Related papers: Fault-Tolerant Logical Clifford Gates from Code Au…
Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. Quantum low-density parity-check (qLDPC) codes, including bivariate bicycle (BB) codes, achieve dramatic…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
The study of holographic bulk-boundary dualities has led to the construction of novel quantum error correcting codes. Although these codes have shed new light on conceptual aspects of these dualities, they have widely been believed to lack…
Stabilizer channels are stabilizer circuits that implement logical operations while mapping from an input stabilizer code to an output stabilizer code. They are widely used to implement fault tolerant error correction and logical operations…
Homomorphic quantum error correction aims to protect quantum data against both unauthorized access and environmental noise during server-based processing. We investigate the algebraic compatibility between quantum homomorphic encryption and…
Topological subsystem color codes add to the advantages of topological codes an important feature: error tracking only involves measuring 2-local operators in a two dimensional setting. Unfortunately, known methods to compute with them were…
We review an approach to fault-tolerant holonomic quantum computation on stabilizer codes. We explain its workings as based on adiabatic dragging of the subsystem containing the logical information around suitable loops along which the…
We consider the problem of Clifford testing, which asks whether a black-box $n$-qubit unitary is a Clifford unitary or at least $\varepsilon$-far from every Clifford unitary. We give the first 4-query Clifford tester, which decides this…
We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes, and topological color codes for error correction. Color codes have a set of transversal…
Clifford Circuit Initializaton improves on initial guess of parameters on Parametric Quantum Circuits (PQCs) by leveraging efficient simulation of circuits made out of gates from the Clifford Group. The parameter space is pre-optimized by…
For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary…
Quantum computers promise to solve problems that are intractable for classical computers, but qubits are vulnerable to many sources of error, limiting the depth of the circuits that can be reliably executed on today's quantum hardware.…
Logical gates constitute the building blocks of fault-tolerant quantum computation. While quantum error-corrected memories have been extensively studied in the literature, explicit constructions and detailed analyses of thresholds and…
Flag-style fault-tolerance has become a linchpin in the realization of small fault-tolerant quantum-error correction experiments. The flag protocol's utility hinges on low qubit overhead, which is typically much smaller than in other…
Using error correcting codes and fault tolerant techniques, it is possible, at least in theory, to produce logical qubits with significantly lower error rates than the underlying physical qubits. Suppose, however, that the gates that act on…
Stabilizer states along with Clifford manipulations (unitary transformations and measurements) thereof -- despite being efficiently simulable on a classical computer -- are an important tool in quantum information processing, with…
We prove that on any two-dimensional lattice of qudits of a prime dimension, every translation invariant Pauli stabilizer group with local generators and with code distance being the linear system size, is decomposed by a local Clifford…
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.
Fault-tolerant quantum computation (FTQC) schemes using large block codes that encode $k>1$ qubits in $n$ physical qubits can potentially reduce the resource overhead to a great extent because of their high encoding rate. However, the…
The homological product is a general-purpose recipe that forges new quantum codes from arbitrary classical or quantum input codes, often providing enhanced error-correcting properties. When the input codes are classical linear codes, it is…