Developing universal logical state-purification strategy for quantum error correcting codes

• URL: http://arxiv.org/abs/2502.01393v1
• Date: Mon, 03 Feb 2025 14:24:25 GMT
• Title: Developing universal logical state-purification strategy for quantum error correcting codes
• Authors: Chandrima B. Pushpan, Tanoy Kanti Konar, Aditi Sen De, Amit Kumar Pal,
• Abstract summary: We develop a protocol for simultaneously purifying arbitrary logical states in multiple quantum error correcting codes with unit fidelity and finite probability. The protocol entails a time evolution caused by an engineered Hamiltonian, which results in transitions between the logical and error subspaces of the quantum error correcting code mediated by the auxiliary qubit. We show that purifying the cardinal states of the logical Bloch sphere corresponding to logical qubits in quantum state transfer is feasible utilizing paradigmatic quantum spin models as the generator of the time evolution.
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• Abstract: We develop a measurement-based protocol for simultaneously purifying arbitrary logical states in multiple quantum error correcting codes with unit fidelity and finite probability, starting from arbitrary thermal states of each code. The protocol entails a time evolution caused by an engineered Hamiltonian, which results in transitions between the logical and error subspaces of the quantum error correcting code mediated by the auxiliary qubit, followed by a projective measurement in an optimum basis on the auxiliary qubit and an appropriate post-selection of the measurement outcomes. We illustrate the results with the three-qubit repetition code and the logical qubit used in quantum state transfer protocol. We further demonstrate that when the measurement base is not optimal, it is possible to achieve both classical fidelity, and fidelity as high as $90\%$ through several iterations of the purifying procedure, thereby establishing its robustness against variations in the measurement basis. By repeating the purification rounds, we show that purifying the cardinal states of the logical Bloch sphere corresponding to logical qubits in quantum state transfer is feasible utilizing paradigmatic quantum spin models as the generator of the time evolution.

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