RCS-VRF (Random Circuit Sampling – Verifiable Random Function) is a protocol for producing certified quantum randomness-— a public stream of random bits that anyone can verify were genuinely generated by a quantum computer and not fabricated classically. It adapts the certified-randomness scheme of Liu et al. (Quantinuum H2-1) into a decentralized setting as a proof-of-useful-work subnet of the Quip Network.
This topic is the home for our research on RCS-VRF. The articles collected here break the work into its core layers — the physics of why the circuits are hard to fake, the certification math that turns noisy quantum samples into guaranteed random bits, and the systems and security engineering of running it soundly at scale. Each sub-topic below dives into one piece of that picture.
Sub-topics:
1. Random Circuit Sampling (RCS) — the circuits at the heart of it
What the challenge circuit actually is: |0…0⟩ → alternating layers of random single-qubit rotations and two-qubit entanglers → measure. Why random circuits, and what “sampling” means here.
2. The Porter–Thomas distribution — the quantum fingerprint
Why a sufficiently deep random circuit produces a characteristic exponential output distribution that a classical uniform sampler can’t fake. (With the honest caveat: it’s an output-distribution property, not the same as Haar-randomness.)
3. Classical simulation cost — tensor networks and treewidth
How you’d try to simulate these circuits classically (tensor-network contraction, not state-vector), and why the cost scales as 2^treewidth. Defines B, the single number that governs everything downstream.
4. Topology is the hardness lever
The flagship finding: at fixed qubit count and depth, the wiring alone swings simulation cost ~20 orders of magnitude. Qubit count plateaus; depth is capped. (Figures: topology_vs_n_contrast, plateau_behavior.)
5. Light cones and connectivity — why topology sets treewidth
The mechanism behind #4: information spreads one gate-hop per layer, connectivity controls how fast the light cone widens, all-to-all → high treewidth at shallow depth → hard. Explains why trapped-ion connectivity matters.
6. Fidelity on real hardware — the NISQ reality
Why an honest device doesn’t produce a perfect Porter–Thomas sample but a fidelity-φ mixture, how fidelity falls with gate count, and why this sets up the certification math (you can’t check for “perfect” quantumness).
7. The time asymmetry — the physical basis of “proof of quantum work”
The QPU samples in seconds; classical simulation of the same circuit takes ~100s on a supercomputer. That gap, inside a response window, is what makes the randomness a proof.