Noise is widely regarded as a major obstacle to quantum computing. Fortunately, this problem can be solved efficiently due to the existence of the threshold theorem. It states that under sufficiently weak noise and universal assumptions, there always exists an active quantum error correction protocol with only logarithmic hardware overhead. One may ask: can a similar result be obtained for autonomous (passive) error correction, where noise is suppressed by natural or engineered dissipation? As I will show, there are successful schemes, but no similar universal noise threshold for autonomous error correction. Instead, the threshold theorem can be replaced by a general bound that guarantees success only if the correcting dissipation rate grows with the physical memory size. Despite this limitation, our result shows the great potential of general autonomous schemes that may prove practical in the foreseeable future.
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https://docs.google.com/document/d/1KDHsYRy1-58intspq7aVyXqC0RftUIR4u-ptJ4gLsXQ/edit?usp=sharing