Quantum computing hardware is improving in robustness, but individual computers still have small number of qubits (for storing quantum information). Computations needing a large number of qubits can only be performed by distributing them over a network of smaller quantum computers. In this paper, we consider the problem of distributing a quantum computation, represented as a quantum circuit, over a homogeneous network of quantum computers, minimizing the number of communication operations needed to complete every step of the computation. We propose a two-step solution: dividing the given circuit’s qubits among the computers in the network, and scheduling communication operations, called migrations, to share quantum information among the computers to ensure that every operation can be performed locally. While the first step is an intractable problem, we present a polynomial-time solution for the second step in a special setting, and a O(log n)-approximate solution in the general setting. We provide empirical results which show that our two-step solution outperforms existing heuristic for this problem by a significant margin (up to 90%, in some cases).
Quantum computing hardware is improving in robustness, but individual computers still have small number of qubits (for storing quantum information). Computations needing a large number of qubits can only be performed by distributing them over a network of smaller quantum computers. In this paper, we consider the problem of distributing a quantum computation, represented as a quantum circuit, over a homogeneous network of quantum computers, minimizing the number of communication operations needed to complete every step of the computation. We propose a two-step solution: dividing the given circuit’s qubits among the computers in the network, and scheduling communication operations, called migrations, to share quantum information among the computers to ensure that every operation can be performed locally. While the first step is an intractable problem, we present a polynomial-time solution for the second step in a special setting, and a O(log n)-approximate solution in the general setting. We provide empirical results which show that our two-step solution outperforms existing heuristic for this problem by a significant margin (up to 90%, in some cases).
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.
Scalability is currently one of the most sought-after objectives in the field of quantum computing. Distributing a quantum circuit across a quantum network is one way to facilitate large computations using current quantum computers. In this paper, we consider the problem of distributing a quantum circuit across a network of heterogeneous quantum computers, while minimizing the number of teleportations (the communication cost) needed to implement gates spanning multiple computers. We design two algorithms for this problem. The first, called Local-Best, initially distributes the qubits across the network, then tries to teleport qubits only when necessary, with teleportations being influenced by gates in the near future. The second, called Zero-Stitching, divides the given circuit into sub-circuits such that each sub-circuit can be executed using zero teleportations and the teleportation cost incurred at the borders of the sub-circuits is minimal. We evaluate our algorithms over a wide range of randomly-generated circuits as well as known benchmarks, and compare their performance to prior work. We observe that our techniques outperform the prior approach by a significant margin (up to 50%).
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%.
When all the qubits needed for solving a problem are not located in a single quantum computer, qubits from different quantum computers can be collectively utilized. In this case, quantum communication is needed for the multiple quantum computers to communicate with each other. Several studies address the problem of minimizing the number of quantum communications when evaluating a general quantum circuit. The solutions proposed typically involve solving some intractable problems. In this paper, we show that we can obtain much better solutions when we focus on solving specific problems (instead of seeking solutions for generic circuits). Specifically, we consider several fundamental quantum circuits and identify communication protocols that need a much smaller number of communication steps than those offered by generic solutions. Our work is in line with traditional parallel and distributed computing research where typically scientists focus on solving specific problems (such as sorting, matrix multiplication, network flow, etc.) in a parallel or distributed setting.
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 up to 95%.