There are two central models considered in (fault-free synchronous) distributed computing: the CONGEST model, in which communication channels have limited bandwidth, and the LOCAL model, in which communication channels have unlimited bandwidth. Very recently, Le Gall and Magniez (PODC 2018) showed the superiority of quantum distributed computing over classical distributed computing in the CONGEST model. In this work we show the superiority of quantum distributed computing in the LOCAL model: we exhibit two computational tasks that can be solved in a constant number of rounds in the quantum setting but require Omega(n) rounds in the classical (randomized) setting, where n denotes the size of the network.
There are two central models considered in (fault-free synchronous) distributed computing: the CONGEST model, in which communication channels have limited bandwidth, and the LOCAL model, in which communication channels have unlimited bandwidth. Very recently, Le Gall and Magniez (PODC 2018) showed the superiority of quantum distributed computing over classical distributed computing in the CONGEST model. In this work we show the superiority of quantum distributed computing in the LOCAL model: we exhibit two computational tasks that can be solved in a constant number of rounds in the quantum setting but require Omega(n) rounds in the classical (randomized) setting, where n denotes the size of the network.
Quantum advantage is well-established in centralized computing, where quantum algorithms can solve certain problems exponentially faster than classical ones. In the distributed setting, significant progress has been made in bandwidth-limited networks, where quantum distributed networks have shown computational advantages over classical counterparts. However, the potential of quantum computing in networks that are constrained only by large distances is not yet understood. We focus on the LOCAL model of computation (Linial, FOCS 1987), a distributed computational model where computational power and communication bandwidth are unconstrained, and its quantum generalization. In this brief survey, we summarize recent progress on the quantum-LOCAL model outlining its limitations with respect to its classical counterpart: we discuss emerging techniques, and highlight open research questions that could guide future efforts in the field.
We present the first local problem that shows a super-constant separation between the classical randomized LOCAL model of distributed computing and its quantum counterpart. By prior work, such a separation was known only for an artificial graph problem with an inherently global definition [Le Gall et al. 2019]. We present a problem that we call iterated GHZ, which is defined using only local constraints. Formally, it is a family of locally checkable labeling problems [Naor and Stockmeyer 1995]; in particular, solutions can be verified with a constant-round distributed algorithm. We show that in graphs of maximum degree Δ, any classical (deterministic or randomized) LOCAL model algorithm will require Ω(Δ) rounds to solve the iterated GHZ problem, while the problem can be solved in 1 round in quantum-LOCAL. We use the round elimination technique to prove that the iterated GHZ problem requires Ω(Δ) rounds for classical algorithms. This is the first work that shows that round elimination is indeed able to separate the two models, and this also demonstrates that round elimination cannot be used to prove lower bounds for quantum-LOCAL. To apply round elimination, we introduce a new technique that allows us to discover appropriate problem relaxations in a mechanical way; it turns out that this new technique extends beyond the scope of the iterated GHZ problem and can be used to e.g. reproduce prior results on maximal matchings [FOCS 2019, PODC 2020] in a systematic manner.
Distributed Quantum Computing (DQC) offers a promising path toward scalable quantum computation by connecting multiple quantum processors through quantum and classical communication channels, helping overcome the limited qubit counts and noise of individual Noisy Intermediate-Scale Quantum (NISQ) devices. Beyond scaling, DQC has been shown to provide a provable computational advantage: Balliu et al. (STOC 2025) proved that certain locally checkable labeling problems require Ω(Δ) rounds classically in the LOCAL model, where Δ is the maximum degree of the graph, yet only a single round in the quantum-LOCAL model. This separation is unconditional, but a practical demonstration on real hardware had not previously been carried out. This thesis addresses that gap through two contributions. First, it covers the background needed to understand distributed quantum computing: quantum gates, entanglement and the GHZ state, classical distributed models such as LOCAL and CONGEST, locally checkable labeling problems, and the operating principles of superconducting quantum computers, including the practical challenges of connecting them across distances. Second, it presents a practical demonstration of the iterated GHZ game, the locally checkable labeling problem underlying the separation above. The quantum-LOCAL winning strategy is proven correct and implemented as a quantum circuit, executed on IQM’s superconducting quantum computers Garnet and Emerald via the IQM Resonance cloud service. Since physically distributed superconducting hardware is not yet publicly available, a chip-partitioning scheme is used, treating regions of a single chip as independent quantum nodes to emulate a distributed network. The results show that Round 1 games consistently exceed the 75% classical winning bound of the GHZ game, confirming that this win-rate quantum advantage is detectable under NISQ-era noise. In a deeper 3-round demonstration, performance degrades in later rounds, suggesting that demonstrating the advantage consistently across deeper circuits will require longer coherence times, higher gate fidelities, or error correction.
