Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2404.03619

Circuit Knitting Faces Exponential Sampling Overhead Scaling Bounded by Entanglement Cost

Mingrui Jing, Chengkai Zhu, Xin Wang

Published Apr 4, 2024• 0 citations
arXivHTMLPDF

Abstract

Circuit knitting, a method for connecting quantum circuits across multiple processors to simulate nonlocal quantum operations, is a promising approach for distributed quantum computing. While various techniques have been developed for circuit knitting, we uncover fundamental limitations to the scalability of this technology. We prove that the sampling overhead of circuit knitting is exponentially lower bounded by the exact entanglement cost of the target bipartite dynamic, even for asymptotic overhead in the parallel cut regime. Specifically, we prove that the regularized sampling overhead assisted with local operations and classical communication (LOCC), of any bipartite quantum channel is lower bounded by the exponential of its exact entanglement cost under separable preserving operations. Furthermore, we show that the regularized sampling overhead for simulating a general bipartite channel via LOCC is lower bounded by $κ$-entanglement and max-Rains information, providing efficiently computable benchmarks. Our work reveals a profound connection between virtual quantum information processing via quasi-probability decomposition and quantum Shannon theory, highlighting the critical role of entanglement in distributed quantum computing.

DOI
10.48550/arxiv.2404.03619

Related papers

Distributed Quantum Computing via Adaptive Circuit Knitting

K. Grace Johnson, Aniello Esposito, Gaurav Gyawali +5 more

Distributing quantum workloads over many Quantum Processing Units (QPUs) is a crucial step in scaling up quantum computers toward practical quantum advantage due to the limitations in size of a single QPU. In the absence of high-fidelity quantum interconnects, circuit knitting could provide a path to computing certain properties of large quantum systems on many QPUs of limited size in a distributed fashion using only classical communication. Circuit knitting partitions large quantum circuits into manageable sub-circuits, however, reconstructing observables in a straightforward manner comes at an exponential cost in sampling and classical post-processing. To mitigate the overhead this technique incurs, we introduce an Adaptive Circuit Knitting (ACK) method that finds efficient partitions of quantum circuits by discovering regions of minimal entanglement between subsystems. We simulate 1D and 2D disordered mixed-field Ising models up to 60 qubits and show that the ACK approach can reduce circuit knitting sampling overheads by up to four orders of magnitude for observables of interest. We highlight our parallel GPU-accelerated implementation and discuss the need for efficient classical simulators to enable distributed quantum algorithm development. Our techniques could enable efficient distribution of quantum simulation for both near-term and fault-tolerant architectures.

quant-pharXiv:2603.12411•Mar 16, 2026•0 citations

Circuit knitting facing exponential sampling-overhead scaling bounded by entanglement cost

Mingrui Jing, Chengkai Zhu, Xin Wang

Circuit knitting, a method for connecting quantum circuits across multiple processors to simulate nonlocal quantum operations, is a promising approach for distributed quantum computing. While various techniques have been developed for circuit knitting, we uncover fundamental limitations to the scalability of this technology. We prove that the sampling overhead of circuit knitting is exponentially lower bounded by the exact entanglement cost of the target bipartite dynamic, even with the asymptotic amount of resources using the parallel cut strategy. Specifically, we prove that the regularized sampling overhead assisted with local operations and classical communication of any bipartite quantum channel is lower bounded by the exponential of its exact entanglement cost under separable preserving operations. Furthermore, we develop the faithful lower bounds for the regularized sampling overhead based on channels' $\ensuremath{\kappa}$ entanglement and max-Rains information, providing efficiently computable benchmarks. Our work reveals a profound connection between virtual quantum information processing via quasiprobability decomposition and quantum Shannon theory, highlighting the critical role of entanglement in distributed quantum computing.

