Qline: Linear Quantum Network Architecture

• Qline is a linear quantum network architecture where photonic qubits traverse a single path with only restricted operations like single-qubit phase rotations.
• It enables multi-client blind quantum computation and prepare-and-measure cryptography, reducing the need for fully connected hardware setups.
• The design preserves composable security and verifiability through adaptive measurements, randomized rotations, and efficient secret-sharing protocols.

Qline is a linear quantum-network architecture in which quantum states traverse a single path through multiple parties, while intermediate nodes perform only restricted quantum operations, typically single-qubit phase rotations. In the literature, this architecture has been developed in two closely related directions: as a linear photonic network for multi-client blind quantum computation and verifiable delegated computation, and as a low-cost prepare-and-measure network for multiparty cryptography and multi-purpose quantum communication. Across these settings, the defining objective is the same: reduce client-side hardware assumptions, avoid the pairwise-connectivity overhead of fully connected quantum networks, and preserve information-theoretic or composable security for distributed tasks (Polacchi et al., 2023, Polacchi et al., 2024, Grilo et al., 28 Apr 2025, Hanouz et al., 3 Mar 2026, Grilo et al., 22 Jun 2026).

1. Architectural model

Qline is described as a modular, linear quantum network configuration. In the delegated-computation realization, a source node $S1$ injects photonic qubits into a one-dimensional link, multiple clients are arranged sequentially along that line, and a tail server $S2$ completes entanglement generation and performs adaptive measurements. In the prepare-and-measure realization, player $1$ acts as a source end, players $2,\dots,J-1$ are inexpensive intermediate devices, and player $J$ is the detection end. A later formalization abstracts the same idea further: end users need only trusted single-qubit rotation devices, while trusted preparation or measurement can be delegated to an untrusted provider under composable security assumptions (Polacchi et al., 2023, Grilo et al., 28 Apr 2025, Grilo et al., 22 Jun 2026).

Qline differs explicitly from star and fully connected topologies. In hub-and-spoke or star networks, many clients connect directly to a central server over separate links, often requiring each client to trust its own source or measurement device. In fully connected networks, hardware, switching, and routing complexity grow rapidly with the number of users. Qline instead serializes participation along a single quantum path: the same qubits pass sequentially through the parties, accumulate local masks or rotations, and are finally measured at an endpoint. This eliminates the need for per-client quantum sources or detectors in several protocol families and replaces $\Theta(J^2)$ secure-link scaling with a single quantum line in the multiparty-secret-sharing setting (Polacchi et al., 2023, Grilo et al., 28 Apr 2025).

A useful way to organize the main realizations is the following.

Realization	End-node functionality	Intermediate-node functionality
Multi-client delegated computation	$S1$ generates resource states; $S2$ performs adaptive measurements	Clients apply trusted single-qubit rotations and send classical messages
Secret sharing of $0$	Player $1$ prepares $S2$0; player $S2$1 measures in Hadamard or circular basis	Players $S2$2 apply $S2$3 with $S2$4
Prepare-and-measure platform	Alice prepares BB84 states; Bob measures with phase modulator, interferometer, and APD	Classical/global-control services and, in generalized Qline, in-line phase operations

This architectural commonality is significant because it makes Qline a network-level primitive rather than a single protocol. The same linear path supports measurement-based delegated computation, secret sharing, oblivious transfer, tokens, and, under later formal reductions, a broad class of single-qubit prepare-and-measure cryptographic protocols (Polacchi et al., 2024, Hanouz et al., 3 Mar 2026, Grilo et al., 22 Jun 2026).

2. Blind quantum computation on a linear pipeline

In blind-quantum-computing applications, Qline combines measurement-based quantum computation (MBQC), universal blind quantum computation (UBQC), and a collaborative Remote State Rotation (RSR) functionality. The central idea is that $S2$5 prepares qubits or entangled pairs, each client adds a private $S2$6-rotation to the flying qubits, and $S2$7 performs the adaptive equatorial measurements required by MBQC. The clients therefore need only trusted single-qubit rotation devices and classical communication; they do not need quantum sources, detectors, or memories (Polacchi et al., 2023).

