We study the impact that two miners equipped with quantum computers purpose-built for quantum Bitcoin mining will have on the 51% attack threshold of the Bitcoin network, given that the miners are playing a competitive game against each other to be the first to mine a block. We extend an existing game-theoretic framework for Bitcoin mining and compute the resultant payoff matrices. From these payoff matrices, we determine optimal quantum mining strategies for two non-colluding and aggressive quantum miners with multiple opportunities at finding a valid block in an otherwise classical Bitcoin network. We show that these optimal quantum mining strategies have a negligible effect on the 51% attack threshold. The novelty of our work is the inclusion of the Aggressive Quantum Mining Strategy and the realistic approach of allowing the quantum miners to restart their search if their measurements do not yield a valid block when determining the optimal quantum mining strategies. Our result is important for evaluating quantum-mining threats on cryptocurrencies based on Proof-of-Work, e.g. Bitcoin
Financial fraud detection is challenged by decentralized data, severe class imbalance, and privacy constraints. This paper presents QuantumChain, a secure Quantum Federated Learning (QFL) framework that combines hybrid quantum-classical neural networks, encrypted federated aggregation, blockchain-based auditability, and quantum-secure communication. Each client trains a local hybrid model in which a variational quantum circuit is embedded between classical neural layers, while model updates are protected through homomorphic encryption, threshold secret sharing, and QKD-based keying. A permissioned blockchain records aggregation events and supports reputation-weighted trust among participants. We evaluate QuantumChain on financial transaction data using a compact, size-matched classical baseline to isolate the effect of the quantum layer. Results show that the HQNN achieves comparable accuracy while improving fraud-class recall in most settings, reaching 94.6% recall compared with 93.2% for the classical model. The Deep QLayer improves performance in full-data settings, suggesting that added circuit depth helps recover representational capacity when the shallow circuit becomes limited. Mixed-state simulations further show that the recall trend persists under non-ideal quantum evolution. In federated deployment with 10 heterogeneous clients, global accuracy increases from 97.7% to 98.8% over five rounds before stabilizing. These results show that QuantumChain can integrate depth-aware hybrid quantum models into a secure federated fraud-detection pipeline while maintaining stable global convergence.
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.
Yongqiang Du, Chen-Xun Weng, Feng Xie, Ming-Yang Li · 13 authors
Popularized by the Bitcoin cryptocurrency, blockchain technology establishes a decentralized digital framework that utilizes cryptographic and consensus protocols to secure data against unauthorized modification. Consequently, blockchain has found broad adoption across diverse fields, including finance, data management, healthcare, and digital asset governance. In the quantum computing era, a paramount objective for blockchain is to preserve its foundational advantages of cryptographic integrity and decentralized fault-tolerant resilience. In principle, quantum digital signatures and quantum Byzantine agreement protocols offer foundational security guarantees and tolerate up to one-half of malicious nodes for blockchain. However, the practical realization of such a quantum-enhanced blockchain remains a significant and multifaceted challenge. Here, we propose and experimentally demonstrate a fully operational hybrid quantum blockchain architecture built on photonic integrated circuits and deployed over commercially available classical telecommunications infrastructure. The system achieves a fault tolerance of nearly one-half, surpassing the classical limit, while reaching consensus on a timescale of seconds. A deployed food traceability application validates the practicality of the proposed architecture, achieving a throughput of approximately 500 transactions per second. This work establishes a foundation for practical quantum blockchains, enabling secure, scalable, and decentralized information processing in the emerging quantum era.
Sai Sakunthala Guddanti, Anupama Ray, Mrunal Arun Kumavat, Anil Prabhakar
This article explores the potential of Quantum Machine Learning (QML), specifically assessing a Quantum Support Vector Machine (QSVM) and a Variational Quantum Classifier (VQC) for detecting anomalies in real-world financial transaction data. While these QML methods outperform statistical methods, they fall short of cutting-edge deep learning techniques. To bridge this gap, we propose a hybrid quantum-classical ensemble framework that leverages the strengths of both domains. We demonstrate its effectiveness in detecting phishing in Ethereum transaction networks by combining complementary algorithms. The QSVM, whether used individually or in an ensemble, consistently delivered the lowest false negatives and higher recall rates, that are crucial for anomaly detection. To enhance individual models, we encoded the data using novel cascaded Quantum Random Access Coding (QRAC) schemes and compared it with the popular encoding ZZ feature map on both simulators and the IBM Heron quantum processor. For both QSVM and VQC, we consistently observed improvements (13% for QRAC-VQC and 3% for QRAC-QSVM) of QRAC over the ZZ feature map. Notably, certain QML algorithms exhibit remarkable resilience on the IBM Heron quantum processor, approaching simulator-level performance on devices with high quantum volume. This observation underscores the promise of QML despite hardware limitations.
