Related papers: The Q-Spellbook: Crafting Surface Code Layouts and…

The development of quantum computing systems for large scale algorithms requires targeted error rates unachievable through hardware advancements alone. Quantum Error Correction (QEC) allows us to use systems with a large number of physical…

We propose a method for universal fault-tolerant quantum computation using concatenated quantum error correcting codes. Namely, other than computational basis state preparation as required by the DiVincenzo criteria [1], our scheme requires…

Quantum computing (QC) is at the cusp of a revolution. Machines with 100 quantum bits (qubits) are anticipated to be operational by 2020 [googlemachine,gambetta2015building], and several-hundred-qubit machines are around the corner.…

Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…

A foundational assumption of quantum error correction theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance. Two major challenges that could become fundamental roadblocks…

Surface codes can protect quantum information stored in qubits from local errors as long as the per-operation error rate is below a certain threshold. Here we propose holonomic surface codes by harnessing the quantum holonomy of the system.…

As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state…

The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…

The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is…

Practical applications of quantum computing depend on fault-tolerant devices with error correction. Today, the most promising approach is a class of error-correcting codes called surface codes. We study the problem of compiling quantum…

The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and…

It is challenging to transform an arbitrary quantum circuit into a form protected by surface code quantum error correcting codes (a variant of topological quantum error correction), especially if the goal is to minimise overhead. One of the…

This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…

Determining the best attainable threshold for qudit magic state distillation is directly related to the question of whether or not contextuality is sufficient for universal quantum computation. We show that the performance of a qudit…

Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…

Magic state distillation (MSD) is a purification protocol that plays a central role in fault tolerant quantum computation. Repeated iteration of the steps of a MSD protocol, generates pure single non-stabilizer states, or magic states, from…

Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…

We propose a new family of error detecting stabilizer codes with an encoding rate 1/3 that permit a transversal implementation of the pi/8-rotation $T$ on all logical qubits. The new codes are used to construct protocols for distilling…

Magic state distillation (MSD) is a quantum algorithm that enables performing logical non-Clifford gates with in principle arbitrarily low noise level. It is herein typically assumed that logical Clifford gates can be executed without…

Quantum low-density parity check (qLDPC) codes are among the leading candidates to realize error-corrected quantum memories with low qubit overhead. Potentially high encoding rates and large distance relative to their block size make them…