DMapS: End-to-end Qubit Mapping and Routing for Distributed Quantum Computing Architectures

Quantum noise is the key challenge in Noisy Intermediate-Scale Quantum (NISQ) computers. Previous work for mitigating noise has primarily focused on gate-level or pulse-level noise-adaptive compilation. However, limited research efforts have explored a higher level of optimization by making the quantum circuits themselves resilient to noise. We propose QuantumNAS, a comprehensive framework for noise-adaptive co-search of the variational circuit and qubit mapping. Variational quantum circuits are a promising approach for constructing QML and quantum simulation. However, finding the best variational circuit and its optimal parameters is challenging due to the large design space and parameter training cost. We propose to decouple the circuit search and parameter training by introducing a novel SuperCircuit. The SuperCircuit is constructed with multiple layers of pre-defined parameterized gates and trained by iteratively sampling and updating the parameter subsets (SubCircuits) of it. It provides an accurate estimation of SubCircuits performance trained from scratch. Then we perform an evolutionary co-search of SubCircuit and its qubit mapping. The SubCircuit performance is estimated with parameters inherited from SuperCircuit and simulated with real device noise models. Finally, we perform iterative gate pruning and finetuning to remove redundant gates. Extensively evaluated with 12 QML and VQE benchmarks on 14 quantum computers, QuantumNAS significantly outperforms baselines. For QML, QuantumNAS is the first to demonstrate over 95% 2-class, 85% 4-class, and 32% 10-class classification accuracy on real QC. It also achieves the lowest eigenvalue for VQE tasks on H2, H2O, LiH, CH4, BeH2 compared with UCCSD. We also open-source TorchQuantum (https://github.com/mit-han-lab/torchquantum) for fast training of parameterized quantum circuits to facilitate future research.

Quantum computing continues to face challenges in scaling both qubit quality and quantity, motivating the shift toward Distributed Quantum Computing (DQC), where multiple interconnected Quantum Processing Units (QPUs) collaboratively solve problems too complex for monolithic systems. In a quantum data center, QPUs distributed across racks can perform remote gate operations by creating entanglement between them, enabling circuit execution through DQC. However, generating end-to-end entangled pairs in a quantum data center often causes congestion and resource contention. To mitigate this, we introduce a resource management framework with efficient schedulers that maximize fidelity-guaranteed throughput while preserving the dependency constraints of sub-circuits derived from the original quantum circuit. We benchmark the scheduling problem using a MixedInteger Linear Programming (MILP) model and then propose a set of lightweight schedulers-Least Resource First (LRF) and its extension, Group LRF (GLRF). These lightweight schedulers provide practical, though less optimal, solutions for handling the high volume of remote gates in DQC workloads. Our initial results on a DCell-based quantum data center show that such heuristics perform well under current DQC conditions, balancing runtime and performance while avoiding the heavy overhead of solvers or machine learning approaches, which often struggle to meet the strict timing demands of short-lived entanglement.

The exploration of distributed quantum computing (DQC) represents a significant frontier in quantum information science, aiming to harness the unique properties of quantum mechanics to solve complex computational problems effectively. This paper discusses the diverse architectures and models that facilitate the distribution of quantum computing tasks across multiple quantum nodes, thereby addressing the limitations inherent in single quantum devices. DQC systems exploit the principles of superposition and entanglement to enhance computational capabilities beyond what classical computing systems can achieve. We examine various DQC architectures, including both quantum-classical hybrid systems and fully quantum distributed systems, highlighting their respective benefits and challenges. Key issues such as coherence, communication overhead, and error correction are discussed in detail, and we analyze specific use cases where DQC demonstrates superior performance relative to classical computing approaches, including optimization problems in logistics and finance, as well as quantum simulations for material science. Furthermore, we identify future research directions aimed at overcoming existing barriers to the practical implementation of DQC systems. By assessing the current landscape and future possibilities of DQC, this paper underscores the transformative potential of distributed quantum computing in various fields, paving the way for realizing more complex quantum algorithms and applications.

