We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold... more We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions combining probabilities of erasures, depolarizing errors, and phenomenological syndrome measurement errors for quantum low-density parity-check codes with logarithmic or larger distances. These threshold estimates are parametrically better than the existing analytical bound based on percolation.
Codeword-stabilized codes are a general class of quantum codes that includes stabilizer codes and... more Codeword-stabilized codes are a general class of quantum codes that includes stabilizer codes and many families of nonadditive codes with good parameters. For such a nonadditive code correcting all t-qubit errors, we propose an algorithm that employs a single measurement to test all errors located on a given set of t qubits. Compared with exhaustive error screening, this reduces the total number of measurements required for error recovery by a factor of about 3(t).
... transformation. We start with a geometric illustration of the regular Zeno effect for a simpl... more ... transformation. We start with a geometric illustration of the regular Zeno effect for a simple two-level system. ... vector. The Pauli matrices have zero trace, and the normalization condition Tr ̂ρ = 1 holds due to the presence of the identity matrix ̂I. ...
We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold... more We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions combining probabilities of erasures, depolarizing errors, and phenomenological syndrome measurement errors for quantum low-density parity-check codes with logarithmic or larger distances. These threshold estimates are parametrically better than the existing analytical bound based on percolation.
Codeword-stabilized codes are a general class of quantum codes that includes stabilizer codes and... more Codeword-stabilized codes are a general class of quantum codes that includes stabilizer codes and many families of nonadditive codes with good parameters. For such a nonadditive code correcting all t-qubit errors, we propose an algorithm that employs a single measurement to test all errors located on a given set of t qubits. Compared with exhaustive error screening, this reduces the total number of measurements required for error recovery by a factor of about 3(t).
... transformation. We start with a geometric illustration of the regular Zeno effect for a simpl... more ... transformation. We start with a geometric illustration of the regular Zeno effect for a simple two-level system. ... vector. The Pauli matrices have zero trace, and the normalization condition Tr ̂ρ = 1 holds due to the presence of the identity matrix ̂I. ...
Uploads
Papers