arXiv:2305.06687 · IEEE International Conference on Quantum Computing and Engineering (QCE)
Mapping Quantum Circuits to Modular Architectures with QUBO
Medina Bandić, Luise Prielinger, Jonas Nüßlein, Anabel Ovide, Santiago Rodrigo, Sergi Abadal, Hans van Someren, Gayane Vardoyan, Eduard Alarcón, Carmen G. Almudéver, Sebastian Feld
Modular quantum computing architectures are a promising alternative to monolithic QPU (Quantum Processing Unit) designs for scaling up quantum devices. They refer to a set of interconnected QPUs or cores consisting of tightly coupled quantum bits that can communicate via quantum-coherent and classical links. In multi-core architectures, it is crucial to minimize the amount of communication between cores when executing an algorithm. Therefore, mapping a quantum circuit onto a modular architecture involves finding an optimal assignment of logical qubits (qubits in the quantum circuit) to different cores with the aim to minimize the number of expensive inter-core operations while adhering to given hardware constraints. In this paper, we propose for the first time a Quadratic Unconstrained Binary Optimization (QUBO) technique to encode the problem and the solution for both qubit allocation and inter-core communication costs in binary decision variables. To this end, the quantum circuit is split into slices, and qubit assignment is formulated as a graph partitioning problem for each circuit slice. The costly inter-core communication is reduced by penalizing inter-core qubit communications. The final solution is obtained by minimizing the overall cost across all circuit slices. To evaluate the effectiveness of our approach, we conduct a detailed analysis using a representative set of benchmarks having a high number of qubits on two different multi-core architectures. Our method showed promising results and performed exceptionally well with very dense and highly-parallelized circuits that require on average 0.78 inter-core communications per two-qubit gate.
Modular quantum computing architectures are a promising alternative to monolithic QPU (Quantum Processing Unit) designs for scaling up quantum devices. They refer to a set of interconnected QPUs or cores consisting of tightly coupled quantum bits that can communicate via quantum-coherent and classical links. In multi-core architectures, it is crucial to minimize the amount of communication between cores when executing an algorithm. Therefore, mapping a quantum circuit onto a modular architecture involves finding an optimal assignment of logical qubits (qubits in the quantum circuit) to different cores with the aim to minimize the number of expensive inter-core operations while adhering to given hardware constraints. In this paper, we propose for the first time a Quadratic Unconstrained Binary Optimization (QUBO) technique to encode the problem and the solution for both qubit allocation and inter-core communication costs in binary decision variables. To this end, the quantum circuit is split into slices, and qubit assignment is formulated as a graph partitioning problem for each circuit slice. The costly inter-core communication is reduced by penalizing inter-core qubit communications. The final solution is obtained by minimizing the overall cost across all circuit slices. To evaluate the effectiveness of our approach, we conduct a detailed analysis using a representative set of benchmarks having a high number of qubits on two different multi-core architectures. Our method showed promising results and performed exceptionally well with very dense and highly-parallelized circuits that require on average 0.78 inter-core communications per two-qubit gate.
Quantum computing platforms are evolving to a point where placing high numbers of qubits into a single core comes with certain difficulties such as fidelity, crosstalk, and high power consumption of dense classical electronics. Utilizing distributed cores, each hosting logical data qubits and logical ancillas connected via classical and quantum communication channels, offers a promising alternative. However, building such a system for logical qubits requires additional optimizations, such as minimizing the amount of state transfer between cores for inter-core two-qubit gates and optimizing the routing of magic states distilled in a magic state factory. In this work, we investigate such a system and its statistics in terms of classical and quantum resources. First, we restrict our quantum gate set to a universal gate set consisting of CNOT, H, T, S, and Pauli gates. We then developed a framework that can take any quantum circuit, transpile it to our gate set using Qiskit, and then partition the qubits using the KaHIP graph partitioner to balanced partitions. Afterwards, we built an algorithm to map these graphs onto the 2D mesh of quantum cores by converting the problem into a Quadratic Assignment Problem with Fixed Assignment (QAPFA) to minimize the routing of leftover two-qubit gates between cores and the total travel of magic states from the magic state factory. Following this stage, the gates are scheduled using an algorithm that takes care of the timing of the gate set. As a final stage, our framework reports detailed statistics such as the number of classical communications, the number of EPR pairs and magic states consumed, and timing overheads for pre- and post- processing for inter-core state transfers. These results help to quantify both classical and quantum resources that are used in distributed logical quantum computing architectures.
