Quantum error correction presents some of the most significant and interesting challenges that must be resolved before building an efficient quantum computer. Quantum error correcting codes allow to successfully run quantum algorithms on unreliable quantum hardware. Because quantum hardware suffers from errors such as decoherence, leakage or qubit loss, and these errors corrupt delicate quantum states, the known error correction techniques are complex and have a high overhead.

In my talk, I first quantify the overhead of quantum error correction using specific examples of algorithms and hardware technologies. Then I describe new techniques that I developed to reduce this overhead. For example, my maximum likelihood decoder (MLD) finds the recovery operation that maximizes the probability of a successful error correction given the observed error syndrome. Numerical simulations of the MLD algorithm for physical error rates around 10% showed a 100-fold reduction of the logical error probability compared to earlier techniques. I also briefly discuss other new code designs tailored for specific error models and physical technologies.