Scaling quantum computers, i.e., quantum processing units (QPUs) to enable the execution of large quantum circuits is a major challenge, especially for applications that should provide a quantum advantage over classical algorithms. One approach to scale QPUs is to connect multiple machines through quantum and classical channels to form clusters or even quantum networks. Using this paradigm, several smaller QPUs can collectively execute circuits that each would not be able on its own. However, communication between QPUs is costly as it requires generating and maintaining entanglement, and hence it should be used wisely. In this paper, we evaluate the architectures, and in particular the entanglement patterns, of variational quantum circuits in a distributed quantum computing (DQC) setting. That is, using Qiskit, we simulate the execution of an eight qubit circuit using four QPUs each with two computational and two communication qubits where non-local CX-gates are performed using the remote-CX protocol. We compare the performance of various circuits on a binary classification task where training is executed under ideal and testing under noisy conditions. The study provides initial results on suitable VQC architectures for the DQC paradigm, and indicates that a standard VQC baseline is not always the best choice, and alternative architectures that use entanglement between QPUs sparingly deliver better results under noise.

Near-term quantum computers will operate in a noisy environment, without error correction. A critical problem for near-term quantum computing is laying out a logical circuit onto a physical device with limited connectivity between qubits. This is known as the qubit mapping and routing (QMR) problem, an intractable combinatorial problem. It is important to solve QMR as optimally as possible to reduce the amount of added noise, which may render a quantum computation useless. In this paper, we present a novel approach for optimally solving the QMR problem via a reduction to maximum satisfiability (MAXSAT). Additionally, we present two novel relaxation ideas that shrink the size of the MAXSAT constraints by exploiting the structure of a quantum circuit. Our thorough empirical evaluation demonstrates (1) the scalability of our approach compared to state-of-the-art optimal QMR techniques (solves more than 3x benchmarks with 40x speedup), (2) the significant cost reduction compared to state-of-the-art heuristic approaches (an average of ~5x swap reduction), and (3) the power of our proposed constraint relaxations.

Distributed quantum computing has been well-known for many years as a system composed of a number of small-capacity quantum circuits. Limitations in the capacity of monolithic quantum computing systems can be overcome by using distributed quantum systems which communicate with each other through known communication links. In our previous study, an algorithm with an exponential complexity was proposed to optimize the number of qubit teleportations required for the communications between two partitions of a distributed quantum circuit (DQC). In this work, a genetic algorithm is used to solve the optimization problem in a more efficient way. The results are compared with the previous study and we show that our approach works almost the same with a remarkable speed-up. Moreover, the comparison of the proposed approach based on GA with a random search over the search space verifies the effectiveness of GA.

According to recent research on the brain and cognition, the microtubule level activities in the brain are in accordance with the quantum mechanical concepts. Consciousness is the emergent phenomenon of the brain’s subsystems and the quantum neural correlates. Based on the global work-space theory and traditional neural networks, investigations in machine consciousness and machine intelligence are reporting new techniques. In this study, a novel approach using circuit-based quantum neural network is proposed and simulated. This approach satisfies all the criteria of quantum computing and is tested for the exclusive OR (XOR) gate’s nonlinear learning. As a result of the use of quantum gates, various quantum circuits, such as quantum adders and subtractors, are also created and included in the designing and simulation of circuit of the quantum neural networks. Moreover, it is also argued that the proposed circuit of quantum neural network may also be tested and implemented on real quantum computer hardware. The present study also stresses the applicability of techniques of machine learning algorithms such as quantum and classical neural networks to various challenges of High Energy Physics.

