Six-qubit GHZ (cat) state preparation

Primitive: GHZ (cat) state preparation on six qubits.

The circuit is the textbook GHZ preparation. Starting from the all-zero register, a Hadamard on qubit 0 puts that qubit into an equal superposition of |0> and |1>. A ladder of five CNOT gates then propagates the value along the chain: qubit 0 controls qubit 1, qubit 1 controls qubit 2, and so on through qubit 5. Because each CNOT acts on a control that is already in superposition, the result is not a copy but a two-branch entangled state. Ideally the final state is (|000000> + |111111>)/sqrt(2), an equal-amplitude superposition of the all-down and all-up configurations, and computational-basis sampling concentrates on the two bitstrings 000000 and 111111 with roughly half the weight each.

This card is inspired by arXiv:2607.28373, "Emergence of a Macroscopic Cat State and Multi-Channel Entanglement in a Frustrated Cluster Spin Chain", and only references it. Per the abstract, the authors study a one-dimensional frustrated spin chain combining cluster-Ising and anisotropic next-nearest-neighbour Ising models, and describe two quantum phases separated by a first order quantum phase transition. The abstract states that on one side the ground state is a ferromagnetic phase showing the presence of macroscopic cat states and a small gap that closes in the thermodynamic limit, with two dominant Schmidt coefficients. On the other side, the abstract says competing interactions avoid a topological phase and give a gapped incommensurate phase with four dominant Schmidt coefficients, corresponding to four bipartite entanglement channels. The abstract also says the authors discuss the utility of the macroscopic cat states for quantum metrology and the experimental feasibility of the system.

The link is conceptual only: a GHZ state is the standard textbook cat state, and it has Schmidt rank two across any bipartition.

This is a deterministic simulator run on Provenova. It is not a reproduction of the paper's numerical or hardware results, it does not implement the paper's Hamiltonian or ground state, and the authors neither endorse nor are associated with this card.