Quantum computing poses a real, broad-based, but bounded and substantially mitigable threat to Bitcoin and Ethereum. We separate the two quantum algorithms that public discussion routinely conflates: Shor's algorithm breaks the elliptic-curve signatures (ECDSA over secp256k1, BLS over BLS12-381) that authorize spending, whereas Grover's algorithm does not meaningfully threaten proof-of-work mining, which is protected by a merely quadratic speedup, fault-tolerant per-operation costs, a square-root parallelization wall, and difficulty adjustment. Folding hardware scaling, the falling resource requirement, a fault-tolerance readiness lag, and expert surveys into a single Monte-Carlo forecast yields a wide, bimodal arrival distribution for a cryptographically relevant quantum computer: about a one-in-six chance by 2035, near 30% by 2040, and about 60% by 2050. Exposure is concentrated and mostly migratable: of Bitcoin's roughly six million quantum-exposed coins only about 2.3 million are irreducibly at risk, while 50 to 65% of Ether sits at key-revealed accounts that can adopt post-quantum signatures. A timely migration beats even an optimistic 2035 machine, so the binding constraint is governance, not technology. A survey of the top twenty cryptocurrencies finds none fully post-quantum. Reproducible models accompany every quantitative claim.
Shor's algorithm represents the main threat of quantum computers to cryptography. In order to precisely understand its feasibility, many authors have worked towards reducing its costs, either at the logical level (assuming a fault-tolerant architecture), or at the physical level (taking into account the constraints of envisioned hardware). In particular, recent works by Chevignard et al. (CRYPTO 2024) and Gidney (arXiv 2025) used improved arithmetic to significantly reduce the qubit cost of factoring RSA public keys. Even more recently, Babbush et al. (arXiv 2026) improved the cost of computing elliptic curve discrete logarithms, with a reduction of a factor 2 to 3 in gate count and qubit count compared to a previous work by Litinski (arXiv 2023). Their result relies on optimized point addition circuits on elliptic curves over prime fields. However they did not reveal their logical quantum circuits, relying instead on a zero-knowledge proof. In this paper, we detail a quantum logical circuit architecture which gives similar results as Babbush et al., with a slightly higher number of qubits (around 1.5% increase) and a slightly smaller Toffoli gate count (between 6.5% and 10% reduction) for the curve secp256k1. We also give gate counts for a generic variant of the circuit, which is valid for any prime field.
Margherita Cozzolino, Stephan Krenn, Thomas Lorünser
While QKD ensures information-theoretic security at the link level, real-world deployments depend on trusted repeaters, creating potential vulnerabilities. In this paper, we thus introduce a topology-hiding connectivity assurance protocol to enhance trust in quantum key distribution (QKD) network infrastructures. Our protocol allows network providers to jointly prove the existence of a secure connection between endpoints without revealing internal topology details. By extending graph-signature techniques to support multi-graphs and hidden endpoints, we enable zero-knowledge proofs of connectivity that ensure both soundness and topology hiding. We further discuss how our approach can certify, e.g., multiple disjoint paths, supporting multi-path QKD scenarios. This work bridges cryptographic assurance methods with the operational requirements of QKD networks, promoting verifiable and privacy-preserving inter-network connectivity.
