Related papers: Error-correcting codes for fermionic quantum simul…
Analysis of quantum error correcting codes is typically done using a stochastic, Pauli channel error model for describing the noise on physical qubits. However, it was recently found that coherent errors (systematic rotations) on physical…
Floquet quantum error-correcting codes provide an operationally economical route to fault tolerance by dynamically generating stabilizer structures using only two-body Pauli measurements. But while it is well established that stabilizer…
Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grows linearly with the code's maximum stabilizer generator weight. For some common distance-three codes, the recent "flag paradigm" uses…
High-fidelity decoding of quantum error correction codes relies on an accurate experimental model of the physical errors occurring in the device. Because error probabilities can depend on the context of the applied operations, the error…
The ubiquity of stabilizer circuits in the design and operation of quantum computers makes techniques to verify their correctness essential. The simulation of stabilizer circuits, which aims to replicate their behavior using a classical…
A compelling application of quantum computers with thousands of qubits is quantum simulation. Simulating fermionic systems is both a problem with clear real-world applications and a computationally challenging task. In order to simulate a…
Quantum error correction is needed for quantum computers to be capable of fault-tolerantly executing algorithms using hundreds of logical qubits. Recent experiments have demonstrated subthreshold error rates for state preservation of a…
We numerically analyze the feasibility of a platform-neutral, general strategy to perform quantum simulations of fermionic lattice field theories under open boundary conditions. The digital quantum simulator requires solely one- and…
Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit,…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
As current experiments already realize small quantum circuits on error corrected qubits, it is important to fully understand the effect of physical errors on the logical error channels of these fault-tolerant circuits. Here, we investigate…
In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for…
This paper builds on the idea of simulating stabiliser circuits through transformations of quadratic form expansions. This is a representation of a quantum state which specifies a formula for the expansion in the standard basis, describing…
Stabiliser codes with large weight measurements can be challenging to implement fault-tolerantly. To overcome this, we propose a Floquetification procedure which, given a stabiliser code, synthesises a novel Floquet code that only uses…
Topological stabilizer codes with different spatial dimensions have complementary properties. Here I show that the spatial dimension can be switched using gauge fixing. Combining 2D and 3D gauge color codes in a 3D qubit lattice,…
In this work we extend the connection between Quantum Error Correction (QEC) and Lattice Gauge Theories (LGTs) by showing that a $\mathbb{Z}_N$ gauge theory with prime dimension $N$ coupled to dynamical matter can be expressed as a qudit…
We construct two quantum error correction codes for pure SU(2) lattice gauge theory in the electric basis truncated at the electric flux $j_{\rm max}=1/2$, which are applicable on quasi-1D plaquette chains, 2D honeycomb and 3D triamond and…
We study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group,…
We introduce homological measurement, a framework for measuring the logical Pauli operators encoded in CSS stabilizer codes. The framework is based on the algebraic description of such codes as chain complexes. Protocols such as lattice…