose.

2. Error Correction: Quantum error correction is critical to ensure reliable computations. Since qubits are highly susceptible to errors, developing robust error-correcting codes and fault-tolerant algorithms can help maintain the integrity of quantum information over longer computations.

3. Scalable Architecture: Designing scalable quantum architectures involves creating interconnections between a large number of qubits. Techniques such as modular quantum computing, where smaller quantum modules are interconnected, can help in building larger, more powerful quantum systems.

4. Efficient Quantum Algorithms: Developing algorithms that are specifically designed to leverage the unique capabilities of quantum computers is crucial. Quantum algorithms like Shor’s for factoring large numbers and Grover’s for search problems already show potential. Further innovations will address more complex problems.

5. Hybrid Systems: Integrating quantum computers with classical supercomputers can harness the strengths of both. Hybrid systems can manage the overall computation, using classical computers for certain tasks and quantum computers for parts that benefit from quantum speedup.