Rapid development has taken place in quantum algorithms, but few of them can be implemented directly on the quantum computer because of the coupling constraint and high error rates of quantum computer operations. Transforming a circuit into an executable one on the quantum computer with the highest fidelity is an NP problem. Therefore, the algorithm tackling the mapping and routing problem of qubits is needed. Following the policy of VQA, a heuristic algorithm to solve the problem is proposed. The algorithm uses the error score derived from quantum operation’s error rate as the heuristic cost. Combining SWAP gates, physical CNOT gates, remote CNOT gates and inverse CNOT gates, the algorithm transforms the input circuit into an executable output circuit on the quantum computer with lower error score in acceptable execution time and moves forward from local optimal to global optimal.

A legend in computer architecture and perhaps best known as a pioneer of ideas that led to reduced instruction set computing, John Cocke has designed machines that still influence processor design today. In conjunction with his winning the inaugural Seymour Cray award, Computer interviewed Cocke in his Westchester, New York, home. Computer talked to Cocke about how he became interested in computers and the projects for which he is famous: the IBM Stretch, Advanced Computer System (ACS), and the 801, RS6000, and PowerPC processors. The project to build the 801 (one of the first RISC processors) used the code-name America. Cocke recounts how he chose the name based on a story about the first America's Cup yacht race. In the interview, Cocke expresses his opinions on the prospects for parallel computing, quantum computing, and future computer architectures.

Quantum computing has already demonstrated great computational potential across multiple domains and has received more and more attention. However, due to the connectivity limitations of Noisy Intermediate-Scale Quantum (NISQ) devices, most of the quantum algorithms cannot be directly executed without the help of inserting SWAP gates. Nevertheless, more SWAP gates lead to a longer execution time and, inevitably, lower fidelity of the algorithm. To this end, this paper proposes an optimized qubit mapping algorithm based on a dynamic look-ahead strategy to minimize the number of SWAP gates inserted. Firstly, a heuristic algorithm is proposed based on maximizing physical qubit connectivity to generate the optimal initial qubit mapping, which reduces the need for logical qubit shifts during subsequent SWAP gate insertion. Secondly, in the form of directed acyclic graphs, we identify quantum gates that violate the constraints of physical coupling and insert SWAP gates to remap qubits, thereby overcoming the limitations of qubit interactions. Finally, the optimal SWAP gate insertion strategy is built by comparing the cost of different SWAP gate insertion strategies through a multi-window look-ahead strategy to reduce the number of SWAP gates inserted. The experimental results show that the strategy in this paper decreases the number of SWAP gate insertions and significantly reduces the depth of quantum circuits when performing qubit mapping compared with state-of-the-art methods.

Recently it has become clear, that a key issue in quantum computation is understanding how interaction with the environment, or decoherence, affects the computational power of quantum computers. We adopt the standard physical method of describing systems which are interwound with their environment by density matrices, and within this framework define a model of decoherence in quantum computation. Our results show that the computational power of decohered quantum computers depends strongly on the amount of parallelism in the computation. We first present a simulation of decohered sequential quantum computers, on a classical probabilistic Turing machine, and prove that the expected slowdown of this simulation is polynomial in time and space of the quantum computation, for any non zero decoherence rate. Similar results hold for quantum computers that are allowed to operate on logarithmic number of qubits at a time. For decohered quantum circuits (with local gates), the situation is more subtle and depends on the decoherence rate, /spl eta/. We find that our simulation is efficient for circuits with decoherence rate /spl eta/ higher than some constant /spl eta//sub 1/ but exponential for a general (random) circuit subjected to decoherence rate lower than some constant /spl eta//sub 2/. The transition from exponential cost to polynomial cost happens in a short range of decoherence rates. We use computer experiments to exhibit the phase transitions in various quantum circuits.

