Realizing Fracton Matter: from Theory, to Quantum Information, to Experiment

We are used to the notion of elementary particles that can be created, destroyed, and – in between – move freely through space according to rules codified by quantum field theory. Hence it came as an immense surprise when, a decade ago, a type of particle was theoretically proposed that defied these notions in two ways – the new particles cannot move at all when they are isolated from others, and they refuse to be described in the language of quantum field theory. The new particles were termed fractons because they could only be created in a quartet, lying on the corners of a fractal. On the quantum information side, the interest in the fracton phases of matter comes from a different perspective — that of quantum memory. Storing quantum information, unlike information in a classical computer, requires battling quantum decoherence, which results in a loss of information over time. To achieve error-resistant quantum memory, one would like to store the information in a quantum superposition of degenerate states engineered in such a way that local sources of noise cannot change one state into another, thus preventing quantum decoherence. The phases with fracton order promise to do just that, and crucially, the capacity of the hypothetical quantum hard drive (given by the ground state degeneracy) grows (sub)extensively with the system size. Unfortunately, the models realizing fractons are not friendly to experimental implementations as they require unnatural interactions among a substantial number (of the order of ten) of qubits. We demonstrate how this limitation can be circumvented by leveraging the long-range quantum entanglement created using only pairwise interactions between the code and ancilla qubits, realizable in programmable tweezer arrays of Rydberg atoms. We demonstrate a blueprint for implementing this idea and show that this platform also allows to detect and correct certain types of errors en route to the goal of error-resistant quantum memory.