Using self-testing methods, scientists validate error-correcting codes on photonic and superconducting systems
Quantum error correction codes protect quantum information from decoherence and quantum noise, and are therefore crucial to the development of quantum computing and the creation of more reliable and complex quantum algorithms. One example is the five-qubit error correction code, five being the minimum number of qubits required to fix single-qubit errors. These contain five physical qubits (a basic off/on unit of quantum information made using trapped ions, superconducting circuits, or quantum dots) to correct one logical qubit (a collection of physical qubits arranged in such a way as to correct errors). Yet imperfections in the hardware can still lead to quantum errors.
A method of testing quantum error correction codes is self-testing. Self-testing is a powerful tool for verifying quantum properties using only input-output statistics, treating quantum devices as black boxes. It has evolved from bipartite systems consisting of two quantum subsystems, to multipartite entanglement, where entanglement is among three or more subsystems, and now to genuinely entangled subspaces, where every state is fully entangled across all subsystems. Genuinely entangled subspaces offer stronger, guaranteed entanglement than general multipartite states, making them more reliable for quantum computing and error correction.
In this research, self-testing techniques are used to certify genuinely entangled logical subspaces within the five-qubit code on photonic and superconducting platforms. This is achieved by preparing informationally complete logical states that span the entire logical space, meaning the set is rich enough to fully characterize the behaviour of the system. They deliberately introduce basic quantum errors by simulating Pauli errors on the physical qubit, which mimics real-world noise. Finally, they use mathematical tests known as Bell inequalities, adapted to the framework used in quantum error correction, to check whether the system evolves in the initial logical subspaces after the errors are introduced.
Extractability measures tell you how close the tested quantum system is to the ideal target state, with 1 being a perfect match. The certification is supported by extractability measures of at least 0.828 ± 0.006 and 0.621 ± 0.007 for the photonic and superconducting systems, respectively. The photonic platform achieved a high extractability score, meaning the logical subspace was very close to the ideal one. The superconducting platform had a lower score but still showed meaningful entanglement. These scores show that the self-testing method works in practice and confirm strong entanglement in the five-qubit code on both platforms.
This research contributes to the advancement of quantum technologies by providing robust methods for verifying and characterizing complex quantum structures, which is essential for the development of reliable and scalable quantum systems. It also demonstrates that device-independent certification can extend beyond quantum states and measurements to more general quantum structures.
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Quantum error correction for beginners by Simon J Devitt, William J Munro and Kae Nemoto (2013)
