(Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne, Switzerland)
The main limitation to large-scale quantum computing are quantum errors, inevitably produced by the interaction with the environment. Similar to errors in classical computers, the main strategy to correct quantum errors is redundancy, which is realized by encoding the state of a logical qubit onto a subspace of the state-space of a larger quantum system. In textbook quantum error correction, the larger space is provided by a set of several physical qubits. The most promising alternative to this standard are bosonic quantum codes. In a bosonic code, a logical qubit is encoded onto a subspace of the state space of the quantum harmonic oscillator. The Schrödinger's cat bosonic code is arguably the most promising of these codes. Here, I will give a pedagogical introduction to bosonic quantum codes and to the cat code in particular. I will then illustrate the link between bosonic codes and dissipative phase transitions. I will conclude by presenting our recent results on a novel regime of operation of the cat code, where the vicinity of a first-order dissipative phase transition, with spontaneous symmetry breaking, enables a considerably improved performance in quantum error suppression, and opens the way to the design and demonstration of the first multi-qubit quantum gates on boson-encoded qubits.
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