Proof-of-work consensus by quantum sampling (2305.19865v3)

Abstract: Since its advent in 2011, boson sampling has been a preferred candidate for demonstrating quantum advantage because of its simplicity and near-term requirements compared to other quantum algorithms. We propose to use a variant, called coarse-grained boson-sampling (CGBS), as a quantum Proof-of-Work (PoW) scheme for blockchain consensus. The users perform boson sampling using input states that depend on the current block information and commit their samples to the network. Afterwards, CGBS strategies are determined which can be used to both validate samples and reward successful miners. By combining rewards for miners committing honest samples together with penalties for miners committing dishonest samples, a Nash equilibrium is found that incentivizes honest nodes. We provide numerical evidence that these validation tests are hard to spoof classically without knowing the binning scheme ahead of time and show the robustness of our protocol to small partial distinguishability of photons. The scheme works for both Fock state boson sampling and Gaussian boson sampling and provides dramatic speedup and energy savings relative to computation by classical hardware.

• The paper presents a novel quantum sampling method that leverages coarse-grained boson sampling to address energy inefficiencies and vulnerabilities in classical PoW systems.
• It introduces dual boson sampling approaches, enabling efficient classical verification while capitalizing on the quantum advantage of photonic devices.
• The protocol’s robustness to imperfections and its integration of game-theoretic incentives offer promising insights for advancing secure, energy-efficient blockchain infrastructures.

Quantum Sampling as a Blockchain Consensus Mechanism

The paper "Proof-of-work consensus by quantum sampling" presents an innovative approach to the current limitations of blockchain technology's consensus mechanisms by introducing a novel quantum-based method. This approach utilizes quantum boson sampling, specifically coarse-grained boson-sampling (CGBS), to provide an energy-efficient and, potentially, more secure proof-of-work (PoW) paradigm. The proposed strategy is aimed at addressing two primary issues with contemporary PoW systems: prohibitive energy consumption and potential vulnerabilities to future quantum computers.

Core Concepts and Contributions

The authors introduce CGBS as an alternative to traditional PoW methods, leveraging its computational complexity to ensure security while mitigating the excessive energy demands associated with classical PoW algorithms. This method exploits two variants of boson sampling: Fock state boson sampling and Gaussian boson sampling, adaptable to different quantum systems.

Boson Sampling and Blockchain Consensus:

• Boson Sampling as Proof-of-Work: Boson sampling is an established quantum algorithm that is efficient to solve on a quantum computer but computationally infeasible on classical hardware, making it a suitable candidate for demonstrating quantum supremacy. In the proposed system, the boson-sampling task provides the computational challenge for blockchain miners, with the problem's complexity ensuring security.
• Coarse-Grained Scenarios: The paper introduces mode-binned and state-binned boson sampling, which coarse-grain the boson-sampling output space to enable efficient classical verification of quantum outputs. These two complementary approaches are applied to validate block proposals and reward miners, respectively.

Implications for Energy Consumption:

• Traditional PoW mechanisms, like Bitcoin's SHA-256 hash inversion, require substantial computational effort and, consequently, energy. Quantum sampling promises greater efficiency. The system potentially reduces the energy costs substantially because photonic devices capable of such quantum calculations (e.g., boson samplers) can outperform classical systems by orders of magnitude in terms of speed and energy efficiency.

Quantum Advantage Over Classical Mining:

• As quantum computing technologies mature, they could disrupt traditional PoW systems by breaking the collision-resistant nature or the progress-free condition assumed in classical algorithms. In this paper, the authors assess that quantum miners will be better prepared to support network consensus given the innate computational strengths of quantum systems in achieving quadratic or exponential speedups over classical counterparts.

Theoretical and Practical Implications

Security and Robustness:

• The authors demonstrate through numerical modeling the robustness of the CGBS protocol to imperfections, such as partial photon distinguishability, ensuring the protocol's practical viability. Furthermore, the difficulty in pre-computing solutions even with classical supercomputers presents a significant security benefit.

Implementation and Future Prospects:

• The practical implementation of this protocol could herald a new era in blockchain technology, with boson-sampling being realized on current noisy intermediate-scale quantum (NISQ) devices. This aligns with the ongoing advancements in quantum optics and photonics, which have already seen experimental demonstrations of boson sampling with tens of input photons.

Game-Theoretic Considerations:

• The proposed scheme integrates a refined game-theoretic strategy to ensure rational miners are incentivized to participate honestly, incorporating utility models that account for both variable and fixed costs associated with quantum device operation. This framing helps in aligning economic incentives with the broader network security.

Conclusion

This paper elaborates on a sophisticated application of quantum computing concepts to redefine traditional blockchain consensus approaches. By pioneering a PoW scheme rooted in quantum mechanics principles, specifically tailored for the anticipated capabilities of quantum hardware, the authors contribute a theoretically sound framework with considerable implications for the future of decentralized systems. As quantum technologies continue progressing toward practical application, this research provides a forward-looking perspective on securing and enhancing blockchain infrastructures against both contemporary and horizon-crossing challenges. Additionally, it sets the stage for further exploration into how quantum advantages can be seamlessly integrated into existing digital frameworks.