Session L55: 20 Years of Quantum Error Correction

Stability, topology, holography: The many facets of quantum error correction

Quantum error correction is a surprising and far-reaching concept, with many implications for science and technology. The theory of quantum error-correcting codes has bolstered our confidence that quantum computing is scalable, deepened our understanding of topological phases of matter, and spawned novel insights into the quantum structure of spacetime.   

Fault Tolerance in Small Experiments

Experiments are finally reaching the size and level of precise control where we can hope to see a truly fault-tolerant experiment within the next few years. I will give a proposal for a 5-qubit fault-tolerant experiment and discuss how to evaluate if an experiment has successfully demonstrated fault tolerance. I will also consider the possibility of using future fault-tolerant experiments to answer important questions about the interaction of fault-tolerant protocols with real experimental errors.   

Quantum Error Correction and the Future of Solid State Quantum Computing

Quantum error correction (QEC) theory has provided a very challenging but well defined goal for the further development of solid state qubit systems: achieve high enough fidelity so that fault-tolerant, error-corrected quantum computation in networks of these qubits becomes possible. I will begin by touching on some historical points: initial work on QEC is actually more than 20 years old, and the landmark work of Kitaev in 1996 which established 2D lattice structures as a suitable host for effective error correction, has its roots in theoretical work in many-body theory from Wegner in the 1970s. I will give some perspective on current developments in the implementation of small fragments of the surface code. The surface-code concept has driven a number of distinct requirements, beyond the reduction of error rates below the 1\% range, that are actively considered as experiments are scaled beyond the 10-qubit level.   

Quantum error correction with trapped ions

Quantum computers promise exponential speed-up compared to their classical counterparts for certain problems. Unfortunately, the states required for quantum computation are fragile and lose their quantum properties with growing system size. In a milestone work, it has been shown that quantum error correction can overcome this problem and enable arbitrary long and arbitrary high quality quantum algorithms. However, current experiments are not able to fulfill the requirements to employ useful quantum error correction procedures. In this talk, I will first review past proof-of-principle experiments in trapped ion quantum information processors. Building on that, I will sketch a way towards a medium-sized trapped ion system that will be capable of running an error correction procedure that outperforms it constituents.   

Quantum error correction in superconducting circuits

Can we prolong the coherence of a two-state manifold in a complex quantum system beyond the coherence of its longest-lived component? This question is the starting point of the main challenges in the construction of a scalable quantum computer, namely the implementation of quantum error correction. The presentation will review the experimental progress that recently occurred in the field of superconducting quantum circuits towards the correction, for a full logical qubit memory, of the combinations of bit flip and phase flip errors.