Practical applications of quantum computers require millions of physical qubits and it will be challenging for individual quantum processors to reach such qubit numbers. It is therefore timely to investigate the resource requirements of quantum algorithms in a distributed setting, where multiple quantum processors are interconnected by a coherent network. We introduce an extension of the Message Passing Interface (MPI) to enable high-performance implementations of distributed quantum algorithms. In turn, these implementations can be used for testing, debugging, and resource estimation. In addition to a prototype implementation of quantum MPI, we present a performance model for distributed quantum computing, SENDQ. The model is inspired by the classical LogP model, making it useful to inform algorithmic decisions when programming distributed quantum computers. Specifically, we consider several optimizations of two quantum algorithms for problems in physics and chemistry, and we detail their effects on performance in the SENDQ model.

Quantum computers promise to perform certain computations exponentially faster than any classical device. Precise control over their physical implementation and proper shielding from unwanted interactions with the environment become more difficult as the space/time volume of the computation grows. Code optimization is thus crucial in order to reduce resource requirements to the greatest extent possible. Besides manual optimization, previous work has adapted classical methods such as constant-folding and common subexpression elimination to the quantum domain. However, such classically-inspired methods fail to exploit certain optimization opportunities across subroutine boundaries, limiting the effectiveness of software reuse. To address this insufficiency, we introduce an optimization methodology which employs annotations that describe how subsystems are entangled in order to exploit these optimization opportunities. We formalize our approach, prove its correctness, and present benchmarks: Without any prior manual optimization, our methodology is able to reduce, e.g., the qubit requirements of a 64-bit floating-point subroutine by 34×.

As quantum computers of non-trivial size become available in the near future, it is imperative to develop tools to emulate small quantum computers. This allows for validation and debugging of algorithms as well as exploring hardware-software co-design to guide the development of quantum hardware and architectures. The simulation of quantum computers entails multiplications of sparse matrices with very large dense vectors of dimension 2n, where n denotes the number of qubits, making this a memory-bound and network bandwidth-limited application. We introduce the concept of a quantum computer emulator as a component of a software framework for quantum computing, enabling a significant performance advantage over simulators by emulating quantum algorithms at a high level rather than simulating individual gate operations. We describe various optimization approaches and present benchmarking results, establishing the superiority of quantum computer emulators in terms of performance.