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:0704.1464 · Physical Review A

Distributed quantum-information processing with minimal local resources

Earl T. Campbell

Published Oct 16, 2007• 37 citations
arXivHTMLPDF

Abstract

We present a protocol for growing graph states, the resource for one-way quantum computing, when the available entanglement mechanism is highly imperfect. The distillation protocol is frugal in its use of ancilla qubits, requiring only a single ancilla qubit when the noise is dominated by one Pauli error, and two for a general noise model. The protocol works with such scarce local resources by never postselecting on the measurement outcomes of purification rounds. We find that such a strategy causes fidelity to follow a biased random walk, and that a target fidelity is likely to be reached more rapidly than for a comparable postselecting protocol. An analysis is presented of how imperfect local operations limit the attainable fidelity. For example, a single Pauli error rate of $20%$ can be distilled down to $\ensuremath{\sim}10$ times the imperfection in local operations.

DOI
10.1103/physreva.76.040302

Related papers

Practical Entanglement Distillation Protocols with Quadratic Error Suppression

Elisa Bäumer Marty

Near-term and early fault-tolerant quantum computing architectures are expected to exhibit highly non-uniform error rates. In particular, local operations within a chip can be substantially more reliable than operations connecting different chips or dilution refrigerators. Such inter-module operations can therefore become a dominant bottleneck, even when quantum error correction is applied. Entanglement distillation provides a natural way to trade additional operations and qubits for higher-fidelity entanglement. Standard distillation protocols, however, are usually formulated in an LOCC resource model, in which several noisy Bell pairs are generated initially and all subsequent processing consists only of local operations and classical communication. Here, we consider a generalized model tailored to modular quantum computing hardware, in which the two modules have access to high-fidelity local operations and to repeated uses of the same noisy inter-module entangling operation during the protocol. We develop practical small-scale entanglement distillation protocols designed to minimize both space and time overhead. Remarkably, our main protocol requires only two qubits per module, yet achieves quadratic error suppression of inter-module errors, assuming local operations are much cleaner. Compared with existing small-scale protocols, our space-optimal protocol provides more space- and time-efficient quadratic error suppression and achieves the best performance in our simulations and experiments on noisy links of current superconducting quantum processors. These results suggest that inter-module-gate-assisted entanglement distillation can be a practical primitive for overcoming noisy links in modular quantum computing architectures.

quant-pharXiv:2605.26757•May 27, 2026•0 citations

Bell-pair distillation under imperfect operations

András Kinyó, Tamás Kiss, Orsolya Kálmán

We recently proposed an entanglement distillation protocol based on local operations and classical communication that probabilistically and universally distills a maximally entangled Bell pair from multiple copies of an unknown two-qubit state [Phys. Rev. Lett. 135, 260202 (2025)]. Here, we investigate the robustness of this protocol against imperfections in its implementation. We consider several incoherent and coherent gate-error models, as well as measurement readout errors, and determine the regimes in which distillation enhances the fidelity with the target Bell state. We find that the protocol remains effective over substantial error ranges, although its robustness depends strongly on the type of error. We further analyze asymmetric errors between the two parties and identify conditions under which complementary postselection outcomes yield identical distillation dynamics, allowing the success probability to be enhanced.

quant-pharXiv:2610.35699•Oct 27, 2026•0 citations

Purification of noisy measurements and faithful distillation of entanglement

Jaerim Kim, Jiyoung Yun, Joonwoo Bae

Abstract We consider entanglement distillation with noisy operations in which quantum measurements that constitute a general quantum operation are particularly noisy. We present a protocol for purifying noisy measurements and show that imperfect local operations can distill entanglement. The protocol works for arbitrary noisy measurements in general and is cost-effective and resource-efficient with single additional qubit per party to resolve the distillation of entanglement. The purification protocol is feasible with currently available quantum technologies and readily applied to entanglement applications.

arXiv:2404.10538•Journal of Physics A Mathematical and Theoretical•Dec 18, 2024•4 citations

Single-Round Graph-State Distribution from Bell Pairs: Exact Fidelity under Resource-Qubit Noise

Soumyojyoti Dutta

I present a protocol that converts |E| elementary two-qubit resource states, one per edge of a target graph G=(V,E), into the distributed graph state |G> using only operations local to each party and classical communication, reaching arbitrary graph topologies rather than the GHZ class of prior walk-based schemes. The elementary step is obtained from the coined discrete-time quantum walk by replacing the position-permuting shift with a diagonal CZ gate, the phase quantum walk (PQW); on each edge it realises the entanglement-assisted non-local CZ gate. Because every gate and correction is diagonal, all edges run in a single round with the local correction C_v = Z_v^{g_v}, verified exhaustively on 22 connected graphs (32,212 outcomes) at F = 1.0. The central result is an exact fidelity theory under independent Pauli noise on the resource qubits, with a separate channel on each. When the noise acts after the local gate, the fidelity factorises over vertices; for depolarising noise F* = prod_v [1 + (1 - 4p/3)^{deg v}]/2, with the degree sequence entering only at second order. When it acts on the stored pair, as link-generation, transmission and storage noise does, it becomes an edge-cover partition function, F* = 2^{-|V|} sum_{S subset V} (1 - 4p/3)^{2|E(S)|}, bounded above by the vertex product and with a leading-order loss coefficient 3/2 times larger. Dephasing gives the same fidelity at both placements. On ibm_kingston, direct fidelity estimation certifies F = 0.815(3) for |L_4>, 0.776(3) for |GHZ_4> and 0.733(3) for |C_4>. Native SWAP-free execution at coupling girth gamma requires target girth at least gamma/3 and maximum degree at most 3; on heavy-hex this forbids triangles, though |K_4>, being LC-equivalent to a star, remains reachable.