The two-client experimental demonstration uses a two-qubit resource. The target joint computation is

$S2$8

where one client holds private classical inputs $S2$9 and the other holds private algorithm parameters $1$0. $1$1 generates

$1$2

Alice applies $1$3, Bob applies $1$4, and $1$5 receives a state whose phases depend only on the accumulated secret angles $1$6. A trusted third party (TTP), or in principle composably secure classical SMPC, computes adaptive blind measurement angles and returns corrected outcomes after classical decryption (Polacchi et al., 2023).

The MBQC layer is standard graph-state MBQC. For a graph state $1$7 with stabilizers

$1$8

computation proceeds by single-qubit measurements on the equator of the Bloch sphere. UBQC uses rotated states

$1$9

and blind measurement angles of the form

$2,\dots,J-1$0

In the Qline-specific multi-client setting, $2,\dots,J-1$1 additionally incorporates data-hiding terms $2,\dots,J-1$2, aggregated random rotations from all clients, and adaptivity determined by previous corrected outcomes. The measurement operator implemented at $2,\dots,J-1$3 is

$2,\dots,J-1$4

The linear network is therefore not a replacement for MBQC, but a transport-and-encryption layer that makes MBQC multi-client and hardware-lightweight (Polacchi et al., 2023).

The protocol generalizes from a two-qubit cluster to arbitrary graph states $2,\dots,J-1$5. For $2,\dots,J-1$6 qubits, the ideal architecture uses $2,\dots,J-1$7 Qlines so that each resource qubit passes the client line once, although multiple qubits can be sent concurrently if client devices support parallel rotations. This makes Qline intrinsically compatible with distributed graph-state computation and with privacy-preserving collaborative workloads such as federated quantum machine learning (Polacchi et al., 2023).

3. Verification and composable security

The initial Qline blind-computing result establishes blindness in the Abstract Cryptography framework. Composing RSR with UBQC yields perfect blindness for any single honest client even if the server is untrusted, and the architecture remains secure against any strict subset of colluding malicious adversaries among server nodes and clients. The operative condition is that at least one honest client lies on each Qline used by the computation; if an adversary does not corrupt all clients on a given line simultaneously, the server’s reduced state is independent of private inputs, algorithm angles, and corrected outputs up to negligible trace distance (Polacchi et al., 2023).

The 2024 extension adds verifiability under untrusted state preparation. Standard verification techniques fail when clients receive quantum states from an untrusted source, which is exactly the Qline setting. The implemented solution introduces random bit flips $2,\dots,J-1$8 in addition to random $2,\dots,J-1$9-rotations, and alternates computation rounds with test rounds that measure the stabilizer $J$0. For the ideal resource state, valid test outcomes satisfy $J$1; the observed test failure fraction $J$2 is compared with a tolerated threshold $J$3, with security controlled by $J$4, an estimated device-noise bound $J$5, and a chosen threshold $J$6 satisfying $J$7 (Polacchi et al., 2024).

This yields explicit completeness and soundness guarantees. For $J$8, the test-round error fraction is $J$9; for $\Theta(J^2)$0, $\Theta(J^2)$1. Both lie below $\Theta(J^2)$2, and the concrete bounds reported are a false-reject probability below $\Theta(J^2)$3 and $\Theta(J^2)$4, respectively, and soundness errors below $\Theta(J^2)$5 and $\Theta(J^2)$6. Blindness is quantified by a Holevo quantity of $\Theta(J^2)$7 bits and fidelities to maximally mixed states $\Theta(J^2)$8 and $\Theta(J^2)$9 (Polacchi et al., 2024).

A subsequent formal development broadens the security interpretation of Qline. It shows, in the Abstract Cryptography framework, that trusted single-qubit rotations suffice to implement delegated single-qubit measurement universally and delegated state preparation under assumptions satisfied by most prepare-and-measure protocols. The rotation family

$S1$0

and the states

$S1$1

become the fundamental trusted primitives. The measurement-delegation theorem gives

$S1$2

while preparation delegation is established through CNOT-based or entanglement-based reductions. A notable consequence is a formal validation of Qline as a versatile architecture for most single-qubit quantum cryptographic protocols, provided the trusted rotation device acts on a genuine single-qubit Hilbert space and classical channels are authenticated (Grilo et al., 22 Jun 2026).

