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Open Problems in Quantum Computing—What’s Still Unsolved?

For all the progresses in quantum computing, some of the field’s most fundamental questions remain wide open. These aren’t just technical hurdles—they’re deep, conceptual challenges that could redefine what quantum computers can actually achieve. Here’s a look at the unsolved problems keeping researchers up at night.

One of the biggest is the quantum memory problem: How do we efficiently store quantum states for long periods? Classical computers rely on robust, persistent memory, but qubits decohere rapidly. Even with error correction, we lack a practical, scalable solution for quantum RAM that doesn’t introduce overwhelming overhead.

Then there’s the compilation gap. Translating high-level quantum algorithms into hardware-native gates is still more art than science. Optimal circuit decomposition for arbitrary algorithms—especially on architectures with limited connectivity—is NP-hard in many cases. We need better tools (or breakthroughs) to make this process efficient.

The noise-resilience question looms large: Can we design algorithms that inherently tolerate noise, or are we stuck waiting for full fault tolerance? Variational methods and error mitigation help, but they’re stopgaps. A deeper theoretical understanding of noise’s impact on computational power is missing.

On the hardware side, material science bottlenecks persist. Whether it’s improving superconducting qubit coherence times, finding better photonic detectors, or stabilizing topological qubits, the underlying physics challenges are far from solved.

Perhaps the most profound open question is how broadly applicable quantum advantage will be. We know quantum computers excel at specific tasks (factoring, simulation), but the boundaries of BQP—the class of problems efficiently solvable by quantum machines—are still fuzzy. Are there practical, commercially relevant problems beyond cryptography and chemistry where quantum will dominate?

Even foundational theory isn’t settled. The quantum PCP conjecture (a quantum analogue of classical computational complexity) remains unresolved, with major implications for quantum optimization. And the relationship between quantum and classical machine learning is still being mapped out.

What’s striking is how many of these open problems span theory, engineering, and physics. Solving them will require more than incremental improvements—it’ll demand entirely new ways of thinking.