Related papers: A slightly smaller surface code S gate

We propose several methods for optimizing the number of qubits in a quantum circuit while preserving the number of non-Clifford gates. One of our approaches consists in reversing, as much as possible, the gadgetization of Hadamard gates,…

SignSGD compresses each stochastic gradient coordinate to a single bit, offering substantial memory and communication savings, but its 1-bit quantization removes magnitude information and is known to leave a generalization gap relative to…

Surface codes are a popular error-correction route to fault-tolerant quantum computation. The so-called exponential backlog problem that can arise when one has to do logical $T$-gates within the surface code demands real-time decoding of…

Topological subsystem codes can combine the advantages of both topological codes and subsystem codes. Suchara et al. proposed a framework based on hypergraphs for construction of such codes. They also studied the performance of some…

This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to…

Transversal gates play a crucial role in suppressing error propagation in fault-tolerant quantum computation, yet they are intrinsically constrained: any nontrivial code encoding a single logical qubit admits only a finite subgroup of…

Transversal gates are the ideal gates in a fault-tolerant scenario; relatively easy to implement, and minimally error propagating. Their availability will maximise fault tolerant thresholds, enabling universal quantum computation in a wider…

Given a quantum gate circuit, how does one execute it in a fault-tolerant architecture with as little overhead as possible? In this paper, we discuss strategies for surface-code quantum computing on small, intermediate and large scales.…

Currently available quantum computers, so called Noisy Intermediate-Scale Quantum (NISQ) devices, are characterized by relatively low number of qubits and moderate gate fidelities. In such scenario, the implementation of quantum error…

We consider an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code. We develop a customised decoder to process the information about the likely…

Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…

In this paper we improve the layered implementation of arbitrary stabilizer circuits introduced by Aaronson and Gottesman in Phys. Rev. A 70(052328), 2004: to obtain a general stabilizer circuit, we reduce their $11$-stage computation…

The measurement of scalar products between two vectors is a common task in scientific computing and, by extension, in quantum computing. In this work, we introduce two alternative quantum circuits for computing scalar products with phase…

The synthesis of quantum operators involves decomposing general quantum gates into the gate set supported by a given quantum device. Multi-controlled gates are essential components in this process. In this work, we present an improved…

The performance of quantum error correction schemes depends sensitively on the physical realizations of the qubits and the implementations of various operations. For example, in quantum dot spin qubits, readout is typically much slower than…

We give a quantum gate construction - composed entirely from incidents of the CNOT gate - that generalises the qubit SWAP gate to higher dimensions. This new construction is more regular than and is an improvement on the WilNOT quantum gate…

This paper proposes a new optimized quantum block-ZXZ decomposition method [7,8,10] that results in more optimal quantum circuits than the quantum Shannon decomposition (QSD)[27], which was introduced in 2006 by Shende et al. The…

We show that with the assistance of a third level of the qubits an n-qubit phase gate can be constructed from $2n-4$ two-qutrit conditional swap gates, a single qutrit-qubit controlled phase gate, and two single-qutrit operations. Unlike…

Estimating and reducing the overhead of fault tolerance (FT) schemes is a crucial step toward realizing scalable quantum computers. Of particular interest are schemes based on two-dimensional (2D) topological codes such as the surface and…

One of the leading quantum computing architectures is based on the two-dimensional (2D) surface code. This code has many advantageous properties such as a high error threshold and a planar layout of physical qubits where each physical qubit…