quant-pharXiv:2604.02169•Apr 3, 2026•0 citations

Near-Term n to k Distillation Protocols Using Graph Codes

Kenneth Goodenough, Sébastian de Bone, Vaishnavi L. Addala +4 more

Noisy hardware forms one of the main hurdles to the realization of a near-term quantum internet. Distillation protocols allows one to overcome this noise at the cost of an increased overhead. We consider here an experimentally relevant class of distillation protocols, which distillntokend-to-end entangled pairs using bilocal Clifford operations, a single round of communication and a possible final local operation depending on the observed measurement outcomes. In the case of permutationally invariant depolarizing noise on the input states, we find a correspondence between these distillation protocols and graph codes. We leverage this correspondence to find provably optimal distillation protocols in this class for several tasks important for the quantum internet. This correspondence allows us to investigate use cases for so-called non-trivial measurement syndromes. Furthermore, we detail a recipe to construct the circuit used for the distillation protocol given a graph code. We use this to find circuits of short depth and small number of two-qubit gates. Additionally, we develop a black-box circuit optimization algorithm, and find that both approaches yield comparable circuits. Finally, we investigate the teleportation of encoded states and find protocols which jointly improve the rate and fidelities with respect to prior art.

arXiv:2303.11465•IEEE Journal on Selected Areas in Communications•Mar 26, 2024•20 citations

Efficient growth of complex graph states via imperfect path erasure

Campbell, E T, Benjamin, S C, Fitzsimons, J +1 more

Given a suitably large and well connected (complex) graph state, any quantum algorithm can be implemented purely through local measurements on the individual qubits. Measurements can also be used to create the graph state: Path erasure techniques allow one to entangle multiple qubits by determining only global properties of the qubits. Here, this powerful approach is extended by demonstrating that even imperfect path erasure can produce the required graph states with high efficiency. By characterizing the degree of error in each path erasure attempt, one can subsume the resulting imperfect entanglement into an extended graph state formalism. The subsequent growth of the improper graph state can be guided, through a series of strategic decisions, in such a way as to bound the growth of the error and eventually yield a high-fidelity graph state. As an implementation of these techniques, we develop an analytic model for atom (or atom-like) qubits in mismatched cavities, under the double-heralding entanglement procedure of Barrett and Kok [Phys. Rev. A 71, 060310 (2005)]. Compared to straightforward postselection techniques our protocol offers a dramatic improvement in growing complex high-fidelity graph states.

