Individual Control of Densely Packed Logical Qubits
Recently, quantum low-density-parity-check (LDPC) codes becomes competitive candidates for fault-tolerant quantum storage and computation, as quantum information is stored more compactly than the celebrated planar surface code architecture. However, the protocols for manipulating quantum information on these codes are not well-developed. In this talk, I will first review some existing methods for performing logical measurements on small quantum codes, including the Shor and Steane methods, and discuss their limitations when applied to large quantum LDPC codes. Then I will show how to circumvent these difficulties by unifying Shor and Steane methods into a single framework called “homomorphic measurements”. Compared to Shor and Steane methods, homomorphic measurements do not require either repetitive measurements or complicated ancilla state preparation procedures. As an example, I will show how to construct homomorphic measurement circuits for hyperbolic surface codes, which has state-of-the-art parameters among codes less than 10,000 physical qubits. The construction connects fault-tolerant logical operation design and the theory of covering spaces from algebraic topology.
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