Experimental demonstration of scalable quantum blockchain with exponentially superior quantum communication complexity

Abstract: To secure modern distributed digital infrastructures, quantum blockchains exploit quantum resources to achieve information-theoretic security and surpass the classical one-third fault-tolerance bound. However, existing high-fault-tolerant protocols face a fundamental scalability challenge: the blockchain trilemma imposes either exponential communication complexity or experimentally demanding multipartite entanglement. Here, we experimentally demonstrate a scalable quantum blockchain protocol based on weak coherent states that achieves an exponential reduction in quantum communication complexity. The protocol employs a circular quantum Byzantine agreement mechanism that preserves information-theoretic security while avoiding multipartite entanglement. We implement this protocol on a photonic integrated circuit platform, realizing a six-node network over commercially available telecommunication infrastructure. Compared with previous schemes, the protocol requires less than 4% of the quantum communication resources. Leveraging this advantage, we further demonstrate a quantum-secured token exchange application achieving a throughput of 805.3 transactions per second with zero failures. These results establish a practical pathway toward scalable quantum blockchain.

• The paper demonstrates a circular quantum Byzantine agreement protocol with quadratic communication complexity, tolerating three Byzantine faults among five users without multipartite entanglement.
• The field trial used silicon photonic chips over metropolitan fiber links up to 30 km, achieving quantum bit error rates of 0.75–1.47% and consensus failure probability of 10⁻¹¹·⁷⁶.
• The token-exchange application achieved zero failures and up to 805.3 transactions per second, while its semi-decentralized certificate-authority model and small network size remain important limitations.

This paper reports an experimental demonstration of a scalable quantum blockchain built on a circular quantum Byzantine agreement (QBA) protocol, implemented over a field-deployed metropolitan fiber network using silicon photonic integrated circuits. The central contribution is an exponential reduction in quantum communication complexity relative to prior high-fault-tolerance QBA schemes, achieved without multipartite entanglement, together with an end-to-end application demonstration of a quantum-secured token exchange reaching 805.3 transactions per second with zero failures (2607.12250).

Motivation and problem statement

Classical blockchain consensus is bounded by the one-third fault-tolerance limit for Byzantine agreement and relies on computational hardness assumptions vulnerable to Shor-type quantum attacks. Quantum blockchain proposals address both weaknesses by exploiting information-theoretic primitives such as quantum digital signatures (QDS). However, existing high-fault-tolerance quantum consensus protocols face a scalability dilemma: fully decentralized schemes incur communication complexity scaling as $\mathcal{O}(N^f)$ or worse—exponential in the tolerated number of malicious nodes $f$—while entanglement-based alternatives rely on fragile multipartite states or heuristic constructions lacking rigorous security proofs. This constraint has confined prior experimental demonstrations to at most two malicious nodes and small node counts.

Circular QBA protocol

The protocol solves the Byzantine generals problem among $N$ nodes—one master $S$ and $N-1$ participants $R_i$—using three-party OTUH-QDS based on LFSR-derived Toeplitz universal$_2$ hashing, whose forgery probability is bounded by $$\varepsilon_{\rm{for}}(m) = m/2^{L_{\mathrm{sig}}-1}$$. A certificate authority (CA) participates solely as signature verifier; it generates no messages and makes no decisions.

The protocol proceeds in three phases:

1. Order distribution: the master signs and distributes orders to each participant via OTUH-QDS.
2. Circular gathering: each participant initiates a clockwise relay cycle in which authenticated message lists are appended, re-signed, and verified by the CA at every step; any invalid signature aborts and restarts the round.
3. Consensus output: all honest participants hold identical authenticated message sets and apply a deterministic function to produce identical outputs.

Security follows from the unforgeability and non-repudiation of OTUH-QDS, with a total failure probability bounded by cumulative forgery risk over all signing operations. The fault-tolerance condition is $N > f+1$, i.e., only two honest participants are required—a relaxation beyond the classical bound. The communication complexity is

$C(N) = N^2 - N,$

quadratic rather than exponential, because the semi-decentralized star topology reduces the required number of quantum channels from $f$0 to $f$1. The trade-off is explicit: the CA-assisted architecture is semi-decentralized rather than fully decentralized, so the polynomial scaling depends on trusting the CA's verification role while excluding it from decision-making.

