A viable approach for building large-scale quantum computers is to interlink small-scale quantum computers with a quantum network to create a larger distributed quantum computer. When designing quantum algorithms for such a distributed quantum computer, one can make use of the added parallelization and distribution abilities inherent in such a system. An added difficulty to consider for distributed quantum computing is that a complex control system to orchestrate the various components is required. In this work, we present distributed and parallel versions of quantum algorithms and discuss potential benefits and we propose a general scheme for controlling the system. Further, we present the Interlin-q simulation platform which aims to simplify designing and simulating parallel and distributed quantum algorithms. Interlin-q's main features are generating and executing control instructions across a simulated quantum network of simulated quantum computers. We demonstrate a simulation of a proposed parallelized algorithm using Interlin-q and discuss steps for developing Interlin-q into a control system for distributed quantum computers.
We explicitly derive a connection between quantum circuits utilising IBM's quantum gate set and multivariate quadratic polynomials over integers modulo 8. We demonstrate that the action of a quantum circuit over input qubits can be written as generalized Walsh-Hadamard transform. Here, we derive the polynomials corresponding to implementations of the Swap gate and Toffoli gate using IBM-Q gate set.
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