Simulating quantum error correction in a small stabilizer code
Typ
Examensarbete för masterexamen
Program
Publicerad
2021
Författare
Andersson, Alexander
Holmin, Sebastian
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
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.
Beskrivning
Ämne/nyckelord
Quantum computing , QEC , Quantum error correction , Stabilizer code , [[5,1,3]] , 5-qubit code , distance-3 , Qiskit , Simulation , Quantum mechanics