Field-deployed network and physical layer

The experiment deploys six nodes (five users plus CA) across Nanning, China, over commercial telecom fiber with link lengths up to 30 km, mean link length 7.1 km, and average channel loss 12.0 dB. All receivers are co-located at the CA in a transmitter–receiver–shared architecture; each user runs a one-decoy-state BB84 protocol with finite-key analysis against a silicon photonic encoder chip, while the CA uses a silicon decoder chip with polarization tracking feeding multichannel SNSPDs. Measured secure key rates per link are 273.82, 229.96, 2.97, 2.64, and 4.99 kbps, with QBERs between 0.75% and 1.47% and phase-error bounds below 4.10%. The roughly two-order-of-magnitude spread in key rates across links directly constrains consensus throughput, since the slowest link ($f$2) limits the system.

Consensus performance and complexity advantage

With signature length $f$3, the consensus rate is bounded by

$f$4

yielding 0.686 tps for $f$5 (failure probability $f$6), 1.289 tps for $f$7, and 2.578 tps for $f$8. The five-node configuration tolerates $f$9 malicious nodes—the highest experimental Byzantine fault tolerance reported for a quantum blockchain. The resource comparison is stark: tolerating $N$0 requires 20 QDS operations under this protocol versus 3,609 for QKD-based QBA and 510 for recursive QBA, i.e., less than 4% of the resources of the best prior scheme (~96% reduction), with the gap widening to several orders of magnitude at larger adversarial thresholds. The demonstration is also the first to combine integrated photonic chips, field deployment, entanglement-free operation, and information-theoretic security in a single system.

Scheme	Users	$N$1	Complexity	Chip	Field	Entanglement-free
Kiktenko et al.	4	1	$N$2	✗	✓	✓
Weng et al.	5	2	$N$3	✗	✗	✓
Jing et al.	3	1	$N$4	✓	✗	✗
Lu et al.	5	2	$N$5	✗	✗	✓
This work	5	3	$N$6	✓	✓	✓

Token exchange application

On top of the consensus layer, the authors implement a two-layer decentralized exchange: a quantum consensus layer providing tamper-resistant transaction ordering, and an application layer executing automated-market-maker smart contracts (constant-product pricing) on a Hyperledger Fabric-style ledger with endorsing peers and chaincode. Benchmarking with Hyperledger Caliper across Swap, Stake, Unstake, and Search workloads shows a 100% success rate at all tested loads, with throughput scaling near-linearly before saturating at 805.3 tps (Search), 721.9 tps (Swap), 684.9 tps (Stake), and 667.6 tps (Unstake); average latency remains below one second up to moderate loads and grows to several seconds at saturation. These figures indicate that the quantum-secured ordering layer does not become the bottleneck for practical DeFi-scale workloads at this network size—an important point, since the consensus-layer rate (0.686 tps for megabit messages) applies to full consensus instances, whereas individual transactions are batched into ordered blocks.

Limitations and open questions

Several caveats qualify the results. First, the semi-decentralized design delegates signature verification to a CA; although the CA cannot forge or alter messages, its availability and integrity are assumptions not present in fully decentralized classical blockchains, and the paper does not analyze CA compromise or denial-of-service scenarios. Second, the fault-tolerance condition $N$7 means the system requires only two honest participants but correspondingly offers weaker resilience guarantees than the classical $N$8 threshold in some regimes; the comparison across schemes in the paper holds adversarial assumptions fixed, but the security model differs structurally from fully decentralized QBA. Third, the demonstrated network size is five users, so the claimed asymptotic $N$9 advantage versus exponential schemes remains extrapolated beyond the tested scale, and key-rate heterogeneity across links will increasingly throttle $S$0 as $S$1 grows since it scales inversely with $S$2. Fourth, the token-exchange benchmarks run in a virtualized environment (VMware, 16 GB RAM) rather than on dedicated hardware, leaving the interaction between consensus latency and real-time transaction finality under adversarial load untested. Open questions include whether the circular gathering mechanism maintains its failure bounds under concurrent multi-round consensus, and how the architecture extends when the trusted-verifier role must be distributed.

Conclusion

The paper demonstrates that replacing exponential-complexity or entanglement-dependent quantum consensus with a CA-assisted circular QBA protocol yields a practically deployable quantum blockchain: quadratic communication scaling, tolerance of three Byzantine faults, chip-integrated hardware, metropolitan fiber deployment, and a functioning token exchange sustaining hundreds of transactions per second with zero failures. The principal structural cost is reliance on a semi-decentralized verifier, and the principal empirical limitation is the small demonstrated network size; both define the immediate boundaries within which the reported complexity and fault-tolerance advantages have been validated.