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.
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.
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.
By connecting multiple quantum computers (QCs) through classical and quantum channels, a quantum communication network can be formed. This gives rise to new applications such as blind quantum computing, distributed quantum computing, and quantum key distribution. In distributed quantum computing, QCs collectively perform a quantum computation. As each device only executes a sub-circuit with fewer qubits than required by the complete circuit, a number of small QCs can be used in combination to execute a large quantum circuit that a single QC could not solve on its own. However, communication between QCs may still occur. Depending on the connectivity of the circuit, qubits must be teleported to different QCs in the network, adding overhead to the actual computation; thus, it is crucial to minimize the number of teleportations. In this paper, we propose an evolutionary algorithm for this problem. More specifically, the algorithm assigns qubits to QCs in the network for each time step of the circuit such that the overall teleportation cost is minimized. Moreover, network-specific constraints such as the capacity of each QC in the network can be taken into account. We run experiments on random as well as benchmarking circuits and give an outline on how this method can be adjusted to be incorporated into more realistic network settings as well as in compilers for distributed quantum computing. Our results show that an evolutionary algorithm is well suited for this problem when compared to the graph partitioning approach as it delivers better results while simultaneously allows the easy integration and consideration of various problem-specific constraints.
Quantum computing has exciting potential but a current technological hurdle lies in the limited number of qubits in a single processor. One way to address this challenge is to assemble small, specialized quantum processors into a larger computing system, named distributed quantum computing. In this work, we focus on a key problem in distributed quantum computing: how to map logical qubits of a specific quantum circuit to different processors in a heterogeneous quantum network with the goal of minimizing the overall communication overhead. To solve this problem, we formulate a probability-aware qubit-to-processor mapping model, where the communication overhead between each pair of processors is determined through probabilistic analyses based on the link entanglement generation rates. We also introduce a multi-flow routing protocol in our model to improve the overall entanglement rates. Afterward, we employ a multistage hybrid simulated annealing algorithm to minimize the total communication overhead. Lastly, we perform extensive simulations to show the superiority of our solutions under a wide range of system settings.
The emerging paradigm of distributed quantum computing promises a potential solution to scaling quantum computing to currently unfeasible dimensions. While this approach itself is still in its infancy, and many obstacles must still be overcome before its physical implementation, challenges from the software and algorithmic side must also be identified and addressed. For instance, this paradigm shift requires a new form of compiler that considers the network constraints in general as well as phenomena arising due to the nature of quantum communication. In distributed quantum computing, large circuits are divided into smaller subcircuits such that they can be executed individually and simultaneously on multiple QPUs that are connected through quantum channels. As quantum communication, for example, in the form of teleportation, is expensive, it must be used sparingly. We address the problem of assigning qubits to QPUs to minimize communication costs in two different ways. First by applying time-aware algorithms that take into account the changing connectivity of a given circuit as well as the underlying network topology. We define the optimization problem, use simulated annealing and an evolutionary algorithm and compare the results to graph partitioning and sequential qubit assignment baselines. In another approach, we propose an evolutionary-based quantum circuit optimization algorithm that adjusts the circuit itself rather than the schedule to reduce the overall communication cost. We evaluate the techniques against random circuits and different network topologies. Both evolutionary algorithms outperform the baseline in terms of communication cost reduction. We give an outlook on how the approaches can be integrated into a compilation framework for distributed quantum computing.
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.