Challenge 1: Peaked Circuits — Provable Quantum Advantage

# Overview

Why Peaked Circuits?

Subnet 63 needed a first challenge that could answer a deceptively simple question: did you actually run this on a quantum computer? Peaked circuits, based on Scott Aaronson and Sabee Zhang's 2024 framework, provide exactly that guarantee. These are quantum circuits specifically engineered so that an ideal quantum computer produces a characteristic "peaked" output distribution — a single bitstring that appears with dramatically higher probability than any other. Classical computers cannot efficiently reproduce this distribution, creating a provable, verifiable benchmark for genuine quantum computation.

This property makes peaked circuits uniquely suited to a decentralized mining environment. Validators can generate circuits whose correct output is known in advance, issue them to miners, and verify the results without needing to trust anything about the miner's hardware or software stack. If the peaked bitstring shows up in the measurement statistics, the miner ran the circuit faithfully.

How the Challenge Works

Validators generate random quantum circuits drawn from the peaked circuit family and send them to miners as QASM circuits. Each circuit has a known peaked output — a specific bitstring that should dominate the output distribution when the circuit is executed on a real quantum simulator or quantum computer. Miners execute the circuit and return measurement results. The validator checks whether the peaked bitstring appears with the expected frequency.

Difficulty scales through qubit count: the easiest challenges use around 12 qubits, while the hardest push beyond 40 — well into the regime where classical brute-force simulation becomes intractable. The scaling function parameterizes difficulty from 0 to 5, with qubit counts following N = floor(10 × log₂(d + 3.9) + 12). Each additional qubit roughly doubles the computational cost, so the gap between easy and hard challenges is enormous.

What Makes This Hard

The key insight behind peaked circuits is computational asymmetry. Generating a peaked circuit and knowing its answer is efficient — the validator can do it quickly. But for a miner who receives only the circuit (without knowing the answer), finding the peaked output requires actually simulating the quantum computation. There is no known shortcut that avoids the exponential cost of full simulation.

This asymmetry is what makes the challenge a genuine proof of quantum work rather than a toy problem. At 39+ qubits, miners need serious GPU hardware and optimized tensor network contraction to solve these circuits competitively. The difficulty ceiling is set by the hardware available to validators for circuit generation, and the team has been continuously pushing that boundary upward.

Read the Full Paper

The complete technical description covers the mathematical foundations of peaked circuits, the generation algorithm, the verification protocol, difficulty scaling, and the security properties that make this challenge resistant to classical shortcuts.

[Download the paper (PDF)](/PeakerCircuitsTecDes.pdf)