An efficient quantum circuit (program) compiler aims to minimize the gate-count - through efficient instruction translation, routing, gate, and cancellation - to improve run-time and noise. Therefore, a high-efficiency compiler is paramount to enable the game-changing promises of quantum computers. To date, the quantum computing hardware providers are offering a software stack supporting their hardware. However, several third-party software toolchains, including compilers, are emerging. They support hardware from different vendors and potentially offer better efficiency. As the quantum computing ecosystem becomes more popular and practical, it is only prudent to assume that more companies will start offering software-as-a-service for quantum computers, including high-performance compilers. With the emergence of third-party compilers, the security and privacy issues of quantum intellectual properties (IPs) will follow. A quantum circuit can include sensitive information such as critical financial analysis and proprietary algorithms. Therefore, submitting quantum circuits to untrusted compilers creates opportunities for adversaries to steal IPs. In this paper, we present a split compilation methodology to secure IPs from untrusted compilers while taking advantage of their optimizations. In this methodology, a quantum circuit is split into multiple parts that are sent to a single compiler at different times or to multiple compilers. In this way, the adversary has access to partial information. With analysis of over 152 circuits on three IBM hardware architectures, we demonstrate the split compilation methodology can completely secure IPs (when multiple compilers are used) or can introduce factorial time reconstruction complexity while incurring a modest overhead (~ 3% to ~ 6% on average).

Distributed quantum computing relies on coordinated operations between remote quantum processing units (QPUs), yet most existing work either assumes full connectivity, unrealistic for large networks, or relies on entanglement swapping. To mitigate the overhead of communication, we propose a scheme for the distribution of collective quantum operations among remote quantum processing units by exploiting distributed fan-out operations to a central node in network architectures similar to those used for high-performance computing, which requires only pre-shared entanglement, local operations and classical communication. We show that a general diagonal gate can be distributed among any number of nodes and provide the ebit cost bounds. For a single distributed multicontrolled gate, this amounts to a single additional Bell pair over the theoretically optimal calculation with all-to-all pre-shared entanglement, demonstrating better scalability when compared to current proposals based on entanglement swapping through a network. We provide a recipe for the lumped distribution of gates such as arbitrarily-sized Toffoli and multicontrolled Z, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{zz}(\theta)$</tex-math></inline-formula> gates. Finally, we provide an exact implementation of a distributed Grover's search algorithm using this protocol to partition the circuit, with Bell pair cost growing linearly with the number of Grover iterations and the number of partitions, and show how these techniques can be applied to other algorithms such as QAOA. Our results show that alternative approaches to entanglement swapping can provide major benefits in distributed quantum computing, pointing to promising avenues for future research.

In order to solve the problem of mapping a quantum circuit to IBM QX architecture and satisfy connectivity constraints. This paper presents a mapping method, which is divided into two parts: Qubit initial mapping and Nearest-neighbor optimization. To solve the problem of initial mapping of qubits, according to the execution order and interaction of quantum gates in quantum circuit, a qubit mapping order method based on the weight of qubits is proposed. Then, according to the qubit interaction degree in the coupling graph, the initial qubit mapping is completed. In order to solve the nearest-neighbor problem in the mapping process, the quantum cost of non-neighbor two-qubit gate is determined by introducing the lookahead quantum cost method. Our algorithm is evaluated on IBM Q 20. Experimental results show that the proposed algorithm can effectively complete the mapping task even in large-scale benchmark tests. The proposed method is verified by experiments and compared with the existing methods, the optimized results were obtained in 74% of the test circuits.

This paper designs quantum testing circuit to detect intermediate malicious node and achieve message integrity in the distributed quantum computing. The proposed mechanism has several improvements shown as follows. The random key generation between Alice and Bob such that an attack cannot break this deriving process. Local unitary operations and quantum teleportation in the entangled particles can be used to transfer quantum information in a secure way. For intermediate node has no capability to differentiate which qubit is quantum superposition state or quantum entangled state. In regard to node detection, the receiver has the capability to judge whether intermediate node is honest or not by using quantum testing circuit. Based on this physical property, quantum circuit could be detect malicious node and achieve message integrity. The proposed circuit is scalable.