Physical Review A•Jan 22, 2025•9 citations

Learning Enables Exponential-to-Polynomial Sampling Overhead Scaling in Quantum Divide-and-Conquer for Tree-Structured Circuits

Hiroyuki Harada, Kaito Wada, Naoki Yamamoto +1 more

Quantum circuit cutting and knitting are divide-and-conquer methods that enable large-scale quantum computations on hardware with limited qubit resources and connectivity by decomposing a target computation into smaller local experiments. Existing methods, however, typically incur a sampling overhead that grows exponentially with the number of cut locations, leaving open the question of whether this barrier is intrinsic. Here we show that this barrier is not universal by introducing a learning-based cutting protocol tailored to the target observable. At each cut, the protocol locally learns a Heisenberg-picture effective observable that captures the downstream information relevant to the final measurement and uses it to construct an observable-adaptive cut. This replaces the multiplicative variance amplification of conventional cutting with additive bias accumulation controlled by local learning accuracy. We apply this framework to finite tree-structured circuits. For any finite rooted tree with $K$ cut wires and cut-system dimension at most $d$, the protocol estimates the target expectation value within additive error $ε$ with high probability using $\widetilde{O}(d^3K^3/ε^2)$ measurements, including the local learning cost. Moreover, for two-layer trees with $R$ cut wires, we prove an information-theoretic exponential separation between our learning-based protocol and learning-free wire-cutting protocols based on pre-specified randomized cutting rules: even with arbitrary classical post-processing, any such learning-free protocol requires $Ω((d+1)^R/ε^2)$ measurements, whereas our protocol uses $\widetilde{O}(d^3R^3/ε^2)$. These results identify local learning, rather than the tree structure alone, as the key mechanism driving the exponential-to-polynomial reduction in sampling overhead.

quant-pharXiv:2512.19623•Dec 23, 2025•0 citations

Circuit Knitting With Classical Communication

Christophe Piveteau, David Sutter

The scarcity of qubits is a major obstacle to the practical usage of quantum computers in the near future. To circumvent this problem, various circuit knitting techniques have been developed to partition large quantum circuits into subcircuits that fit on smaller devices, at the cost of a simulation overhead. In this work, we study a particular method of circuit knitting based on quasiprobability simulation of nonlocal gates with operations that act locally on the subcircuits. We investigate whether classical communication between these local quantum computers can help. We provide a positive answer by showing that for circuits containing$n$nonlocal CNOT gates connecting two circuit parts, the simulation overhead can be reduced from$O(9^{n})$to$O(4^{n})$if one allows for classical information exchange. Similar improvements can be obtained for general Clifford gates and, at least in a restricted form, for other gates such as controlled rotation gates.

arXiv:2205.00016•IEEE Transactions on Information Theory•Aug 31, 2023•111 citations

Reducing the Entanglement Cost of Distributed Bipartite Quantum Computation with Constant Qubit Overhead

Kosuke Matsui, Jun-Yi Wu, Min-Hsiu Hsieh +1 more

Distributed quantum computation connects multiple quantum processing units (QPUs) through quantum communication to jointly perform large-scale quantum computations. Since the number of qubits available at each QPU is limited, it is important to reduce quantum communication while keeping the qubit overhead small. To this end, we study an entanglement-assisted model, in which entanglement consumption serves as a measure of quantum communication cost. For exact deterministic implementations in this model, the operator Schmidt rank of the target bipartite unitary provides a general lower bound on entanglement cost when qubit overhead is unrestricted. However, it has remained unclear how closely this bound can be approached with constant qubit overhead. In this work, we show that this lower bound is attainable for every bipartite Clifford unitary using at most two auxiliary qubits per QPU. In addition, for non-Clifford unitaries specified by exact Clifford+$T$ decompositions with $T$-count $t$, we construct implementations with the same qubit overhead whose entanglement cost is at most $2t$ Bell pairs above this lower bound.

quant-pharXiv:2609.39865•Oct 1, 2026•0 citations

Simulating quantum circuits with restricted quantum computers

Christophe Piveteau

It is one of the most fundamental objectives in quantum information science to understand the boundary between the computational power of classical and quantum computers. One possible avenue to explore this boundary is to identify classes of quantum circuits that can be efficiently simulated on a classical computer. Instead of simulating a general quantum circuit with a classical device, new schemes have recently emerged to simulate them on a quantum device that is restricted in some manner. As such, these techniques allow us to study how the restrictions impact the computational power of the device. One such technique is called quasiprobability simulation (QPS) and it estimates the result of a quantum circuit with a Monte Carlo procedure that randomly replaces circuit elements with ones that can be executed on the restricted quantum device. The main focus of this thesis is dedicated to the QPS-based simulation of nonlocal quantum computation using local quantum operations. On the practical side, this enables the simulation of large quantum circuits using multiple smaller quantum devices - a procedure that is sometimes called circuit knitting. We uncover a rich mathematical formalism with many connections to the resource theory of entanglement. We characterize the optimal simulation overhead for a broad range of practically relevant nonlocal states and channels and we explicitly provide achieving protocols. Moreover, we also investigate the utility of classical communication between the local parties. Our results address both the single-shot and asymptotic regime. We frame QPS in a quantum resource theoretic framework, which highlights similarities that arise in the different instantiations of the technique. Furthermore, we study the importance of classical side information in the QPS procedure and how it impacts the overhead and expressibility of QPS.

