[Paper Review] Quantum-Assisted Blockchain

D. A. Sapaev, D. A. Bulychkov+3 more|arXiv (Cornell University)|Feb 19, 2018

Quantum Computing Algorithms and Architecture5 references3 citations

TL;DR

This paper proposes a quantum-assisted blockchain mining protocol using a modified Grover’s algorithm to accelerate the search for a valid blockchain nonce. By leveraging quantum parallelism and oracle-based amplitude amplification on a 48-qubit nonce register, the method reduces mining time from ~465 days (classical) to just 2 seconds, demonstrating a quadratic speedup in proof-of-work consensus.

ABSTRACT

Bitcoin and blockchain in general is a hot topic nowadays. In the paper we propose a quantum empowering of this technology and show how to speed-up the mining procedure using the modified Grover's algorithm.

Motivation & Objective

• To explore the integration of quantum computing with blockchain technology to accelerate the mining process.
• To address the challenge of applying Grover’s algorithm to blockchain mining, where classical hashing operations must be implemented quantumly.
• To resolve issues arising from quantum entanglement and non-uniform amplitude distributions during the Grover iteration process.
• To adjust the mining difficulty threshold to maintain a single valid solution probability, ensuring compatibility with existing blockchain security models.
• To provide a practical quantum algorithmic framework for quantum-assisted blockchain mining with realistic qubit requirements.

Proposed method

• Implement a quantum circuit with separate qubit registers for nonce (48 qubits), hash (256 qubits), service qubits, and a functional qubit for the oracle.
• Apply the Hadamard transform to the nonce register to create a uniform superposition of all possible nonce values.
• Use a reversible quantum implementation of the SHA-3 hashing function to compute the hash value for all nonce values in superposition.
• Design a controlled oracle function that marks the hash states below the target threshold using controlled-NOT and CCNOT gates.
• Apply the Grover diffusion operator to the nonce register after uncomputing all ancillary qubits to restore initial states and preserve amplitude amplification.
• Repeat the oracle and diffusion steps approximately π√(2^48)/4 ≈ 13 million times to maximize the amplitude of the correct nonce state.

Experimental results

Research questions

• RQ1 Can Grover’s quantum search algorithm be effectively adapted to accelerate blockchain mining in a proof-of-work system?
• RQ2 How can classical cryptographic hashing functions like SHA-3 be implemented in a reversible, unitary quantum circuit for use in quantum mining?
• RQ3 What modifications are required to handle entanglement between nonce, hash, and ancillary qubits during Grover iteration?
• RQ4 How should the mining difficulty threshold be adjusted to maintain a single valid solution probability in a quantum mining context?
• RQ5 What is the expected speedup in mining time when using a quantum computer compared to classical hardware under realistic conditions?

Key findings

• Quantum-assisted mining using Grover’s algorithm reduces the number of required operations from 2^48 (classical) to approximately 13 million (quantum), achieving a quadratic speedup.
• Classical mining of a 48-bit nonce requires about 465 days (11,000 hours) at 7 million operations per second, while quantum mining completes in just 2 seconds at 1 billion gates per second.
• The probability of finding a valid solution with 48-bit nonce and 256-bit hash is maintained near 1/2 when the first 49 bits of the hash are set to zero, aligning with current Bitcoin network difficulty.
• The algorithm requires careful uncomputation of ancillary qubits after each oracle call to preserve the integrity of the Grover diffusion step and avoid measurement collapse.
• The implementation of SHA-3 in a reversible quantum circuit is feasible using CNOT, CCNOT, and Pauli-X gates for XOR, AND, and NOT operations, respectively.
• Extending the nonce register to 48 qubits ensures that the expected number of valid solutions is approximately 2^207, making the probability of multiple solutions negligible.