Quantum computing represents a paradigm shift in computation, offering the potential to solve complex problems intractable for classical computers. Although current quantum processors already consist of a few hundred qubits, their scalability remains a significant challenge. Modular quantum computing architectures have emerged as a promising approach to scale up quantum computing systems. This article delves into the critical aspects of distributed multi-core quantum computing, focusing on quantum circuit mapping, a fundamental task to successfully execute quantum algorithms across cores while minimizing inter-core communications. We derive the theoretical bounds on the number of non-local communications needed for random quantum circuits and introduce the Hungarian Qubit Assignment (HQA) algorithm, a multi-core mapping algorithm designed to optimize qubit assignments to cores with the aim of reducing inter-core communications. Our exhaustive evaluation of HQA against state-of-the-art circuit mapping algorithms for modular architectures reveals a 4.9× and 1.6× improvement in terms of execution time and non-local communications, respectively, compared to the best-performing algorithm. HQA emerges as a very promising scalable approach for mapping quantum circuits into multi-core architectures, positioning it as a valuable tool for harnessing the potential of quantum computing at scale.
Current monolithic quantum computer architectures have limited scalability. One promising approach for scaling them up is to use a modular or multi-core architecture, in which different quantum processors (cores) are connected via quantum and classical links. This new architectural design poses new challenges such as the expensive inter-core communication. To reduce these movements when executing a quantum algorithm, an efficient mapping technique is required. In this paper, a detailed critical discussion of the quantum circuit mapping problem for multi-core quantum computing architectures is provided. In addition, we further explore the performance of a mapping method, which is formulated as a partitioning over time graph problem, by performing an architectural scalability analysis.
Modular quantum processor architectures are envisioned as a promising solution for the scalability of quantum computing systems beyond the Noisy Intermediate Scale Quantum (NISQ) era. Based upon interconnecting tens to hundreds of quantum processors (i.e cores) via quantum coherent and classical links, this approach unravels the pressing limitations of densely qubit-packed monolithic processors, mainly by mitigating the requirements of qubit control and enhancing qubit isolation. Therefore, this new architectural design enables executing large-scale algorithms in a distributed manner. In order to assess the performance and optimize such architectures, it is crucial to analyze the quantum state transfers occurring via inter-core communication networks, referred to as inter-core qubit traffic. This would provide insights to improve the software and hardware stack for multi-core quantum computers. To this aim, we present a characterization of the spatio-temporal inter-core qubit traffic for different large-scale quantum algorithms. The programs are compiled on an all-to-all connected multi-core architecture that supports up to around 1000 qubits. We characterize the qubit traffic based on multiple performance metrics to assess the computational process and the communication overhead. Based on the showcased results, we conclude on the parallelization and scalability of presented algorithms, qualitatively evaluate the resource requirements as we scale circuit sizes, and lay the foundations of application-oriented benchmarking of large-scale multi-core architectures.
Modular quantum computing architectures offer a promising alternative to monolithic designs for overcoming the scaling limitations of current quantum computers. To achieve scalability beyond small prototypes, quantum architectures are expected to adopt a modular approach, featuring clusters of tightly connected quantum bits with sparser connections between these clusters. Efficiently distributing qubits across multiple processing cores is critical for improving quantum computing systems' performance and scalability. To address this challenge, we propose the Hungarian Qubit Assignment (HQA) algorithm, which leverages the Hungarian algorithm to improve qubit-to-core assignment. The HQA algorithm considers the interactions between qubits over the entire circuit, enabling fine-grained partitioning and enhanced qubit utilization. We compare the HQA algorithm with state-of-the-art alternatives through comprehensive experiments using both real-world quantum algorithms and random quantum circuits. The results demonstrate the superiority of our proposed approach, outperforming existing methods, with an average improvement of 1.28×.
Abstract Modular quantum architectures have emerged as a promising approach for scaling quantum computing systems by connecting multiple Quantum Processing Units (QPUs). However, this approach introduces significant challenges due to costly inter-core operations between chips and quantum state transfers, which contribute to noise and quantum decoherence. This paper presents QARMA, a novel Qubit mapping using Attention-based deep Reinforcement learning (DRL) for Modular quantum Architectures, along with its extension QARMA-R that incorporates dynamic qubit reuse capabilities. Our approach combines an attention-based mechanism with Graph Neural Networks (GNN) to learn optimal qubit allocation, routing, and reuse strategies that minimize inter-core communications.Our experimental results show significant improvements over state-of-the-art approaches. Compared to highly-optimized Qiskit with modular architecture configuration, QARMA-R reduces inter-core communications by up to 100% (on average 86%), while QARMA maintains 15-40% improvement for larger circuits without reuse. Against traditional modular qubit mapping, our approach achieves 97-100% reduction in inter-core operation.The proposed methods advance quantum circuit compilation techniques and enable the execution of more extensive quantum algorithms on resource-constrained modular quantum systems, contributing to the growing body of research on scalable quantum computing architectures.