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 re-source 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%.
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 re-source 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%.
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%.
Distributing quantum circuits across a network of quantum devices is a recent approach to improve the scalability of quantum computation. Entangled pairs of qubits distributed across network nodes are used as a communication resource for executing inter-node (remote) gates. However, establishing these entanglement pairs incurs significant latency, and doing so during the circuit's execution may lead to the decoherence of logical qubits. Instead, it may be beneficial to distribute certain entanglement pairs before the circuit is executed. Thus, we consider the problem of distributing a quantum circuit across a quantum network containing some pre-distributed entanglement pairs and seek to minimize the execution time of the circuit.
We address this problem in three steps. First, given the quantum network and (optionally) a probability distribution over training circuits, we determine a set of pre-distributed entanglement pairs under a specified budget. Second, we compute a qubit-to-memory allocation that minimizes the expected execution time given these pre-distributed resources. Finally, we identify any additional entanglement pairs required during execution, generate them concurrently, and execute the circuit gates. We evaluate our methods on a broad range of benchmark circuits.
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 40 to 50% on average and up to 95% in some cases.
Distribution of quantum circuits (DQC) is a promising strategy to enable large-scale quantum computations by utilizing a network of quantum computers. However, executing distributed quantum programs entails generating entanglements (to execute remote gates), which can incur significant latency and lead to qubits’ decoherence. Prior works on the problem of distributing quantum circuits with minimum circuit-execution time have only considered a static allocation of qubits to network nodes, presumably for simplicity. In this work, we show that distributing quantum circuits with a dynamic allocation of qubits, i.e., qubit allocation (over the quantum computers) that changes during the circuit execution, can lower circuit execution time. For this DQC problem wherein qubit allocation can be dynamic (i.e., change over time), we design efficient algorithms and demonstrate the effectiveness of designed techniques via extensive simulations over NetSquid, a quantum network simulator; our techniques outperform the best prior work (using static qubit allocation) by up to 50%.
As quantum computing continues to scale, the ability to execute quantum circuits across distributed quantum networks is becoming increasingly important. While prior work has largely focused on distributing a single circuit to optimize the number of entanglement pairs (EPs) used or the execution time, future applications will require the efficient scheduling and execution of multiple circuits on a shared quantum network. Therefore, we study the problem of efficiently distributing multiple quantum circuits across a shared quantum network under decoherence and network constraints and seek to minimize the execution time required to execute all circuits (makespan). Solving the above problem involves jointly determining when and where each circuit should be executed, and how to schedule concurrent EP generation required to execute remote gates. We propose several algorithmic approaches for this multi-circuit distribution problem and provide theoretical performance guarantees for special cases. To assess the practical effectiveness of our methods, we conduct extensive simulations using the NetSquid quantum network simulator.
Near-term quantum computers can hold only a small number of qubits. One way to facilitate large-scale quantum computations is through a distributed network of quantum computers. In this work, we consider the problem of distributing quantum programs represented as quantum circuits across a quantum network of heterogeneous quantum computers, in a way that minimizes the overall communication cost required to execute the distributed circuit. We consider two ways of communicating: cat-entanglement that creates linked copies of qubits across pairs of computers, and teleportation. The heterogeneous computers impose constraints on cat-entanglement and teleportation operations that can be chosen by an algorithm. We first focus on a special case that only allows cat-entanglements and not teleportations for communication. We provide a two-step heuristic for solving this specialized setting: (i) finding an assignment of qubits to computers using Tabu search, and (ii) using an iterative greedy algorithm designed for a constrained version of the set cover problem to determine cat-entanglement operations required to execute gates locally. For the general case, which allows both forms of communication, we propose two algorithms that subdivide the quantum circuit into several portions and apply the heuristic for the specialized setting on each portion. Teleportations are then used to stitch together the solutions for each portion. Finally, we simulate our algorithms on a wide range of randomly generated quantum networks and circuits, and study the properties of their results with respect to several varying parameters.