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.

Near-term quantum computers will soon reach sizes that are challenging to directly simulate, even when employing the most powerful supercomputers. Yet, the ability to simulate these early devices using classical computers is crucial for calibration, validation, and benchmarking. In order to make use of the full potential of systems featuring multi- and many-core processors, we use automatic code generation and optimization of compute kernels, which also enables performance portability. We apply a scheduling algorithm to quantum supremacy circuits in order to reduce the required communication and simulate a 45-qubit circuit on the Cori II super-computer using 8, 192 nodes and 0.5 petabytes of memory. To our knowledge, this constitutes the largest quantum circuit simulation to this date. Our highly-tuned kernels in combination with the reduced communication requirements allow an improvement in time-to-solution over state-of-the-art simulations by more than an order of magnitude at every scale.

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.