4. Multiparty cryptography and quantum communication services

Qline has also been used as a low-cost multiparty cryptographic substrate. A 2025 protocol distributes additive secret sharing of $S1$3 directly on a Qline. Player $S1$4 prepares states in $S1$5, intermediate players apply quarter-turn $S1$6-rotations $S1$7 with $S1$8, and player $S1$9 measures in the Hadamard or circular basis. After authenticated broadcast, random-subset revelation, sifting, error estimation, syndrome-based error correction, and linear privacy amplification, the parties obtain shares $S2$0 satisfying

$S2$1

except with correctness failure probability $S2$2 (Grilo et al., 28 Apr 2025).

The protocol is composably secure in Abstract Cryptography. Its main theorem states

$S2$3

where $S2$4 is the number of honest players and $S2$5 is the distinguishing advantage inherited from the corresponding two-party finite-key QKD proof. The QBER-like test statistic is

$S2$6

and the finite-key analysis gives an explicit $S2$7 bound in terms of $S2$8, $S2$9, $0$0, $0$1, $0$2, $0$3, $0$4, and $0$5. The outputs can then be used for additive secret sharing of an arbitrary secret, anonymous veto, and symmetric key establishment between any pair (Grilo et al., 28 Apr 2025).

A distinct but compatible line of work uses VeriQloud’s Qline as a programmable prepare-and-measure platform and exact-fidelity emulator for tasks beyond QKD. The software stack has three layers: hardware or emulator, a global counter aligning pulse indices and exposing FIFO buffers, and an application layer implementing QKD, quantum oblivious transfer (OT), or quantum tokens. A central methodological claim is that user-defined applications run unchanged on simulated and real backends, because the emulator reproduces the hardware’s inputs, outputs, losses, and errors (Hanouz et al., 3 Mar 2026).

On this platform, OT is instantiated with finite-size security bounds, commit-and-open using SHA-256 with truncation, LDPC-based error correction, and SHAKE-256 as the pseudorandom generator. For the reported implementation, the measured QBER is $0$6, $0$7, the LDPC parity-check matrix is $0$8, and the chosen security parameters are $0$9, giving overall $1$0. The required shortest raw-key subset length is $1$1, and the experiment uses $1$2 received pulses to ensure $1$3 with at least $1$4 probability (Hanouz et al., 3 Mar 2026).

Quantum tokens are also implemented at proof-of-principle level, but the current Qline hardware is detection-limited. In insecure demonstration runs with $1$5 and $1$6, the measured detection probability is approximately $1$7 and the QBER approximately $1$8. To reach $1$9 with the measured biases and $S2$00, the required detection probabilities are approximately $S2$01 and $S2$02, i.e. about $S2$03 and $S2$04 higher than measured (Hanouz et al., 3 Mar 2026).

5. Experimental platforms and performance

The multi-client blind-computing Qline was demonstrated on a photonic polarization platform. $S2$05 is a Sagnac interferometer with a $S2$06-mm ppKTP crystal pumped by a $S2$07 nm CW laser and generating entangled photons at $S2$08 nm. Alice and Bob implement single-qubit $S2$09-rotations with liquid crystals whose random parameters are supplied by an ID Quantique QRNG. $S2$10 uses two measurement stations: the first with QWP+HWP+PBS, the second with PC+HWP+PBS, both with APD detectors. A fast electronic circuit converts the first measurement outcome into high-voltage pulses driving the Pockels cell for real-time feed-forward. A delay of approximately $S2$11 m of single-mode fiber, corresponding to about $S2$12 ns, is used to match detector response and PC activation; the PC rise time is about $S2$13 ns, and voltages of $S2$14, $S2$15, and $S2$16 V implement $S2$17, $S2$18, and $S2$19 phase shifts, respectively (Polacchi et al., 2023).

The reported photonic metrics support both correctness and blindness. The entanglement quality at $S2$20 is quantified by a CHSH Bell parameter of $S2$21. In a quantum-output case, the reconstructed output for Bob’s $S2$22 achieves fidelity $S2$23 with the ideal state. Blindness is witnessed by averaged output states near the maximally mixed state: for the single-qubit output, $S2$24 and $S2$25; for the two-qubit initial cluster, $S2$26 and $S2$27 (Polacchi et al., 2023).

