Related papers: A Genus-two Surface Code
Recent work has shown that fabrication defects can be well-handled using a strategy relying on the mid-error-correction-cycle state. In this work we present two improvements to the original prescription. First, we quantify the impact of the…
Twist defects in surface codes can be used to encode more logical qubits, improve the code rate, and implement logical gates. In this work we provide a rigorous formalism for constructing surface codes with twists generalizing the…
The design and performance analysis of quantum error correction (QEC) codes are often based on incoherent and independent noise models since it is easy to simulate. However, these models fail to capture realistic hardware noise sources,…
Current approaches for building quantum computing devices focus on two-level quantum systems which nicely mimic the concept of a classical bit, albeit enhanced with additional quantum properties. However, rather than artificially limiting…
The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate…
In this work we use arithmetic, geometric, and combinatorial techniques to compute the cohomology of Weil divisors of a special class of normal surfaces, the so-called rational ruled toric surfaces. These computations are used to study the…
The requirement of performing both single-qubit and two-qubit operations in the implementation of universal quantum logic often leads to very demanding constraints on quantum computer design. We show here how to eliminate the need for…
Quantum computing (QC) promises significant advantages on certain hard computational tasks over classical computers. However, current quantum hardware, also known as noisy intermediate-scale quantum computers (NISQ), are still unable to…
Fault-tolerant quantum computing (FTQC) is emerging as the architectural regime in which practical large-scale quantum workloads will execute. In this setting, however, multiprogramming is no longer a matter of partitioning a flat pool of…
We consider the surface code under errors featuring both coherent and incoherent components and study the coherence of the corresponding logical noise channel and how this impacts information-theoretic measures of code performance, namely…
We consider a two-dimensional quantum memory of qubits on a torus which encode the extended Fibonaccistring-net code, and devise strategies for error correction when those qubits are subjected to depolarizing noise.Building on the concept…
The non-local interactions in several quantum device architectures allow for the realization of more compact quantum encodings while retaining the same degree of protection against noise. Anticipating that short to medium-length codes will…
The topological color code and the toric code are two leading candidates for realizing fault-tolerant quantum computation. Here we show that the color code on a $d$-dimensional closed manifold is equivalent to multiple decoupled copies of…
In this paper, we formally describe the three challenges of mapping surface code on superconducting devices, and present a comprehensive synthesis framework to overcome these challenges. The proposed framework consists of three…
We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving…
Surface codes are one of the most important topological stabilizer codes in the theory of quantum error correction. In this paper, we provide an efficient way to obtain surface codes through Measurement-based quantum computation (MBQC)…
We consider the problem of mapping a logical quantum circuit onto a given hardware with limited two-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes…
The surface code is a spin-1/2 lattice system that can exhibit non-trivial topological order when defects are punctured in the lattice and thus can be used as a stabiliser code. The protocols developed to create defects in the system have…
In this work we introduce two code families, which we call the heavy hexagon code and heavy square code. Both code families are implemented by assigning physical data and ancilla qubits to both vertices and edges of low degree graphs. Such…
Motivated by recent advances in locally testable codes and quantum LDPCs based on robust testability of tensor product codes, we explore the local testability of tensor products of (an abstraction of) algebraic geometry codes. Such codes…