Simulating quantum error correction in a small stabilizer code

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Examensarbete för masterexamen
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2021
Författare
Andersson, Alexander
Holmin, Sebastian
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Quantum error correction is an essential precondition for scaling up the current noisy intermediate-scale quantum (NISQ) computing of today. However, only rudimentary parts of quantum error correction have so far been experimentally demonstrated. Specifically, active correction of errors in distance-3 or above error correcting codes, capable of identifying arbitrary single qubit errors, has so far not been realized. In this work, we simulate repeated rounds of error correction with incoherent noise using the [[5, 1, 3]] error-correcting code, which is the smallest possible fulfilling this requirement, with the aim of determining its viability on a 7-qubit device being designed at the Wallenberg Center for Quantum Technology (WACQT) at Chalmers University of Technology. We find that the error-correcting code suffers from a large number of incorrectly decoded errors caused by noise during the detection step, which we identify as the primary bottleneck. The lifetime of the logical qubit can be improved by introducing a delay between the cycles of error correction, and by splitting the error measurements over two ancillary qubits. Using the lifetime parameters T1 = 40 μs and T2 = 60 μs, representing the decay of the |1i and |+i states for the constituent single qubits respectively, we reach a logical qubit lifetime of TL = 39 μs, which is narrowly below the break-even point. For cases where T2 T1 (including T1 = 40 μs and T2 = 70 μs), we find that the lifetime of the logical qubit may exceed the single qubits when comparing the worst case initial conditions. The stronger condition of TL > T1, T2 is reached at T1 = T2 = 120 μs. A more robust error-decoding scheme, perhaps from improved parallelism or fault-tolerant stabilizer circuits, would significantly lower the barrier to the error-correction break-even point and make the code more effective.
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Quantum computing, QEC, Quantum error correction, Stabilizer code, [[5,1,3]], 5-qubit code, distance-3, Qiskit, Simulation, Quantum mechanics
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