SpiderCat · Optimal Fault-Tolerant Cat State Preparation

Fault-tolerant preparation of an n-qubit CAT state

This webpage visualises different circuit constructions for a CAT state. It compares constructions with different resource trade-offs, and benchmarks them against external baselines — flag at origin and MQT.

arXiv Paper → PDF GitHub
SpiderCat Pipeline
CAT State Specification → Fault-Equivalent ZX Graph → t-robust Marked 3-regular Graph → CNOT-optimal CAT circuit
n = 20
t = 4

Method comparison

Click a card to inspect the construction in more detail.

Construction detail

Compare Different Methods

How every construction scales with the target size n at the current fault weight t, side by side in CNOT count, CNOT depth, and ancilla count.

How SpiderCat Improves on Existing Methods?

Recursive

Theorem 3.1 gives a scalable recursive construction with n(1 + log2(t + 1)) - 2(t + 1) CNOTs, n/2 ancillae, and depth 2 log2(t) + 2.

Optimal graph-based

Proposition 5.4 and Theorem 5.5 turn the CAT-state problem into finding marked 3-regular graphs with the best vertex ratio r_t.

Optimal shallow

Theorem 5.6 trades more ancilla for constant CNOT depth 3 while staying linear in n.