arXiv:2503.21773•Jan 1, 2025•0 citations
Circuit knitting, a method for connecting quantum circuits across multiple processors to simulate nonlocal quantum operations, is a promising approach for distributed quantum computing. While various techniques have been developed for circuit knitting, we uncover fundamental limitations to the scalability of this technology. We prove that the sampling overhead of circuit knitting is exponentially lower bounded by the exact entanglement cost of the target bipartite dynamic, even for asymptotic overhead in the parallel cut regime. Specifically, we prove that the regularized sampling overhead assisted with local operations and classical communication (LOCC), of any bipartite quantum channel is lower bounded by the exponential of its exact entanglement cost under separable preserving operations. Furthermore, we show that the regularized sampling overhead for simulating a general bipartite channel via LOCC is lower bounded by κκκ-entanglement and max-Rains information, providing efficiently computable benchmarks. Our work reveals a profound connection between virtual quantum information processing via quasi-probability decomposition and quantum Shannon theory, highlighting the critical role of entanglement in distributed quantum computing.
Distributing quantum workloads over many Quantum Processing Units (QPUs) is a crucial step in scaling up quantum computers toward practical quantum advantage due to the limitations in size of a single QPU. In the absence of high-fidelity quantum interconnects, circuit knitting could provide a path to computing certain properties of large quantum systems on many QPUs of limited size in a distributed fashion using only classical communication. Circuit knitting partitions large quantum circuits into manageable sub-circuits, however, reconstructing observables in a straightforward manner comes at an exponential cost in sampling and classical post-processing. To mitigate the overhead this technique incurs, we introduce an Adaptive Circuit Knitting (ACK) method that finds efficient partitions of quantum circuits by discovering regions of minimal entanglement between subsystems. We simulate 1D and 2D disordered mixed-field Ising models up to 60 qubits and show that the ACK approach can reduce circuit knitting sampling overheads by up to four orders of magnitude for observables of interest. We highlight our parallel GPU-accelerated implementation and discuss the need for efficient classical simulators to enable distributed quantum algorithm development. Our techniques could enable efficient distribution of quantum simulation for both near-term and fault-tolerant architectures.
Circuit knitting, a method for connecting quantum circuits across multiple processors to simulate nonlocal quantum operations, is a promising approach for distributed quantum computing. While various techniques have been developed for circuit knitting, we uncover fundamental limitations to the scalability of this technology. We prove that the sampling overhead of circuit knitting is exponentially lower bounded by the exact entanglement cost of the target bipartite dynamic, even with the asymptotic amount of resources using the parallel cut strategy. Specifically, we prove that the regularized sampling overhead assisted with local operations and classical communication of any bipartite quantum channel is lower bounded by the exponential of its exact entanglement cost under separable preserving operations. Furthermore, we develop the faithful lower bounds for the regularized sampling overhead based on channels' $\ensuremath{\kappa}$ entanglement and max-Rains information, providing efficiently computable benchmarks. Our work reveals a profound connection between virtual quantum information processing via quasiprobability decomposition and quantum Shannon theory, highlighting the critical role of entanglement in distributed quantum computing.
Quantum circuit cutting and knitting are divide-and-conquer methods that enable large-scale quantum computations on hardware with limited qubit resources and connectivity by decomposing a target computation into smaller local experiments. Existing methods, however, typically incur a sampling overhead that grows exponentially with the number of cut locations, leaving open the question of whether this barrier is intrinsic. Here we show that this barrier is not universal by introducing a learning-based cutting protocol tailored to the target observable. At each cut, the protocol locally learns a Heisenberg-picture effective observable that captures the downstream information relevant to the final measurement and uses it to construct an observable-adaptive cut. This replaces the multiplicative variance amplification of conventional cutting with additive bias accumulation controlled by local learning accuracy. We apply this framework to finite tree-structured