# Introduction

Quantum: Proof Aggregation Layer for Ethereum

### Why Quantum?

ZK proofs have emerged as a game-changer, enabling infinite scalability and playing a pivotal role in transforming Ethereum into a global settlement layer. While the proving schemes continue to evolve, offering improved proof generation times, the verification cost remains a bottleneck that remains unaddressed.

**The Challenges Ahead:**

The high verification cost on Ethereum presents two major challenges that must be overcome to fully harness the potential of ZK proofs:

*Low frequency proof submission:*ZK-enabled protocols face limitations in submitting proofs on-chain at high frequencies, as the cost of the protocol increases linearly with the number of proofs submitted. Even low frequency periodic submission the cost can escalate to millions of dollars, as evident in this dune dashboard.

*Independence in choosing proving schemes:*ZK-enabled protocols are restricted in their ability to choose the most suitable proving scheme for their use case. Certain proving schemes, such as Groth16, are subsidised using precompiles, resulting in cheaper verification costs compared to other protocols. This lack of flexibility hinders innovation and optimisation.

Quantum solves these key challenges by developing an aggregation layer on top of Ethereum.

### What is Quantum?

Quantum is an aggregation layer which leverages zk-recursion to aggregate proofs from different protocols and across different proving schemes and aggregating them into a single *Superproof* . This *Superproof* is then verified on Ethereum, this amortizes the cost of verification between protocols and hence enables cheap verification for individual protocols.

If $n$ are the number of protocols utilising Quantum at any given time, the cost borne by individual protocol be $c_{protocol}$. The obvious relation turns out to be:

Let's re-discuss the above mentioned challenges:

*Low frequency proof submission:*Since Quantum enables cheaper verification for individual protocols, the protocols can submit proofs at higher frequencies. The protocol can increase its proof submission frequency by $n$

times, still the total cost borne by the protocol will remain same.

*Independence in choosing proving schemes:*Quantum protocol makes proof verification cost independent of the proving scheme used by the protocol. Hence it gives protocols complete independence to choose any proving scheme as long as it's supported by the Quantum aggregation layer.

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