Thiago Bergamaschi

Ryan Babbush, Adam Zalcman, Craig Gidney et al.

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.

Tai-Hsuan Yang, Mehdi Soleimanifar, Thiago Bergamaschi et al.

A naive classical representation of an n-qubit state requires specifying exponentially many amplitudes in the computational basis. Past works have demonstrated that classical neural networks can succinctly express these amplitudes for many physically relevant states, leading to computationally powerful representations known as neural quantum states. What underpins the efficacy of such representations? We show that conditional correlations present in the measurement distribution of quantum states control the performance of their neural representations. Such conditional correlations are basis dependent, arise due to measurement-induced entanglement, and reveal features not accessible through conventional few-body correlations often examined in studies of phases of matter. By combining theoretical and numerical analysis, we demonstrate how the state's entanglement and sign structure, along with the choice of measurement basis, give rise to distinct patterns of short- or long-range conditional correlations. Our findings provide a rigorous framework for exploring the expressive power of neural quantum states.