Ryan Babbush, Adam Zalcman, Craig Gidney, Michael Broughton · 9 authors
This whitepaper seeks to elucidate implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and mitigation strategies. First, we provide new resource estimates for breaking the 256-bit Elliptic Curve Discrete Logarithm Problem, the core of modern blockchain cryptography. We demonstrate that Shor's algorithm for this problem can execute with either <1200 logical qubits and <90 million Toffoli gates or <1450 logical qubits and <70 million Toffoli gates. In the interest of responsible disclosure, we use a zero-knowledge proof to validate these results without disclosing attack vectors. On superconducting architectures with 1e-3 physical error rates and planar connectivity, those circuits can execute in minutes using fewer than half a million physical qubits. We introduce a critical distinction between fast-clock (such as superconducting and photonic) and slow-clock (such as neutral atom and ion trap) architectures. Our analysis reveals that the first fast-clock CRQCs would enable on-spend attacks on public mempool transactions of some cryptocurrencies. We survey major cryptocurrency vulnerabilities through this lens, identifying systemic risks associated with advanced features in some blockchains such as smart contracts, Proof-of-Stake consensus, and Data Availability Sampling, as well as the enduring concern of abandoned assets. We argue that technical solutions would benefit from accompanying public policy and discuss various frameworks of digital salvage to regulate the recovery or destruction of dormant assets while preventing adversarial seizure. We also discuss implications for other digital assets and tokenization as well as challenges and successful examples of the ongoing transition to Post-Quantum Cryptography (PQC). Finally, we urge all vulnerable cryptocurrency communities to join the ongoing migration to PQC without delay.
Bitcoin already faces a quantum threat through Shor attacks on elliptic-curve signatures. This paper isolates the other component that public discussion often conflates with it: mining. Grover's algorithm halves the exponent of brute-force search, promising a quadratic edge to any quantum miner of Bitcoin. Exactly how large that edge grows depends on fault-tolerant hardware. No prior study has costed that hardware end to end. We build an open-source estimator that sweeps the full attack surface: reversible oracles for double-SHA-256 mining and RIPEMD-based address preimages, surface-code factory sizing, fleet logistics under Nakamoto-consensus timing, and Kardashev-scale energy accounting. A parametric sweep over difficulty bits b, runtime caps, and target success probabilities reveals a sharp transition. At the most favourable partial-preimage setting (b = 32, 2^224 marked states), a superconducting surface-code fleet still requires about 10^8 physical qubits and about 10^4 MW. That load is comparable to a large national grid. Tightening to Bitcoin's January 2025 mainnet difficulty (b about 79) explodes the bill to about 10^23 qubits and about 10^25 W, approaching the Kardashev Type II threshold. These numbers settle a narrower question than "Is Bitcoin quantum-secure?" Once Grover mining is lifted from asymptotic query counts to fault-tolerant physical cost, practical quantum mining collapses under oracle, distillation, and fleet overhead. To push mining into non-trivial consensus effects, one must invoke astronomical quantum fleets operating at energy scales that lie far above present-day civilization.
Quantum computing provides a feasible multi-layered security challenge to classical blockchain networks. Quantum blockchains that rely on quantum key distribution (QKD) to establish secure channels can address this feasible threat. Whereas, there are still architecture limitations to practical security resulted in the measurement devices while implementing the QKD-secured blockchains in physical layer. This paper presents a quantum-classical hybrid architecture in a distributed blockchain to address the connectivity and distance limitations of the blockchain-embedded quantum networks. A decoupled architecture is designed felicitously so that it pairs a linearly scalable measurement-device-independent (MDI) physical layer with a decentralized consensus. It can optimize the complexity of infrastructure from quadratic to linear scaling, ascribed to leveraging the twin-field (TF) QKD protocol with the MDI-structurized star topology. Additionally, the dual-key stratification strategy transforms symmetric information-theoretic security into publicly auditable forward-secret blockchain evidence. This architecture can integrate the exact information-theoretic security (ITS) with distributed consensus mechanisms, allowing the scalable system to overcome the potential rate-loss limits inherent in classical security-weakened blockchains.
Sybil resistance is a key requirement of decentralized consensus protocols. It is achieved by introducing a scarce resource (such as computational power, monetary stake, disk space, etc.), which prevents participants from costlessly creating multiple fake identities and hijacking the protocol. Quantum states are generically uncloneable, which suggests that they may serve naturally as an unconditionally scarce resource. In particular, uncloneability underlies quantum position-based cryptography, which is unachievable classically. We design a consensus protocol that combines classical hybrid consensus protocols with quantum position verification as the Sybil resistance mechanism, providing security in the standard model, and achieving improved energy efficiency compared to hybrid protocols based on Proof-of-Work. Our protocol inherits the benefits of other hybrid protocols, namely the faster confirmation times compared to pure Proof-of-Work protocols, and resilience against the compounding wealth issue that plagues protocols based on Proof-of-Stake Sybil resistance. We additionally propose a spam prevention mechanism for our protocol in the Random Oracle model.