This paper considers the triangle finding problem in the CONGEST model of distributed computing. Recent works by Izumi and Le Gall (PODC'17), Chang, Pettie and Zhang (SODA'19) and Chang and Saranurak (PODC'19) have successively reduced the classical round complexity of triangle finding (as well as triangle listing) from the trivial upper bound O(n) to O~(n1/3), where~n denotes the number of vertices in the graph. In this paper we present a quantum distributed algorithm that solves the triangle finding problem in O~(n1/4) rounds in the CONGEST model. This gives another example of quantum algorithm beating the best known classical algorithms in distributed computing. Our result also exhibits an interesting phenomenon: while in the classical setting the best known upper bounds for the triangle finding and listing problems are identical, in the quantum setting the round complexities of these two problems are now O~(n1/4) and Θ~(n1/3), respectively. Our result thus shows that triangle finding is easier than triangle listing in the quantum CONGEST model.
In this thesis, I study how quantum computation and quantum communication can help large networks of computers to solve computational problems faster. I also connect the notion of locality between various models, including distributed quantum algorithms and online graph algorithms, and show that locality in online graph algorithms can be used to provide bounds for distributed quantum advantage. Towards proving distributed quantum advantage, I present the first family of LCL problems which shows a quantum advantage for distributed graph algorithms. Here LCLs, or Locally Checkable Labeling problems, are a family of graph problems described by a finite set of local constraints, and I mainly focus on them in this thesis. The models of distributed computing which this result separates are the classical LOCAL model and the quantum-LOCAL model. In both of these models, a network of computers exchanges messages in synchronous rounds, and the running time of the algorithm directly corresponds with locality, that is, how far the computers see in the network. In this thesis, I also introduce new models of computing that capture locality in stronger settings. Most notably, I introduce the online-LOCAL model which captures the locality of online graph algorithms, and show that it is, asymptotically, roughly as strong as the classical LOCAL model for solving LCL problems on rooted regular trees. I provide an online-LOCAL algorithm for finding a 3-coloring of a bipartite graph with lower locality than is possible in the classical LOCAL model, and show that the algorithm is tight. To draw things together, I show that quantum-LOCAL and online-LOCAL are indeed related to each other: any quantum-LOCAL algorithm can be simulated in the randomized online-LOCAL model. The converse does not hold in general, but an online-LOCAL algorithm solving an LCL problem in rooted, possibly non-regular, trees can be simulated in the classical LOCAL model—and thus in the quantum-LOCAL model—with an exponential cost in locality, putting indirectly a bound on the maximum possible attainable quantum advantage. Finally, I consider the sinkless orientation problem, which holds a central role in our understanding of the locality of LCL problems in the classical LOCAL model, and provide a simpler and more direct proof for its hardness using the supported LOCAL model. I also provide a simpler algorithm solving sinkless orientation in the SLOCAL model, which is a sequential version of the LOCAL model.
We present the first local problem that shows a super-constant separation between the classical randomized LOCAL model of distributed computing and its quantum counterpart. By prior work, such a separation was known only for an artificial graph problem with an inherently global definition [Le Gall et al. 2019]. We present a problem that we call iterated GHZ, which is defined using only local constraints. Formally, it is a family of locally checkable labeling problems [Naor and Stockmeyer 1995]; in particular, solutions can be verified with a constant-round distributed algorithm. We show that in graphs of maximum degree Δ, any classical (deterministic or randomized) LOCAL model algorithm will require Ω(Δ) rounds to solve the iterated GHZ problem, while the problem can be solved in 1 round in quantum-LOCAL. We use the round elimination technique to prove that the iterated GHZ problem requires Ω(Δ) rounds for classical algorithms. This is the first work that shows that round elimination is indeed able to separate the two models, and this also demonstrates that round elimination cannot be used to prove lower bounds for quantum-LOCAL. To apply round elimination, we introduce a new technique that allows us to discover appropriate problem relaxations in a mechanical way; it turns out that this new technique extends beyond the scope of the iterated GHZ problem and can be used to e.g. reproduce prior results on maximal matchings [FOCS 2019, PODC 2020] in a systematic manner.