•Feb 22, 2007•7 citations
We present a protocol for growing graph states, the resource for one-way quantum computing, when the available entanglement mechanism is highly imperfect. The distillation protocol is frugal in its use of ancilla qubits, requiring only a single ancilla qubit when the noise is dominated by one Pauli error, and two for a general noise model. The protocol works with such scarce local resources by never postselecting on the measurement outcomes of purification rounds. We find that such a strategy causes fidelity to follow a biased random walk, and that a target fidelity is likely to be reached more rapidly than for a comparable postselecting protocol. An analysis is presented of how imperfect local operations limit the attainable fidelity. For example, a single Pauli error rate of 2020%20 can be distilled down to \ensuremath∼10\ensuremath{\sim}10\ensuremath∼10 times the imperfection in local operations.
Near-term and early fault-tolerant quantum computing architectures are expected to exhibit highly non-uniform error rates. In particular, local operations within a chip can be substantially more reliable than operations connecting different chips or dilution refrigerators. Such inter-module operations can therefore become a dominant bottleneck, even when quantum error correction is applied. Entanglement distillation provides a natural way to trade additional operations and qubits for higher-fidelity entanglement. Standard distillation protocols, however, are usually formulated in an LOCC resource model, in which several noisy Bell pairs are generated initially and all subsequent processing consists only of local operations and classical communication. Here, we consider a generalized model tailored to modular quantum computing hardware, in which the two modules have access to high-fidelity local operations and to repeated uses of the same noisy inter-module entangling operation during the protocol. We develop practical small-scale entanglement distillation protocols designed to minimize both space and time overhead. Remarkably, our main protocol requires only two qubits per module, yet achieves quadratic error suppression of inter-module errors, assuming local operations are much cleaner. Compared with existing small-scale protocols, our space-optimal protocol provides more space- and time-efficient quadratic error suppression and achieves the best performance in our simulations and experiments on noisy links of current superconducting quantum processors. These results suggest that inter-module-gate-assisted entanglement distillation can be a practical primitive for overcoming noisy links in modular quantum computing architectures.
We recently proposed an entanglement distillation protocol based on local operations and classical communication that probabilistically and universally distills a maximally entangled Bell pair from multiple copies of an unknown two-qubit state [Phys. Rev. Lett. 135, 260202 (2025)]. Here, we investigate the robustness of this protocol against imperfections in its implementation. We consider several incoherent and coherent gate-error models, as well as measurement readout errors, and determine the regimes in which distillation enhances the fidelity with the target Bell state. We find that the protocol remains effective over substantial error ranges, although its robustness depends strongly on the type of error. We further analyze asymmetric errors between the two parties and identify conditions under which complementary postselection outcomes yield identical distillation dynamics, allowing the success probability to be enhanced.
Abstract We consider entanglement distillation with noisy operations in which quantum measurements that constitute a general quantum operation are particularly noisy. We present a protocol for purifying noisy measurements and show that imperfect local operations can distill entanglement. The protocol works for arbitrary noisy measurements in general and is cost-effective and resource-efficient with single additional qubit per party to resolve the distillation of entanglement. The purification protocol is feasible with currently available quantum technologies and readily applied to entanglement applications.
I present a protocol that converts |E| elementary two-qubit resource states, one per edge of a target graph G=(V,E), into the distributed graph state |G> using only operations local to each party and classical communication, reaching arbitrary graph topologies rather than the GHZ class of prior walk-based schemes. The elementary step is obtained from the coined discrete-time quantum walk by replacing the position-permuting shift with a diagonal CZ gate, the phase quantum walk (PQW); on each edge it realises the entanglement-assisted non-local CZ gate. Because every gate and correction is diagonal, all edges run in a single round with the local correction C_v = Z_v^{g_v}, verified exhaustively on 22 connected graphs (32,212 outcomes) at F = 1.0. The central result is an exact fidelity theory under independent Pauli noise on the resource qubits, with a separate channel on each. When the noise acts after the local gate, the fidelity factorises over vertices; for depolarising noise F* = prod_v [1 + (1 - 4p/3)^{deg v}]/2, with the degree sequence entering only at second order. When it acts on the stored pair, as link-generation, transmission and storage noise does, it becomes an edge-cover partition function, F* = 2^{-|V|} sum_{S subset V} (1 - 4p/3)^{2|E(S)|}, bounded above by the vertex product and with a leading-order loss coefficient 3/2 times larger. Dephasing gives the same fidelity at both placements. On ibm_kingston, direct fidelity estimation certifies F = 0.815(3) for |L_4>, 0.776(3) for |GHZ_4> and 0.733(3) for |C_4>. Native SWAP-free execution at coupling girth gamma requires target girth at least gamma/3 and maximum degree at most 3; on heavy-hex this forbids triangles, though |K_4>, being LC-equivalent to a star, remains reachable.
Noisy hardware forms one of the main hurdles to the realization of a near-term quantum internet. Distillation protocols allows one to overcome this noise at the cost of an increased overhead. We consider here an experimentally relevant class of distillation protocols, which distillntokend-to-end entangled pairs using bilocal Clifford operations, a single round of communication and a possible final local operation depending on the observed measurement outcomes. In the case of permutationally invariant depolarizing noise on the input states, we find a correspondence between these distillation protocols and graph codes. We leverage this correspondence to find provably optimal distillation protocols in this class for several tasks important for the quantum internet. This correspondence allows us to investigate use cases for so-called non-trivial measurement syndromes. Furthermore, we detail a recipe to construct the circuit used for the distillation protocol given a graph code. We use this to find circuits of short depth and small number of two-qubit gates. Additionally, we develop a black-box circuit optimization algorithm, and find that both approaches yield comparable circuits. Finally, we investigate the teleportation of encoded states and find protocols which jointly improve the rate and fidelities with respect to prior art.
Given a suitably large and well connected (complex) graph state, any quantum algorithm can be implemented purely through local measurements on the individual qubits. Measurements can also be used to create the graph state: Path erasure techniques allow one to entangle multiple qubits by determining only global properties of the qubits. Here, this powerful approach is extended by demonstrating that even imperfect path erasure can produce the required graph states with high efficiency. By characterizing the degree of error in each path erasure attempt, one can subsume the resulting imperfect entanglement into an extended graph state formalism. The subsequent growth of the improper graph state can be guided, through a series of strategic decisions, in such a way as to bound the growth of the error and eventually yield a high-fidelity graph state. As an implementation of these techniques, we develop an analytic model for atom (or atom-like) qubits in mismatched cavities, under the double-heralding entanglement procedure of Barrett and Kok [Phys. Rev. A 71, 060310 (2005)]. Compared to straightforward postselection techniques our protocol offers a dramatic improvement in growing complex high-fidelity graph states.