Quantum Byzantine agreement (QBA), a cornerstone of quantum blockchain, offers inherent advantages in security and fault tolerance over classical protocols, guaranteed by the laws of quantum mechanics. However, existing multiparty QBA protocols face challenges for large-scale deployment due to exponential communication complexity or reliance on complex multi-particle entanglement. To address this, we propose a multiparty circular QBA protocol that adopts a semi-decentralized architecture, leveraging circular message gathering and quantum digital signatures to achieve quadratic communication complexity and enhanced fault tolerance. Our protocol is experimentally feasible, requiring only weak coherent states, and is compatible with existing star-shaped quantum networks. Simulations conducted on a global satellite-to-ground network demonstrate that the protocol sustains high consensus rates among multiple users, even when employing different key generation protocols under realistic conditions. This work presents a scalable framework for large-scale QBA networks, establishing the foundation for a practical quantum blockchain that enables secure and fault-tolerant decentralized services.
The long-term security of public blockchains strictly depends on the hardness assumptions of the underlying digital signature schemes. In the current scenario, most deployed cryptocurrencies and blockchain platforms rely on elliptic-curve cryptography, which is vulnerable to quantum attacks due to Shor's algorithm. Therefore, it is important to understand how post-quantum (PQ) digital signatures behave when integrated into real blockchain systems. This report presents a blockchain prototype that supports multiple quantum-secure signature algorithms, focusing on CRYSTALS-Dilithium, Falcon and Hawk as lattice-based schemes. This report also describes the design of the prototype and discusses the performance metrics, which include key generation, signing, verification times, key sizes and signature sizes. This report covers the problem, background, and experimental methodology, also providing a detailed comparison of quantum-secure signatures in a blockchain context and extending the analysis to schemes such as HAETAE.
Rapid advancements in quantum computing and machine learning threaten the long-term security of classical blockchain systems, whose protection mechanisms largely rely on computational difficulties. In this study, we propose a quantum blockchain protocol whose protection mechanism is directly derived from quantum mechanical principles. The protocol combines high-dimensional Bell states, time-entanglement, entanglement switching, and high-dimensional superdense coding. Encoding classical block information into time-delimited qudit states allows block identity and data verification to be implemented through the causal sequencing of quantum measurements instead of cryptographic hash functions. High-dimensional coding increases the information capacity per quantum carrier and improves noise resistance. Time-entanglement provides distributed authentication, non-repudiation, and tamper detection across the blockchain. Each block derives its own public-private key pair directly from the observed quantum correlations by performing high-dimensional Bell state measurements in successive time steps. Because these keys are dependent on the time ordering of measurements, attempts to alter block data or disrupt the protocol's timing structure inevitably affect the reconstructed correlations and are revealed during validation. Recent advances in the creation and detection of high-dimensional time-slice entanglement demonstrate that the necessary quantum resources are compatible with emerging quantum communication platforms. Taken together, these considerations suggest that the proposed framework can be evaluated as a viable and scalable candidate for quantum-secure blockchain architectures in future quantum network environments.
We study non-interactive zero-knowledge proofs (NIZKs) for NP satisfying: 1) statistical soundness, 2) computational zero-knowledge and 3) certified-everlasting zero-knowledge (CE-ZK). The CE-ZK property allows a verifier of a quantum proof to revoke the proof in a way that can be checked (certified) by the prover. Conditioned on successful certification, the verifier's state can be efficiently simulated with only the statement, in a statistically indistinguishable way. Our contributions regarding these certified-everlasting NIZKs (CE-NIZKs) are as follows: - We identify a barrier to obtaining CE-NIZKs in the CRS model via generalizations of known interactive zero-knowledge proofs that satisfy CE-ZK. - We circumvent this by constructing CE-NIZK from black-box use of NIZK for NP satisfying certain properties, along with OWFs. As a result, we obtain CE-NIZKs for NP in the CRS model, based on polynomial hardness of the learning with errors (LWE) assumption. - In addition, we observe that the aforementioned barrier does not apply to the shared EPR model. We leverage this fact to construct a CE-NIZK for NP in this model based on any statistical binding hidden-bits generator, which can be based on LWE. The only quantum computation in this protocol involves single-qubit measurements of the shared EPR pairs.
