Abstract The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an
oscillator has recently been followed by cat-and binomial-code proposals. Numerically …

The quantum computing devices of today have tens to hundreds of qubits that are highly
susceptible to noise due to unwanted interactions with their environment. The theory of …

Quantum error correction is believed to be a necessity for large-scale fault-tolerant quantum
computation. In the past two decades, various constructions of quantum error-correcting …

Error correction procedures are considered which are designed specifically for the
amplitude damping channel. Amplitude damping errors are analyzed in the stabilizer …

Quantum channels can describe all transformations allowed by quantum mechanics. We
adapt two existing works [S. Lloyd and L. Viola, Phys. Rev. A 65, 010101 (2001) and E …

With the intense interest in small, noisy quantum computing devices comes the push for
larger, more accurate—and hence more useful—quantum computers. While fully fault …

We present analytic estimates of the performances of various approximate quantum error-
correction schemes for the generalized amplitude-damping (GAD) qubit channel …

The maximum overlap problem: Let KH be a positive semidefinite trace-class operator on
KH, and let MLH be positive semidefinite bounded operator on LH, where H, K, and L are …

We give asymptotically converging semidefinite programming hierarchies of outer bounds
on bilinear programs of the form Tr\big H (D ⊗ E)\big Tr H (D⊗ E), maximized with respect to …

We develop a theory for finding quantum error correction (QEC) procedures which are
optimized for given noise channels. Our theory accounts for uncertainties in the noise …