Quantum bit commitment on IBM QX

Abstract

Quantum bit commitment (QBC) is a quantum version of the classical bit commitment security primitive. As other quantum security primitives and protocols, QBC improves on cheating detection over its classical counterpart. The implementation of the QBC protocol below relies on the use of common quantum gates: the Hadamard gate used for orthonormal bases and the CNOT gate used to swap qubits. The protocol was run and tested on IBM quantum experience (IBM QX). IBM QX offers two different quantum environments: as a simulator and as a real quantum machine. In our implementation, honest and dishonest participants were considered. Results of both the simulation and the quantum execution were compared against the theoretical expectations. The IBM QX simulator gives results that match the theoretical model. The IBM QX real computer deviates from the expected behavior by a measurable amount. Using the standard deviation and the Hamming distance, the conclusion is that the quantum computer is usable as the difference to the simulator is within an acceptable margin of error. The QBC protocol of choice is fully secure against cheating by Bob. The only way Alice can cheat is using multi-dimensional entanglement. The cost for Alice to cheat is exponential in the number of qubits used, namely O(2 6n+3k+1).