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A quantum computer can solve hard problems - such as prime factoring, database searching, and quantum simulation - at the cost of needing to protect fragile quantum states from error. Quantum error correction provides this protection, by…
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…
Quantum error correction is an essential component for practical quantum computing on noisy quantum hardware. However, logical operations on error-corrected qubits require a significant resource overhead, especially for high-precision and…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
We give a fault tolerant construction for error correction and computation using two punctured quantum Reed-Muller (PQRM) codes. In particular, we consider the $[[127,1,15]]$ self-dual doubly-even code that has transversal Clifford gates…
Color codes are a leading class of topological quantum error-correcting codes with modest error thresholds and structural compatibility with two-dimensional architectures, which make them well-suited for fault-tolerant quantum computing…
To ensure resilience against the unavoidable noise in quantum computers, quantum information needs to be encoded using an error-correcting code, and circuits must have a particular structure to be fault-tolerant. Compilation of…
Quantum computing is poised to solve practically useful problems which are computationally intractable for classical supercomputers. However, the current generation of quantum computers are limited by errors that may only partially be…
A defining feature in the field of quantum computing is the potential of a quantum device to outperform its classical counterpart for a specific computational task. By now, several proposals exist showing that certain sampling problems can…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
A common approach to studying the performance of quantum error correcting codes is to assume independent and identically distributed single-qubit errors. However, the available experimental data shows that realistic errors in modern…
Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to…
Correcting errors in real time is essential for reliable large-scale quantum computations. Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations,…
To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information…
Quantum error correction and fault-tolerance have provided the possibility for large scale quantum computations without a detrimental loss of quantum information. A very natural class of gates for fault-tolerant quantum computation is the…
In many architectures for fault tolerant quantum computing universality is achieved by a combination of Clifford group unitary operators and preparation of suitable nonstabilizer states, the so-called magic states. Universality is possible…
We compute the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates, when both qubit and measurement errors are present. By mapping the problem onto a…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
In this work, we propose and study in depth a universal quantum computing architecture based on a quantum construction of transistors. Our teleportation-based quantum transistors, called ``telesistors'', are ground states of systems with…
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…