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Blind Quantum Computation (BQC) is a delegation computing protocol that allows a client to utilize a remote quantum server to implement desired quantum computations while keeping her inputs, outputs, and algorithms private. However, qubit…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
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…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
We present and analyze protocols for fault-tolerant quantum computing using color codes. We present circuit-level schemes for extracting the error syndrome of these codes fault-tolerantly. We further present an integer-program-based…
A fault-tolerant quantum computer must decode and correct errors faster than they appear. The faster errors can be corrected, the more time the computer can do useful work. The Union-Find (UF) decoder is promising with an average time…
Fast decoding algorithms are decisive for real-time quantum error correction and for analyzing properties of error correction codes. Here, we develop variants of the union-find decoder that simplify its implementation and provide potential…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct…
Quantum computation can be performed by encoding logical qubits into the states of two or more physical qubits, and controlling a single effective exchange interaction and possibly a global magnetic field. This "encoded universality"…
An efficient decoder is essential for quantum error correction, and data-driven neural decoders have emerged as promising, flexible solutions. Here, we introduce a diffusion model framework to infer logical errors from syndrome measurements…
The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes…
Sparse coding provides a versatile framework for efficiently capturing and representing crucial data (information) concisely, which plays an essential role in various computer science fields, including data compression, feature extraction,…
High-rate and large-distance quantum codes are expected to make fault-tolerant quantum computing more efficient, but most of them lack efficient fault-tolerant encoded-state preparation methods. We propose such a fault-tolerant encoder for…
Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information storage and transmission. We report the implementation of a concatenated quantum error-correcting code able to correct…
With the advent of noisy intermediate-scale quantum (NISQ) devices, practical quantum computing has seemingly come into reach. However, to go beyond proof-of-principle calculations, the current processing architectures will need to scale up…
This paper investigates quantum error correction schemes for fully-correlated noise channels on an $n$-qubit system, where error operators take the form $W^{\otimes n}$, with $W$ being an arbitrary $2\times 2$ unitary operator. In previous…
We consider realistic, multi-parameter error models and investigate the performance of the surface code for three possible fault-tolerant superconducting quantum computer architectures. We map amplitude and phase damping to a diagonal Pauli…
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…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…