Abstract
Fault-tolerant quantum error correction is a necessity for any quantum architecture destined to tackle interesting, large-scale problems. Its theoretical formalism has been well founded for nearly two decades. However, we still do not have an appropriate compiler to produce a fault-tolerant, error-corrected description from a higher-level quantum circuit for state-of the-art hardware models. There are many technical hurdles, including dynamic circuit constructions that occur when constructing fault-tolerant circuits with commonly used error correcting codes. We introduce a package that converts high-level quantum circuits consisting of commonly used gates into a form employing all decompositions and ancillary protocols needed for fault-tolerant error correction. We call this form the (I)initialisation, (C)NOT, (M)measurement form (ICM) and consists of an initialisation layer of qubits into one of four distinct states, a massive, deterministic array of CNOT operations and a series of time-ordered X- or Z-basis measurements. The form allows a more flexible approach towards circuit optimisation. At the same time, the package outputs a standard circuit or a canonical geometric description which is a necessity for operating current state-of-the-art hardware architectures using topological quantum codes.
Highlights
(C)NOT, (M)measurement form (ICM) and consists of an initialisation layer of qubits into one of four distinct states, a massive, deterministic array of CNOT operations and a series of time-ordered X- or
We introduce a package that converts high-level quantum circuits consisting of commonly used gates into a form employing all decompositions and ancillary protocols needed for fault-tolerant error correction
This is enabled by bringing high-level quantum circuits consisting of commonly used gates into the ICM form, which employs all decompositions and ancillary protocols needed for fault-tolerant error correction
Summary
(C)NOT, (M)measurement form (ICM) and consists of an initialisation layer of qubits into one of four distinct states, a massive, deterministic array of CNOT operations and a series of time-ordered X- or. Despite the significant quantity of research in this area, much of the early work omitted details of fault-tolerant error correction protocols These protocols are instrumental in implementing any quantum algorithm, beyond a handful of qubits, but place constraints on the cost metrics used when assessing optimal circuit constructions for a higher-level algorithm [39]. The majority of scalable architectures proposed either use the two-dimensional (2D) surface code [40,41,42], or the 3-dimensional (3D) Raussendorf model [43, 44] as the underlying error correction method
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