Quantum factoring may not be quite as far distant as you might think Most importantly, Shor is not the algorithm of choice for first-gen hardware where the cen

Quantum factoring may not be quite as far distant as you might think Most importantly, Shor is not the algorithm of choice for first-gen hardware where the central challenge is likely to be circuit depth due to error correction overhead. The current front-runner is a probably proposal by Regev [0] with a space-optimization by Ragavan et al. [1], which factors an n-bit integer with O(n log n) logical qubits and a circuit depth of O(n). What you should be looking for when studying quantum computing press releases is "fault tolerance": A central problem in QC is that the underlying hardware needs to be better than an (architecture-specific) threshold, before error-correction can be applied without introducing more errors than it corrects. Nobody has really crossed the threshold yet with scalable hardware, and when someone does, the overhead will be abysmal (2 or 3 layers of error correction, each with a factor ~100 overhead in space and time). Still, there are two reasons to be optimistic: One reason is that once a system crosses the threshold, any improvement in hardware will result in exponential improvements in the encoded operations, meaning that there will be a Moore-style exponential development. Another reason is that there are several "dark mode" VC-funded companies working towards intrinsically scalable systems based on optical QC: If any of these achieve fault tolerance, they will be scalable from day one. [0]: http://arxiv.org/abs/2308.06572 http://arxiv.org/abs/2308.06572 [1]: http://arxiv.org/abs/2310.00899 http://arxiv.org/abs/2310.00899