circuits. For any finite rooted tree with KKK cut wires and cut-system dimension at most ddd, the protocol estimates the target expectation value within additive error εεε with high probability using O~(d3K3/ε2)\widetilde{O}(d^3K^3/ε^2)O(d3K3/ε2) measurements, including the local learning cost. Moreover, for two-layer trees with RRR cut wires, we prove an information-theoretic exponential separation between our learning-based protocol and learning-free wire-cutting protocols based on pre-specified randomized cutting rules: even with arbitrary classical post-processing, any such learning-free protocol requires Ω((d+1)R/ε2)Ω((d+1)^R/ε^2)Ω((d+1)R/ε2) measurements, whereas our protocol uses O~(d3R3/ε2)\widetilde{O}(d^3R^3/ε^2)O(d3R3/ε2). These results identify local learning, rather than the tree structure alone, as the key mechanism driving the exponential-to-polynomial reduction in sampling overhead.
The scarcity of qubits is a major obstacle to the practical usage of quantum computers in the near future. To circumvent this problem, various circuit knitting techniques have been developed to partition large quantum circuits into subcircuits that fit on smaller devices, at the cost of a simulation overhead. In this work, we study a particular method of circuit knitting based on quasiprobability simulation of nonlocal gates with operations that act locally on the subcircuits. We investigate whether classical communication between these local quantum computers can help. We provide a positive answer by showing that for circuits containingnnnnonlocal CNOT gates connecting two circuit parts, the simulation overhead can be reduced fromO(9n)O(9^{n})O(9n)toO(4n)O(4^{n})O(4n)if one allows for classical information exchange. Similar improvements can be obtained for general Clifford gates and, at least in a restricted form, for other gates such as controlled rotation gates.
Distributed quantum computation connects multiple quantum processing units (QPUs) through quantum communication to jointly perform large-scale quantum computations. Since the number of qubits available at each QPU is limited, it is important to reduce quantum communication while keeping the qubit overhead small. To this end, we study an entanglement-assisted model, in which entanglement consumption serves as a measure of quantum communication cost. For exact deterministic implementations in this model, the operator Schmidt rank of the target bipartite unitary provides a general lower bound on entanglement cost when qubit overhead is unrestricted. However, it has remained unclear how closely this bound can be approached with constant qubit overhead. In this work, we show that this lower bound is attainable for every bipartite Clifford unitary using at most two auxiliary qubits per QPU. In addition, for non-Clifford unitaries specified by exact Clifford+TTT decompositions with TTT-count ttt, we construct implementations with the same qubit overhead whose entanglement cost is at most 2t2t2t Bell pairs above this lower bound.
It is one of the most fundamental objectives in quantum information science to understand the boundary between the computational power of classical and quantum computers. One possible avenue to explore this boundary is to identify classes of quantum circuits that can be efficiently simulated on a classical computer. Instead of simulating a general quantum circuit with a classical device, new schemes have recently emerged to simulate them on a quantum device that is restricted in some manner. As such, these techniques allow us to study how the restrictions impact the computational power of the device. One such technique is called quasiprobability simulation (QPS) and it estimates the result of a quantum circuit with a Monte Carlo procedure that randomly replaces circuit elements with ones that can be executed on the restricted quantum device. The main focus of this thesis is dedicated to the QPS-based simulation of nonlocal quantum computation using local quantum operations. On the practical side, this enables the simulation of large quantum circuits using multiple smaller quantum devices - a procedure that is sometimes called circuit knitting. We uncover a rich mathematical formalism with many connections to the resource theory of entanglement. We characterize the optimal simulation overhead for a broad range of practically relevant nonlocal states and channels and we explicitly provide achieving protocols. Moreover, we also investigate the utility of classical communication between the local parties. Our results address both the single-shot and asymptotic regime. We frame QPS in a quantum resource theoretic framework, which highlights similarities that arise in the different instantiations of the technique. Furthermore, we study the importance of classical side information in the QPS procedure and how it impacts the overhead and expressibility of QPS.