Blockchain with proof of quantum work

TL;DR

This work has refined the blockchain framework to incorporate the probabilistic nature of quantum mechanics, ensuring stability against sampling errors and hardware inaccuracies, and serves as a proof of concept for a meaningful application of quantum computing.

Abstract

We propose a blockchain architecture in which mining requires a quantum computer. The consensus mechanism is based on proof of quantum work, a quantum-enhanced alternative to traditional proof of work that leverages quantum supremacy to make mining intractable for classical computers. We have refined the blockchain framework to incorporate the probabilistic nature of quantum mechanics, ensuring stability against sampling errors and hardware inaccuracies. To validate our approach, we implemented a prototype blockchain on four D-Wave(TM) quantum annealing processors geographically distributed within North America, demonstrating stable operation across hundreds of thousands of quantum hashing operations. Our experimental protocol follows the same approach used in the recent demonstration of quantum supremacy [King et al. Science 2025], ensuring that classical computers cannot efficiently perform the same computation task. By replacing classical machines with quantum systems for mining, it is possible to significantly reduce the energy consumption and environmental impact traditionally associated with blockchain mining while providing a quantum-safe layer of security. Beyond serving as a proof of concept for a meaningful application of quantum computing, this work highlights the potential for other near-term quantum computing applications using existing technology.

Figures (16)

• Figure 1: Illustration of Bitcoin blocks. The Bitcoin block structure is sufficient for our proof-of-concept implementation; modifications may be useful for mitigation of weaknesses as discussed in Appendix \ref{['attacks']}.
• Figure 2: Illustration of the quantum hash generation and its use as proof of work for block security.
• Figure 3: Operation of an example blockchain with $50$ miners using four publicly accessible Advantage and Advantage2 QPUs. The mining difficulty was set to $\mathcal{N}_{\rm zeros}=32$ with basic +/-1 Chainwork defined in \ref{['softreject']}. Orange blocks show soft (resolved) forks, these blocks are included in no strongest chains (have been rejected by all miners). Blue blocks are immutable, included in all strongest chains (agreed upon by all miners). Gray and black blocks are in contention: common to some (but not all) strongest chains. Only black blocks are candidates for maximum Chainwork (are being mined) and have the potential for further branching. Blocks are labeled by the order of broadcast with the genesis block on the left and most recently mined block on the right. Either of the paths terminating in black nodes might be extended, but the orange path is no longer a candidate for the strongest chain. Blocks 10, 11, 12 and 13 contain delayed transactions, that require further mining (fork resolution) in order to be confirmed. A majority of miners believe node 13 has maximum Chainwork, and in this experiment all miners consolidate on this branch as the chain develops (see Figure \ref{['typical-blockchain']}).
• Figure 4: The same blockchain as described in Figure \ref{['typical-blockchain-14nodes']} after 219 block broadcasts with matching color scheme. The data was collected over a two-day period. The mining process is accelerated without impact on statistical outcomes (further details and results are contained in Appendix \ref{['ExperimentImplementationSection']}). The thickness of lines is proportional to the number of miners transferring to the block at the time of its broadcast. The genesis block is placed centrally with blocks placed on a spiral in the order of broadcast. Approximately 70% of block broadcasts are immutable (blue).
• Figure 5: Mining efficiency, i.e., the fraction of blocks joining the strongest chain. The Chainwork uses either the simple +/-1 weighting, or the confidence-based weighting with $\mathcal{N}_{\rm max}=1,$$2$ or $3$ with a constant $\delta W_{\alpha}$ extracted from experimental data. Confidence-weighted strongest chains are more efficient. The mining process is accelerated without impact on statistical outcomes as described in Appendix \ref{['ResamplingWitnessesSection']}. Results are obtained with resampling from experimentally-parameterized witness distributions to accelerate analysis, each point an average on 16 chains of length 512-1024. Resampling statistics are in agreement with full-experiment efficiencies reported in Figures \ref{['typical-blockchain']} and \ref{['typical-blockchain2']}. Further experimental details and statistics are contained in Appendix \ref{['ExperimentImplementationSection']}.