The verifiable extension uses two parallel fiber Qlines and retains the photonic-control logic while adding $S2$28-masking via half-wave plates. The second station’s Pockels cell has an activation time of approximately $S2$29 ns, again matched to an approximately $S2$30 m fiber delay. The experiment implements two target algorithms with $S2$31 and inputs $S2$32. Total round counts are $S2$33 and $S2$34, and roughly $S2$35 and $S2$36 of computation rounds match the expected output classes for the two algorithms (Polacchi et al., 2024).

The prepare-and-measure Qline platform uses BB84 time-bin/phase encoding. Alice’s photonics comprise a laser, amplitude modulator, and phase modulator; Bob’s comprise a phase modulator, interferometer, and a single APD. The repetition rate is $S2$37 MHz, the QBER is typically between $S2$38 and $S2$39, and the total channel-loss budget is up to $S2$40 dB. White-Rabbit switches distribute clocks and provide deterministic synchronization, while a control API decouples data generation from consumption. Classical post-processing runs on a standard computer with an Intel i7-14700T, $S2$41 GB RAM, and $S2$42 GB SSD (Hanouz et al., 3 Mar 2026).

For OT on this platform, the average rate is approximately $S2$43 OT per minute, with total wall-clock time about $S2$44 s per OT. The measured time breakdown is $S2$45 s for quantum reception ($S2$46), $S2$47 s for commitment ($S2$48), $S2$49 s for LDPC decoding ($S2$50), and $S2$51 s for privacy amplification ($S2$52). The paper attributes the dominant performance bottlenecks to quantum reception time, commitment compute cost, and the single-APD interferometric readout, which imposes intrinsic losses (Hanouz et al., 3 Mar 2026).

6. Limitations, trade-offs, and outlook

Qline’s principal advantage is reduced hardware burden at the network edge. In the blind-computing setting, clients require only trusted single-qubit rotations and classical connectivity; in the secret-sharing setting, intermediate nodes need only phase re-randomization; in the communication-platform setting, a single quantum line replaces $S2$53 pairwise QKD links. This makes Qline appealing for distributed architectures, federated quantum machine learning, and secure multi-party delegated tasks (Polacchi et al., 2023, Polacchi et al., 2024, Grilo et al., 28 Apr 2025).

The trade-offs are equally explicit. Linear topology serializes participation and can limit parallelism. Multi-client blind computation requires precise timing, fast feed-forward electronics, matched optical delays, and either a trusted TTP or a composably secure SMPC layer. Large graph-state MBQC ideally requires multiple parallel Qlines, since each resource qubit should pass all clients once. In the 2023 blind-computing implementation, verification was absent; the 2024 work addresses this for untrusted state preparation, but device-independent variants remain challenging (Polacchi et al., 2023, Polacchi et al., 2024).

The prepare-and-measure Qline platform faces a different set of constraints. OT is feasible on current hardware, but throughput remains modest, and memory limits emerge in high-QBER regimes because commitments may span $S2$54 bits. Quantum tokens are not yet secure on the present single-APD hardware because the detection probability is too low; the proposed remedy is improved detectors such as SNSPDs and higher-quality photon sources. The authors also call for a compiler translating ideal-world protocol security to real-world physical error-and-loss models (Hanouz et al., 3 Mar 2026).

The 2026 rotation-based formalization sharpens the conceptual outlook. It shows that trusted sources and detectors are not fundamental requirements for most single-qubit quantum cryptographic protocols if trusted single-qubit rotations are available instead. This suggests that Qline’s long-term significance lies not only in a specific linear network layout, but in a broader architectural reduction: quantum-network functionality can be concentrated into a single photonic path and a small set of trusted local operations, while security is shifted to composable reductions and protocol-level parameter estimation (Grilo et al., 22 Jun 2026).

Taken together, these results position Qline as a family of linear quantum-network constructions spanning delegated computation, prepare-and-measure cryptography, and network services beyond QKD. Its defining features are a single quantum pipeline, minimal intermediate-node functionality, and security arguments compatible with adversarial sources, detectors, and multi-client collusion models. The remaining open problems are engineering rather than conceptual: higher detection efficiency, tighter finite-key analyses, scalable verification, integration with error correction and quantum-internet interconnects, and broader deployment of authenticated classical-control layers (Polacchi et al., 2023, Polacchi et al., 2024, Grilo et al., 28 Apr 2025, Hanouz et al., 3 Mar 2026).