Quantum researchers have proposed an innovative alternative to existing Proof-of-Work methods in blockchain technologies. Based in boson sampling, the proposed solution promises to drastically cut the significant carbon footprint of blockchain technologies.

## Whether it is in the form of cryptocurrencies (such as bitcoin), smart contracts, or non-fungible tokens, a blockchain provides an alternative means to record transactions that is secure, transparent and traceable.

Blockchain technologies distinguish themselves by not relying on a centralised authority, and instead leverage a network of participating nodes distributed across the internet. One or more transactions are recorded in new blocks added to the blockchain, and each participating node is able to validate transactions and record them in a new block to the chain.

**A matter of trust**

To establish trust between the parties, algorithms are deployed to ensure consensus – one such example is “proof of work” (e.g. “bitcoin mining”). In this algorithm, to append a block to the blockchain, a participant must solve a cryptographic puzzle that requires a specified level of computational power. Nodes compete to find (“mine”) a solution, and once found, the remaining nodes can quickly authenticate it. Since there is a work and time requirement, this provides a disincentive to dishonest actors.

However, proof of work comes with a heavy environmental cost. Since the cryptographic puzzles are designed to be difficult – and to scale with number of participating nodes – the required computing power can grow rapidly. Bitcoin alone is now estimated to have an annual energy consumption close to that of a mid-sized country (e.g. Argentina). Innovators are actively searching for solutions that provide the same robustness of existing proof-of-work mechanisms while minimising carbon footprint.

A recent paper proposes an innovative new solution to this environment cost, through application of a quantum technology known as *boson sampling*.

**What is boson sampling?**

## A boson is a particle with an “integer spin” – for example, a photon (which has a spin value of 1).

This provides a quantum mechanical degree of freedom to the photon, since it can exist in a state ‘zero’ and in a state ‘one’, and also in a ‘superposition’ of the two (i.e. a combination of both state zero and state one such that, when measured, the photon will exist in either one state or the other with different probabilities).

By propagating a photon through a linear optical array of beamsplitters and phase shifters, it is possible to construct an infinite number of superposition states of zero and one states for the photon. Additionally, multiple photons can be passed through a network of linear optics to produce multiple outputs, with the final quantum state depending on the initial state of the photons and the nature of the optics network. In general, when there are *n* photons, there are *n!* ways for the photons to propagate through the linear optical system.

When multiple photons are input, the final state of the multiple photons can exist in a wide range of possible output states, at a given probability for each state. These probabilities can be represented mathematically in a matrix – however, actually calculating these probabilities would require exponentially high amounts of classical resources.

The probabilities can nevertheless be determined by taking *samples* using a linear optical circuit (called a boson sampler) of the photons that are output by the system – hence the name, ‘boson sampling’.

**Applying boson sampling to blockchain**

As explained in the paper, the boson sampling process can be adapted for use as a consensus mechanism in blockchain. A boson sampler may be constructed from a linear optical circuit with multiple inputs and multiple outputs. Providing photons into different inputs of the boson sampler will produce different outputs.

In the proposed consensus protocol, when a new block is created to encode transactions, the block is created with a *header* that includes a parameter set that is a hash derived from information including the transactions information and a hash of the previous block header. This parameter set defines the input locations for photons in a linear optic array of the boson sampler. Participants in the proof of work protocol can then vary their input parameters and take samples of the output photons and commit the samples to the network. After a finite mining time, committed samples are then computed to determine if the committed sample distributions match the correct solution.

The quantum consensus protocol has similarities to the classical proof of work protocol (in that nodes compete to find a hash), and the probability of success for finding a solution is independent of any previous attempts. However, unlike classical proof-of-work, the boson sampling protocol is significantly more efficient.

The energy cost comes in the cost to cool the photon detectors, and the researchers report for N = 25 photons, the boson sampler is ** 29,569**times more efficient than a supercomputer. Boson sampling thus shows considerable promise as a solution to the increasingly costly demands from blockchain systems.

**Revolutionising adjacent fields**

## The intersection of two fields is a common place to find innovation, and solutions provided in one field may find completely unexpected application in another.

Boson sampling has been known about for some time, but considered to have limited or no practical application. However, by considering this quantum mechanical approach in the new context of blockchain, boson sampling has moved from a ‘solution looking for a problem’ to providing a solution to a technical problem of great significance.

Such a step is a clear indicator of inventive activity (indeed, from the perspective of the European Patent Office, identifying a technical solution to a technical problem is a central part of the patent examination process). Such innovative steps can be seen in other technical fields that have applied quantum solutions for example, in Artificial Intelligence (our analysis and analysis from the European Patent Office shows a significant increase in the number of patent applications in quantum AI) and space-based applications (again, analysis from the European Patent Office shows an increase in patent applications in this area).

It is clear that quantum technologies are not just promising in their own right, but they can provide real and impactful applications to adjacent fields. So, if you are seeking to innovate, perhaps the answer to the problem you’re trying to solve might lie in quantum.