Application-specific quantum computers offer the most efficient means to tackle problems intractable by classical computers. Realizing these architectures necessitates a deep understanding of quantum circuit properties and their relationship to execution outcomes on quantum devices. Our study aims to perform for the first time a rigorous examination of quantum circuits by introducing graph theory-based metrics extracted from their qubit interaction graph and gate dependency graph alongside conventional parameters describing the circuit itself. This methodology facilitates a comprehensive analysis and clustering of quantum circuits. Furthermore, it uncovers a connection between parameters rooted in both qubit interaction and gate dependency graphs, and the performance metrics for quantum circuit mapping, across a range of established quantum device and mapping configurations. Among the various device configurations, we particularly emphasize modular (i.e., multi-core) quantum computing architectures due to their high potential as a viable solution for quantum device scalability. This thorough analysis will help us to: i) identify key attributes of quantum circuits that affect the quantum circuit mapping performance metrics; ii) predict the performance on a specific chip for similar circuit structures; iii) determine preferable combinations of mapping techniques and hardware setups for specific circuits; and iv) define representative benchmark sets by clustering similarly structured circuits.

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 of qubits, their scalability remains a significant challenge. Modular quantum computing architectures have emerged as a promising approach to scale up quantum computing systems. This paper 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.

Quantum algorithms, represented as quantum circuits, can be used as benchmarks for assessing the performance of quantum systems. Existing datasets, widely utilized in the field, suffer from limitations in size and versatility, leading researchers to employ randomly generated circuits. Random circuits are, however, not representative benchmarks as they lack the inherent properties of real quantum algorithms for which the quantum systems are manufactured. This shortage of `useful' quantum benchmarks poses a challenge to advancing the development and comparison of quantum compilers and hardware. This research aims to enhance the existing quantum circuit datasets by generating what we refer to as `realistic-looking' circuits by employing the Transformer machine learning architecture. For this purpose, we introduce KetGPT, a tool that generates synthetic circuits in OpenQASM language, whose structure is based on quantum circuits derived from existing quantum algorithms and follows the typical patterns of human-written algorithm-based code (e.g., order of gates and qubits). Our three-fold verification process, involving manual inspection and Qiskit framework execution, transformer-based classification, and structural analysis, demonstrates the efficacy of KetGPT in producing large amounts of additional circuits that closely align with algorithm-based structures. Beyond benchmarking, we envision KetGPT contributing substantially to AI-driven quantum compilers and systems.

Efficiently mapping quantum circuits onto hardware is an integral part of the quantum compilation process, wherein a circuit is modified in accordance with the stringent architectural demands of a quantum processor. Many techniques exist for solving the quantum circuit mapping problem, in addition to several theoretical perspectives that relate quantum circuit mapping to problems in classical computer science. This work considers a novel perspective on quantum circuit mapping, in which the routing process of a simplified circuit is viewed as a composition of quantum operations acting on density matrices representing the quantum circuit and processor. Drawing on insight from recent advances in quantum circuit complexity and information geometry, we show that a minimal SWAP-gate count for executing a quantum circuit on a device emerges via the minimization of the distance between quantum states using the quantum Jensen-Shannon divergence, which we dub the lightcone bound. Additionally, we develop a novel initial placement algorithm based on a graph similarity search that selects the partition nearest to a graph isomorphism between interaction and coupling graphs. From these two ingredients, we construct an algorithm for calculating the lightcone bound, which is directly compared alongside the IBM Qiskit compiler for over $600$ realistic benchmark experiments, as well as against a brute-force method for smaller benchmarks. In our simulations, we unambiguously find that neither the brute-force method nor the Qiskit compiler surpasses our bound, signaling utility for estimating minimal overhead when realizing quantum algorithms on constrained quantum hardware. This work also constitutes the first use of quantum circuit uncomplexity to practically-relevant quantum computing. We anticipate that this method may have diverse applicability outside of the scope of quantum information science.

Efficiently mapping quantum circuits onto hardware is an integral part of the quantum compilation process, wherein a quantum circuit is modified in accordance with the stringent architectural demands of a quantum processor. Many techniques exist for solving the quantum circuit mapping problem, many of which relate quantum circuit mapping to classical computer science. This work considers a novel perspective on quantum circuit mapping, in which the routing process of a simplified circuit is viewed as a composition of quantum operations acting on density matrices representing the quantum circuit and processor. Drawing on insight from recent advances in quantum information theory and information geometry, we show that a minimal SWAP gate count for executing a quantum circuit on a device emerges via the minimization of the distance between quantum states using the quantum Jensen-Shannon divergence. Additionally, we develop a novel initial placement algorithm based on a graph similarity search that selects the partition nearest to a graph isomorphism between interaction and coupling graphs. From these two ingredients, we then construct a polynomial-time algorithm for calculating the SWAP gate lower bound, which is directly compared alongside the IBM Qiskit compiler for over 600 realistic benchmark experiments, as well as against a brute-force method for smaller benchmarks. In our simulations, we unambiguously find that neither the brute-force method nor the Qiskit compiler surpass our bound, implying utility as a precise estimation of minimal overhead when realizing quantum algorithms on constrained quantum hardware. This work constitutes the first use of quantum circuit uncomplexity to practically-relevant quantum computing. We anticipate that this method may have diverse applicability outside of the scope of quantum information science, and we discuss several of these possibilities.

Modular quantum processor architectures are envisioned as a promising solution for the scalability of quantum computing systems beyond the Noisy Intermediate Scale Quantum (NISQ) devices era. Based upon interconnecting tens to hundreds of quantum cores via a quantum intranet, this approach unravels the pressing limitations of densely qubit-packed monolithic processors, mainly by mitigating the requirements of qubit control and enhancing qubit isolation, and therefore enables executing large-scale algorithms on quantum computers. In order to 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 also provide insights to improve the software and hardware stack for multi-core quantum computers. To this aim, we present a pioneering characterization of the spatio-temporal inter-core qubit traffic in large-scale circuits. The programs are executed 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 scalability of the presented algorithms, provide a set of guidelines to improve mapping quantum circuits to multi-core processors, and lay the foundations of benchmarking large-scale multi-core architectures.

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.

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.

Quantum many-core processors are envisioned as the ultimate solution for the scalability of quantum computers. Based upon Noisy Intermediate-Scale Quantum (NISQ) chips interconnected in a sort of quantum intranet, they enable large algorithms to be executed on current and close future technology. In order to optimize such architectures, it is crucial to develop tools that allow specific design space explorations. To this aim, in this paper we present a technique to perform a spatio-temporal characterization of quantum circuits running in multi-chip quantum computers. Specifically, we focus on the analysis of the qubit traffic resulting from operations that involve qubits residing in different cores, and hence quantum communication across chips, while also giving importance to the amount of intra-core operations that occur in between those communications. Using specific multi-core performance metrics and a complete set of benchmarks, our analysis showcases the opportunities that the proposed approach may provide to guide the design of multi-core quantum computers and their interconnects.

The progress in developing quantum hardware with functional quantum processors integrating tens of noisy qubits, together with the availability of near-term quantum algorithms has led to the release of the first quantum computers. These quantum computing systems already integrate different software and hardware components of the so-called “full-stack”, bridging quantum applications to quantum devices. In this paper, we will provide an overview on current full-stack quantum computing systems. We will emphasize the need for tight co-design among adjacent layers as well as vertical cross-layer design to extract the most from noisy intermediate-scale quantum (NISQ) processors which are both error-prone and severely constrained in resources. As an example of co-design, we will focus on the development of hardware-aware and algorithm-driven compilation techniques.