Related papers: Methodology for quantum logic gate constructions

We present two new constructions for the Toffoli gate which substantially reduce resource costs in fault-tolerant quantum computing. The first contribution is a Toffoli gate requiring Clifford operations plus only four $T =…

We present a method to create a variety of interesting gates by teleporting quantum bits through special entangled states. This allows, for instance, the construction of a quantum computer based on just single qubit operations, Bell…

It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions…

The difficulty in producing precisely timed and controlled quantum gates is a significant source of error in many physical implementations of quantum computers. Here we introduce a simple universal primitive, adiabatic gate teleportation,…

A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes. In particular, it is shown that one can fault-tolerantly map between different encoded representations of a…

We introduce a fault-tolerant construction to implement a composite quantum operation of four overlapping Toffoli gates. The same construction can produce two independent Toffoli gates. This result lowers resource overheads in designs for…

Efficient constructions for quantum logic are essential since quantum computation is experimentally challenging. This thesis develops quantum logic synthesis as a paradigm for reducing the resource overhead in fault-tolerant quantum…

Quantum computers promise dramatic speed ups for many computational tasks. For large-scale quantum computation however, the inevitable coupling of physical qubits to the noisy environment imposes a major challenge for a real-life…

Fault-tolerant logical operations for qubits encoded by CSS codes are discussed, with emphasis on methods that apply to codes of high rate, encoding k qubits per block with k>1. It is shown that the logical qubits within a given block can…

Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that…

Fault-tolerant quantum computation using quantum error-correcting codes requires fault-tolerant constructions of nontransversal gates. Shor proposed a fault-tolerant construction of a nontransversal gate, i.e., the Toffoli gate for a family…

We simulate the implementation of a T-gate, or $\frac{\pi}{8}$-gate, for a [7,1,3] encoded logical qubit in a non-equiprobable error environment. We demonstrate that the use of certain non-fault tolerant methods in the implementation may…

We present simplification schemes for probabilistic and controlled teleportation of the unknown quantum states of both one-particle and two-particle and construct efficient quantum logic networks for implementing the new schemes by means of…

We introduce a general framework for weak transversal gates -- probabilistic implementation of logical unitaries realized by local physical unitaries -- and propose a novel partially fault-tolerant quantum computing architecture that…

We present an architecture for early fault-tolerant quantum computers based on the smallest interesting colour code (Earl Campbell, 2016). It realizes a universal logical gate set consisting of single-qubit measurements and preparations in…

We show how to carry out quantum logical operations (controlled-not and Toffoli gates) on encoded qubits for several encodings which protect against various 1-bit errors. This improves the reliability of these operations by allowing one to…

Certain quantum codes allow logic operations to be performed on the encoded data, such that a multitude of errors introduced by faulty gates can be corrected. An important class of such operations are {\em transversal}, acting bitwise…

Fault-tolerant quantum computation is a basic problem in quantum computation, and teleportation is one of the main techniques in this theory. Using teleportation on stabilizer codes, the most well-known quantum codes, Pauli gates and…

The implementation of fault-tolerant quantum gates on encoded logic qubits is considered. It is shown that transversal implementation of logic gates based on simple geometric control ideas is problematic for realistic physical systems…

In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…