Quantum implementation of the Shor-code on multiple simulator platforms

Abstract

Running general quantum algorithms on quantum computers is hard, especially in the early stage of development of the quantum computer that we are in today. Many resources are required to transform a general problem to be run on a quantum computer, for instance to satisfy the topology constraints of the quantum hardware. Furthermore, quantum computers need to operate at temperatures close to absolute zero, and hence resources are required to keep the quantum hardware at that level. Therefore, simulating small instances of a quantum algorithm is often preferred over running it on actual quantum hardware. This is both cheaper and gives debugging capabilities which are unavailable on actual quantum hardware, such as the evaluation of the full quantum state, at intermediate points in the algorithm as well as at the end of the algorithm. By simulating small instances of quantum algorithms, the quantum algorithm can be checked for errors and be debugged before implementing and running it on actual quantum hardware for larger instances. There are multiple initiatives to create quantum simulators and while looking alike, there are difference among them. In this work we compare seven often used quantum simulators offered by various parties by implementing the Shor-code, an error-correcting technique. The Shor-code can detect and correct all single qubit errors in a quantum circuit. For most multi-qubit errors, correct detection and correction is not possible. We compare the seven quantum simulators on different aspects, such as how easy it is to implement the Shor-code, what its capabilities are regarding translation to actual quantum hardware and what the possibilities of simulating noise are. We also discuss aspects such as topology restrictions and the programming interface.