There is now a huge international effort to realise a quantum computer that can be scaled to solve problems that are intractable with modern technology. Realising a quantum computer is challenging because its individual components, known as qubits, will invariably experience errors that will cause the system to fail before a computation is completed. To deal with the issue we encode qubits in quantum error-correcting codes. These are robust many-body systems that will preserve their encoded logical information, even if their individual components suffer errors. They are designed such that we can run diagnostics to identify and repair errors provided the rate at which the system experiences errors is suitably low. We can protect the encoded information arbitrarily well by increasing the size of the quantum error-correcting code if our noisy qubits experience errors below some threshold rate. It is presently very challenging to construct and control our best available designs of quantum error-correcting codes using modern laboratory technology. To alleviate this problem we must search more robust codes that are more resource efficient than our current proposals. This will make the machines we seek to build more experimentally amenable. Our leading code designs for fault-tolerant quantum computation are based on phases of condensed quantum matter. Specifically, we synthesise physical systems with the fundamental properties of exotic phases to find robust designs for scalable quantum computation. There have been a number of recent developments, including the discovery of new phases of matter, that may help us overcome the issues that keep us from realising a quantum computer. I will examine new developments in condensed-matter physics to design robust new quantum error-correcting codes that can be realised experimentally to show that we can scale a quantum computer to solve problems that are presently intractable.
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