On-demand authentication is critical for scalable quantum systems, yet many existing quantum signature and message-authentication schemes are signer-initiated, requiring advance distribution of authentication material even when no verification occurs. We introduce verifier-initiated quantum digital signatures (VIQDS), in which the verifier requests authentication only when needed and the signer responds once; after issuance, verification proceeds without further interaction. Practically, shifting authentication to a verifier-driven, on-demand workflow reduces avoidable communication and storage overhead and aligns with deployments where verification is sporadic, such as distributed services and audit-oriented infrastructures. Our approach leverages quantum zero-knowledge techniques so that verification reveals nothing about the signer’s secret key beyond the fact that the signature is valid. We present a general conversion principle from suitable quantum proof protocols to VIQDS, together with a concrete realization based on elementary qubit platforms. Here, we show information-theoretic security against forgery and privacy against curious verifiers without computational hardness assumptions. The authors introduce a verifier-initiated quantum message-authentication method, in which authentication is requested only when needed. Their approach uses quantum zero knowledge techniques to protect information about the signer’s secret key while providing information-theoretic security against forgery
Quantum computers have the potential to break classical cryptographic systems by efficiently solving problems such as the elliptic curve discrete logarithm problem using Shor's algorithm. While resource estimates for factoring-based cryptanalysis are well established, comparable evaluations for Shor's elliptic curve algorithm under realistic architectural constraints remain limited. In this work, we propose a carry-lookahead quantum adder that achieves Toffoli depth $\log n + \log\log n + O(1)$ with only $O(n)$ ancillas, matching state-of-the-art performance in depth while avoiding the prohibitive $O(n\log n)$ space overhead of existing approaches. Importantly, our design is naturally compatible with the two-dimensional nearest-neighbor architectures and introduce only a constant-factor overhead. Further, we perform a comprehensive resource analysis of Shor's elliptic curve algorithm on two-dimensional lattices using the improved adder. By leveraging dynamic circuit techniques with mid-circuit measurements and classically controlled operations, our construction incorporates the windowed method, Montgomery representation, and quantum tables, and substantially reduces the overhead of long-range gates. For cryptographically relevant parameters, we provide precise resource estimates. In particular, breaking the NIST P-256 curve, which underlies most modern public-key infrastructures and the security of Bitcoin, requires about $4300$ logical qubits and logical Toffoli fidelity about $10^{-9}$. These results establish new benchmarks for efficient quantum arithmetic and provide concrete guidance toward the experimental realization of Shor's elliptic curve algorithm.
Quantum blockchains provide inherent resilience against quantum adversaries and represent a promising alternative to classical blockchain systems in the quantum era. However, existing quantum blockchain architectures largely depend on entanglement to maintain inter-block connections, facing challenges in stability, consensus efficiency, and system verification. To address these issues, this work proposes a novel quantum blockchain framework based on quantum walks, which reduces reliance on entanglement while improving stability and connection efficiency. We further propose a quantum consensus mechanism based on a weighted quantum voting protocol, which enables a fairer voting process while reflecting the weights of different nodes. To validate the proposed framework, we conduct circuit simulations to evaluate the correctness and effectiveness of both the quantum walk-based block construction and the quantum voting consensus mechanism. Compared with existing entanglement-dependent approaches, our framework achieves stronger stability and enables simpler verification of block integrity, making it a practical candidate for quantum-era blockchain applications.
We formulate automated market maker (AMM) \emph{rebalancing} as a binary detection problem and study a hybrid quantum--classical self-attention block, \textbf{Quantum Adaptive Self-Attention (QASA)}. QASA constructs quantum queries/keys/values via variational quantum circuits (VQCs) and applies standard softmax attention over Pauli-$Z$ expectation vectors, yielding a drop-in attention module for financial time-series decision making. Using daily data for \textbf{BTCUSDC} over \textbf{Jan-2024--Jan-2025} with a 70/15/15 time-series split, we compare QASA against classical ensembles, a transformer, and pure quantum baselines under Return, Sharpe, and Max Drawdown. The \textbf{QASA-Sequence} variant attains the \emph{best single-model risk-adjusted performance} (\textbf{13.99\%} return; \textbf{Sharpe 1.76}), while hybrid models average \textbf{11.2\%} return (vs.\ 9.8\% classical; 4.4\% pure quantum), indicating a favorable performance--stability--cost trade-off.
