This work addresses the complexities involved in designing distributed quantum algorithms, highlighting that quantum entanglement does not bypass the Fischer-Lynch-Paterson (FLP) impossibility theorem in asynchronous networks. Although quantum resources such as entanglement offer potential speedups, the inherent constraints of classical communication remain. We develop a leader election algorithm as a proof of concept, demonstrating how entanglement can enhance efficiency while still contending with asynchronous delays. This algorithm serves as a foundation for a broader blueprint for future distributed quantum algorithms, providing insights into both the real performance gains and the limitations that entanglement offers in a distributed setting.
This work addresses the complexities involved in designing distributed quantum algorithms, highlighting that quantum entanglement does not bypass the Fischer-Lynch-Paterson (FLP) impossibility theorem in asynchronous networks. Although quantum resources such as entanglement offer potential speedups, the inherent constraints of classical communication remain. We develop a leader election algorithm as a proof of concept, demonstrating how entanglement can enhance efficiency while still contending with asynchronous delays. This algorithm serves as a foundation for a broader blueprint for future distributed quantum algorithms, providing insights into both the real performance gains and the limitations that entanglement offers in a distributed setting.
Quantum computing and distributed systems may enter a mutually beneficial partnership in the future. On the one hand, it is much easier to build a number of small quantum computers rather than a single large one. On the other hand, the best results concerning some of the fundamental problems in distributed computing can potentially be dramatically improved upon by taking advantage of the superior resources and processing power that quantum mechanics offers. This survey has the purpose to highlight both of these benefits. We first review the current results regarding the implementation of arbitrary quantum algorithms on distributed hardware. We then discuss existing proposals for quantum solutions of leader election - a fundamental problem from distributed computing. Quantum mechanics allows leader election to be solved with no communication, provided that certain pre-shared entanglement is already in place. Further, an impossibility result from classical distributed computing is circumvented by the quantum solution of anonymous leader election - a unique leader is elected in finite time with certainty. Finally, we discuss the viability of these proposals from a practical perspective. Although, theoretically, distributed quantum computing looks promising, it is still unclear how to build quantum hardware and how to create and maintain robust large-scale entangled states. Moreover, it is not clear whether the costs of creating entangled states and working with them are smaller than the costs of existing classical solutions.
This article gives a separation between quantum and classical models in pure (i.e., noncryptographic) computing abilities with no restriction on the amount of available computing resources, by considering the exact solvability of the leader election problem in anonymous networks, a celebrated unsolvable problem in classical distributed computing. The goal of the leader election problem is to elect a unique leader from among distributed parties. In an anonymous network, all parties with the same number of communication links are identical. It is well-known that no classical algorithm can exactly solve (i.e., in bounded time without error) the leader election problem in anonymous networks, even if the number of parties is given. This article devises a quantum algorithm that, if the number of parties is given, exactly solves the problem for any network topology in polynomial rounds with polynomial communication/time complexity with respect to the number of parties, when the parties are connected with quantum communication links and they have the ability of quantum computing. Our algorithm works even when only an upper bound of the number of parties is given. In such a case, no classical algorithm can solve the problem even under the zero-error setting, the setting in which error is not allowed but running time may be unbounded.
Distributed consensus is possible for asynchronous communication networks when assisted by quantum mechanical effects. Previous results are extended to show that consensus is possible even in the presence of byzantine process failures. This result directly contradicts the FLP impossibility result which states that distributed consensus is impossible when even one faulty networked process exists in the group. PODC’08, August 18–21, 2008, p445, Toronto, Ontario, Canada. ACM 978-1-59593-9890/08/08. 1. DISTRIBUTED COMPUTING IS PHYSICAL Distributed computing is concerned with what can be accomplished using systems of networked processors. As with all information processing devices, these systems are necessarily physical and ultimately bound by the laws of physics[Land88]. Therefore, when proving impossibility results and bounds on algorithmic efficiency, it only makes sense to consider the possibilities offered, not only by classical information processing, but also the effects of quantum mechanics[NC00]. Recent results have shown that shared quantum resources make problems like anonymous leader election and distributed consensus possible under conditions where no classical algorithm could perform the same tasks[DP06]. These results are extended here to show that shared quantum resources allow fault-tolerant consensus in direct contradiction of previous impossibility results[FLP85]. Although this research is largely self-contained, a basic understanding of distributed computing is assumed of the reader along with a passing understanding of linear algebra which is necessary to understand the reasoning behind the algorithm detailed in section 4. A thorough understanding of quantum mechanics is recommended, although a reference of the specific quantum mechanical notation required to follow later reasoning in section 4 is detailed in section 3. A computer scientist unfamiliar with quantum mechanics would be well served to reference chapter 2 of [NC00] in order to gain a deeper understanding of the notation covered in section 3 of this paper. Likewise, a quantum physicist would be well served to reference chapter 15 of [Garg04] to more deeply understand the fault modeling of distributed computing covered in section 2 and section 5.
We present new distributed quantum algorithms for fundamental distributed computing problems, namely, leader election, broadcast, Minimum Spanning Tree (MST), and Breadth-First Search (BFS) tree, in arbitrary networks. These algorithms are (essentially) optimal with respect to their communication (message) complexity in the {\em quantum routing model} introduced in [PODC 2025]. The message complexity of our algorithms is O~(n) for leader election, broadcast, and MST, and O~(mn) for BFS (n and m are the number of nodes and edges of the network, respectively). These message bounds are nearly tight in the quantum routing model since we show almost matching corresponding quantum message lower bounds.
Our results significantly improve on the prior work of [PODC 2025], who presented distributed quantum algorithms under the same model that had a message complexity of O~(mn) for leader election. Our algorithms demonstrate the significant communication advantage that quantum routing has over classical in distributed computing, since Ω(m) is a well-established classical message lower bound for leader election, broadcast, MST, and BFS that applies even to randomized Monte-Carlo algorithms [JACM 2015]. Thus, our quantum algorithms can, in general, give a quadratic advantage in the communication cost for these fundamental problems.
A main technical tool we use to design our distributed algorithms is quantum walks based on electric networks. We posit a framework for using quantum walks in the distributed setting to design communication-efficient distributed quantum algorithms. Our framework can be used as a black box to significantly reduce communication costs and may be of independent interest. Additionally, our lower-bound technique for establishing distributed quantum message lower bounds can also be applied to other problems.
This paper gives the first separation of quantum and classical pure (i.e., non-cryptographic) computing abilities with no restriction on the amount of available computing resources, by considering the exact solvability of a celebrated unsolvable problem in classical distributed computing, the ``leader election problem'' on anonymous networks. The goal of the leader election problem is to elect a unique leader from among distributed parties. The paper considers this problem for anonymous networks, in which each party has the same identifier. It is well-known that no classical algorithm can solve exactly (i.e., in bounded time without error) the leader election problem in anonymous networks, even if it is given the number of parties. This paper gives two quantum algorithms that, given the number of parties, can exactly solve the problem for any network topology in polynomial rounds and polynomial communication/time complexity with respect to the number of parties, when the parties are connected by quantum communication links.