Simulation of error correction in quatum networks

OData support
Supervisor:
Dr. Bacsárdi László
Department of Networked Systems and Services

Quantum computing differs from classical computing in its core concepts. Instead

of the well known bit which can have two discrete values one or zero, quantum bits

(or qubits) are used. Qubits can be represented by a complex vector, which can take

infinite number of values, as far as certain requirements are made.

Transmission of qubits from one point to another is error prone just like in the

classical case, but qubits may have many different types of errors. For example,

a bit can flip, get a phase error, get depolarized, participle carrying the quantum

information can be lost etc. These may all affect any quantum operations afterwards

for example the measurement used to convert back to classical information from

qubits.

In the classical case, linear codes can be used to detect and correct errors on an

error prone channel. Usage of these codes in quantum computing is not possible beca-

use a quantum bit cannot be cloned. Instead a quantum phenomenon is relied called

entanglement. A multi qubit entangled states can be created from input qubit(s) and

sent, at receiver side errors are corrected (if possible), and finally state is decoded.

In our work, a simulation have been made capable of testing usual quantum er-

ror correcting codes (Bit-flip code, Shor code, Steane code, 5 qubit code) and

a special 4 qubit code for amplitude damping channels, using common channel

models like depolarizing or amplitude damping channel. The program runs in Linux

terminal and supports multithreading. Every single transmission’s measured ancilla

bits and result are logged to standard output for further analysis. Channel informa-

tion is read from a network descriptor file, this can be used to specify even a multi

error channel or larger network of communication participants.

Results suggest usage of 5 qubit code for depolarizing channel. If amplitude dam-

ping error is present, the codes used turned out to be worse than no coding or had

little effect. When both errors have some effects, Shor code was working decently

enough.

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