This study presents a comprehensive empirical comparison between quantum machine learning (QML) and classical machine learning (CML) approaches in Automated Market Makers (AMM) and Decentralized Finance (DeFi) trading strategies through extensive backtesting on 10 models across multiple cryptocurrency assets. Our analysis encompasses classical ML models (Random Forest, Gradient Boosting, Logistic Regression), pure quantum models (VQE Classifier, QNN, QSVM), hybrid quantum-classical models (QASA Hybrid, QASA Sequence, QuantumRWKV), and transformer models. The results demonstrate that hybrid quantum models achieve superior overall performance with 11.2\% average return and 1.42 average Sharpe ratio, while classical ML models show 9.8\% average return and 1.47 average Sharpe ratio. The QASA Sequence hybrid model achieves the highest individual return of 13.99\% with the best Sharpe ratio of 1.76, demonstrating the potential of quantum-classical hybrid approaches in AMM and DeFi trading strategies.
Cross-chain bridges and oracle DAOs represent some of the most vulnerable components of decentralized systems, with more than 2.8 billion lost due to trust failures, opaque validation behavior, and weak incentives. Current oracle designs are based on multisigs, optimistic assumptions, or centralized aggregation, exposing them to attacks and delays. Moreover, predictable committee selection enables manipulation, which threatens data integrity across chains. We propose V-ZOR, a verifiable oracle relay that integrates zero-knowledge proofs, quantum-grade randomness, and cross-chain restaking to mitigate these risks. Each oracle packet includes a Halo 2 proof verifying that the reported data was correctly aggregated using a deterministic median. To prevent committee manipulation, VZOR reseeds its VRF using auditable quantum entropy, ensuring unpredictable and secure selection of reporters. Reporters stake once on a shared restaking hub; any connected chain can submit a fraud proof to trigger slashing, removing the need for multisigs or optimistic assumptions. A prototype in Sepolia and Scroll achieves sub-300k gas verification, one-block latency, and a $\mathbf{1 0} \times$ increase in collusion cost. V-ZOR demonstrates that combining ZK attestation with quantum-randomized restaking enables a trust-minimized, high-performance oracle layer for cross-chain DeFi.
This paper provides an in-depth review of the evolving role of quantum computing in the financial sector, emphasizing both its computational potential and cybersecurity implications. Distinguishing itself from existing surveys, this work integrates classical quantum computing applications - such as portfolio optimization, risk analysis, derivative pricing, and Monte Carlo simulations with a thorough examination of blockchain technologies and post-quantum cryptography (PQC), which are crucial for maintaining secure financial operations in the emerging quantum era. We propose a structured four-step framework to assess the feasibility and expected benefits of implementing quantum solutions in finance, considering factors such as computational scalability, error tolerance, data complexity, and practical implementability. This framework is applied to a series of representative financial scenarios to identify domains where quantum approaches can surpass classical techniques. Furthermore, the paper explores the vulnerabilities quantum computing introduces to digital finance-related applications and blockchain security, including risks to digital signatures, hash functions, and randomness generation, and discusses mitigation strategies through PQC and quantum-resilient alternatives of classical digital finance tools and blockchain architectures. By addressing both quantum blockchain, quantum key distribution (QKD) as well as quantum communication networks, his review presents a more holistic perspective than prior studies, offering actionable insights for researchers, financial practitioners, and policymakers navigating the intersection of quantum computing, blockchain, and secure financial systems.
Pierre-Luc Dallaire-Demers, William Doyle, Timothy Foo
Precise suites of benchmarks are required to assess the progress of early fault-tolerant quantum computers at economically impactful applications such as cryptanalysis. Appropriate challenges exist for factoring but those for elliptic curve cryptography are either too sparse or inadequate for standard applications of Shor's algorithm. We introduce a difficulty-graded suite of elliptic curve discrete logarithm (ECDLP) challenges that use Bitcoin's curve y^2=x^3+7 mod p while incrementally lowering the prime field from 256 down to 6 bits. For each bit-length, we provide the prime, the prime group order, and two deterministic nothing-up-my-sleeve (NUMS) points in compressed SEC1 form. All challenges are generated by a deterministic, reproducible procedure, and no private challenge scalar is chosen in advance. We calibrate classical cost against Pollard's rho records and quantum cost against resource estimation results for Shor's algorithm. We compile Shor's ECDLP circuit to logical counts and map them to physical resources for various parameters of the surface code, the repetition cat code and the LDPC cat codes. Under explicit and testable assumptions on physical error rates, code distances, and non-Clifford supply, our scenarios place the full 256-bit instance within a 2027--2033 window. The challenge ladder thus offers a transparent ruler to track fault-tolerant progress on a cryptanalytic target of immediate relevance, and it motivates proactive migration of digital assets to post-quantum signatures.