Quantum algorithms are usually described as monolithic circuits, becoming large at modest input size. Near-term quantum architectures can only manage a small number of qubits. We develop an automated method to distribute quantum circuits over multiple agents, minimising quantum communication between them. We reduce the problem to hypergraph partitioning and then solve it with state-of-the-art optimisers. This makes our approach useful in practice, unlike previous methods. Our implementation is evaluated on five quantum circuits of practical relevance.PACS numbers: 03.67.Ac; 03.67.Lx I. INTRODUCTIONQuantum computation [1-3] employs the laws of quantum mechanics to design systems capable of outperforming classical computers in certain problems [4][5][6]. Over the past couple of decades, this idea has rapidly developed from theoretical results into actual quantum technology [7][8][9].Although there are other approaches [10], the dominant way to present a quantum algorithm is as a quantum circuit [11]: a description of how quantum devices, chosen from a fixed finite set, are applied to different parts of the input system; see Figure 1 for an example. Each of the 'wires' that quantum devices act upon typically consist of a two level quantum system called a quantum bit or qubit. The qubit count grows with the input size, and for relevant problems such as the unique shortest vector problem (with applications in cryptography [12]) the circuit grows large: lattice dimension 3 already requires 842 qubits and 95,624 gates [13].Near-term quantum computing architectures are not capable of executing such large circuits. We are currently entering the era of Noisy Intermediate-Scale Quantum (NISQ) technology [14], being able to fabricate small quantum computing units (QPU for short) ranging from 10 to almost 100 qubits. Much effort is being dedicated to further increase the number of qubits that QPUs can manage, but as the number of qubits grows, the challenge of addressing each qubit individually and shielding them from unwanted interactions and decoherence rapidly becomes unmanageable [15]. To scale up beyond this point, researchers are proposing distributed quan-

A while loop tests a termination condition on every iteration. On a quantum computer, such measurements perturb the evolution of the algorithm. We define a while loop primitive using weak measurements, offering a trade-off between the perturbation caused and the amount of information gained per iteration. This trade-off is adjusted with a parameter set by the programmer. We provide sufficient conditions that let us determine, with arbitrarily high probability, a worst-case estimate of the number of iterations the loop will run for. As an example, we solve Grover's search problem using a while loop and prove the quadratic quantum speed-up is maintained.

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