Related papers: Exact Performance of Concatenated Quantum Codes
In this work, a quantum error correction (QEC) procedure with the concatenated five-qubit code is used to construct a near-perfect effective qubit channel (with a error below $10^{-5}$) from arbitrary noise channels. The exact performance…
Quantum error correction protects logical quantum information against environmental decoherence by encoding logical qubits into entangled states of physical qubits. One of the most important near-term challenges in building a scalable…
The fragile nature of quantum information limits our ability to construct large quantities of quantum bits suitable for quantum computing. An important goal, therefore, is to minimize the amount of resources required to implement quantum…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
We compare the effect of single qubit incoherent and coherent errors on the logical error rate of the Steane [[7,1,3]] quantum error correction code by performing an exact full-density-matrix simulation of an error correction step. We find…
There is currently a significant need for robust and efficient methods for characterizing quantum devices. While there has been significant progress in this direction, there remains a crucial need to precisely determine the strength and…
In this paper, we provise an implementation of five, seven and nine-qubits error correcting codes on a classical computer using the quantum simulator Feynman program. We also compare the three codes by computing the fidelity when double…
A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing…
Coherent parity check (CPC) codes are a new framework for the construction of quantum error correction codes that encode multiple qubits per logical block. CPC codes have a canonical structure involving successive rounds of bit and phase…
A quantum channel models the interaction between the system we are interested in and its environment. Such a model can capture the main features of the interaction but because of the complexity of the environment we can not assume that it…
We demonstrate how insights gained from reformulating the problem of quantum teleportation into one of reversing quantum operations, and designing optimum completely positive maps for teleportation, can enable one to explore optimal…
We study universal quantum codes for entanglement-assisted quantum communication over compound quantum channels. In this setting, sender and receiver do not know the specific channel that will be used for communication, but only know the…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
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"…
We study how well topological quantum codes can tolerate coherent noise caused by systematic unitary errors such as unwanted $Z$-rotations. Our main result is an efficient algorithm for simulating quantum error correction protocols based on…
Quantum error correction (QEC) is an essential element of physical quantum information processing systems. Most QEC efforts focus on extending classical error correction schemes to the quantum regime. The input to a noisy system is embedded…
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…
The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…
Quantum Surface codes are a kind of quantum topological stabilizer codes whose stabilizers and qubits are geometrically related. Due to their special structures, surface codes have great potential to lead people to large-scale quantum…
This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit…