Related papers: Direct measurement of Bacon-Shor code stabilizers
Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabilizer codes, surface code computations consist of a syndrome decoding step where measured stabilizer…
Utilizing the framework of $\mathbb{Z}_2$ lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic…
This paper generalizes and expands upon the work [Phys. Rev. Lett. 102, 070502 (2009)] where we introduced a scheme for fault-tolerant holonomic quantum computation (HQC) on stabilizer codes. HQC is an all-geometric strategy based on…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…
We study subsystem codes whose gauge group has local generators in the 2D geometry. It is shown that there exists a family of such codes defined on lattices of size LxL with the number of logical qubits k and the minimum distance d both…
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…
We explore the feasibility of implementing a small surface code with 9 data qubits and 8 ancilla qubits, commonly referred to as surface-17, using a linear chain of 171Yb+ ions. Two-qubit gates can be performed between any two ions in the…
The theory of stabilizer quantum error correction allows us to actively stabilize quantum states and simulate ideal quantum operations in a noisy environment. It is critical is to correctly diagnose noise from its syndrome and nullify it…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…
Inspired by Knill's scheme for message passing error detection, here we develop a scheme for message passing error correction for the nine-qubit Bacon-Shor code. We show that for two levels of concatenated error correction, where classical…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…
Dynamical stabilizer codes (DSCs) have recently emerged as a powerful generalization of static stabilizer codes for quantum error correction, replacing a fixed stabilizer group with a sequence of non-commuting measurements. This dynamical…
The usual scenario in fault tolerant quantum computation involves certain amount of qubits encoded in each code block, transversal operations between them and destructive measurements of ancillary code blocks. We introduce a new approach in…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their simple syndrome readout circuits and potential applications in fault-tolerant quantum computing. However, all families of quantum…
Methods borrowed from the world of quantum information processing have lately been used to enhance the signal-to-noise ratio of quantum detectors. Here we analyze the use of stabilizer quantum error-correction codes for the purpose of…