  Present quantum computers are constrained by limited qubit capacity and
restricted physical connectivity, leading to challenges in large-scale quantum
computations. Distributing quantum computations across a network of quantum
computers is a promising way to circumvent these challenges and facilitate
large quantum computations. However, distributed quantum computations require
entanglements (to execute remote gates) which can incur significant generation
latency and, thus, lead to decoherence of qubits. In this work, we consider the
problem of distributing quantum circuits across a quantum network to minimize
the execution time. The problem entails mapping the circuit qubits to network
memories, including within each computer since limited connectivity within
computers can affect the circuit execution time. We provide two-step solutions
for the above problem: In the first step, we allocate qubits to memories to
minimize the estimated execution time; for this step, we design an efficient
algorithm based on an approximation algorithm for the max-quadratic-assignment
problem. In the second step, we determine an efficient execution scheme,
including generating required entanglements with minimum latency under the
network resource and decoherence constraints; for this step, we develop two
algorithms with appropriate performance guarantees under certain settings or
assumptions. We consider multiple protocols for executing remote gates, viz.,
telegates and cat-entanglements. With extensive simulations over NetSquid, a
quantum network simulator, we demonstrate the effectiveness of our developed
techniques and show that they outperform a scheme based on prior work by up to
95%.
