#### Alladi Ramakrishnan Hall

#### Critical noise parameters for fault tolerant quantum computation

#### Pavithran S. Iyer

##### Institute Quantique, Universit ́e de Sherbrooke

*Noise is imminent to a quantum computing process. In theory it is often modelled by the action of Pauli errors on a computational state. In reality, however, it is often not the case. Instead the action of noise can be viewed as a generic quantum channel whose input is the state of the system prior to the noise. It is nevertheless possible to perform reliable quantum computations in the precense of noise — quantum error correcting codes exist to this effect. The logical information in a qubit can be preserved by encoding it in a system of several physical qubits and by performing the gates in a fault tolerant manner. However, it is important to know the noise model at the physical level, in order to estimate the overhead required for fault tolerant quantum computation. On the other hand, it is often unclear as to what parameters of a noise model are critical to the logical error rate of a qubit.*

In this work, we aim to determine the parameters of a single qubit channel that can tightly bound the logical error rate of the concatenated Steane code. We do not assume any a priori structure for the physical quantum channel, except that it is a CPTP map. Our method of estimating the logical error rate differs significantly from the standard and computationally expensive Monte-Carlo sampling of the error distribution. We employ a technique to compute the complete effect of a physical CPTP map, at the logical level, with just one round of error correction. By such numerical simulations with random quantum channels, we have studied the predictive power of several physical noise metrics on the logical error rate, and show that, on their own, none of the natural physical metrics lead to accurate predictions about the logical error rate. We then show how machine learning techniques help us to explore which features of a random quantum channel are important in predicting its effect at the logical level.

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