Exact & formalBell / entanglement
Bell state measurement
A two-qubit entanglement example with a return contract and distribution check.
Explore quantum algorithms and circuits, with resource estimates, verification evidence, and sources.
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The defining behavior was checked exactly: a mathematical identity, a full statevector or stabilizer simulation, or an exhaustive basis-state truth table.
The design was verified by construction plus measured evidence: statistical re-execution, small-instance analytic agreement, sub-block, echo, or invariant checks. Scale-specific bugs can still survive.
The record rests on external authority: peer-reviewed papers, standard textbooks, expert review, or evidence carried over from related verified entries. Nothing here was re-executed by this catalog.
Only automated (LLM-assisted) review or an unreviewed community submission backs this record so far. Treat it as a starting point, not evidence.
A two-qubit entanglement example with a return contract and distribution check.
A bank of disjoint Bell-pair preparations that exposes parallel two-qubit-gate structure.
A width-scaled GHZ preparation circuit with one Hadamard and a nearest-neighbor CNOT chain.
A linear graph-state preparation circuit using one Hadamard per qubit and nearest-neighbor CZ edges.
A cyclic graph-state preparation circuit with Hadamards followed by CZ interactions around a ring.
Sample from the output distribution of a rudimentary optical device: identical photons are generated, sent through a network of beamsplitters and phase shifters, and then non-adaptively measured to count the photons in each mode. The question is whether a classical computer can do the same sampling efficiently.
The symmetric Dicke state |D²₄⟩: a uniform superposition over every 4-qubit basis string with exactly 2 excitations.
A reusable GHZ state preparation circuit with simulator-only evidence.
Prepare the thermal Gibbs state of an interacting quantum system on a quantum computer, and use that preparation to evaluate the system's partition function to a target accuracy.
A graph state built on a 4-cycle rather than an open chain, illustrating how stabilizer generators follow directly from graph adjacency.
The single-qubit magic state |T⟩ = T|+⟩, the standard resource state consumed by gate teleportation to implement a fault-tolerant non-Clifford T gate.
The maximally mixed state ρ = I/2ⁿ: the unique n-qubit state invariant under every unitary, carrying zero information and maximal (n-bit) von Neumann entropy.
Compute the ground-state energy of an atom or molecule, a calculation whose time the paper states scales exponentially with system size on a classical computer.
The NOON state (|N,0⟩+|0,N⟩)/√2: a two-mode entangled state with all N particles in one mode or the other, the standard resource for Heisenberg-limited interferometric phase estimation.
The Hadamard-basis (X-basis) states |+⟩ and |−⟩: the eigenstates of the Pauli-X operator, produced from |0⟩/|1⟩ by a single Hadamard gate.
Puts a list of 2ⁿ probabilities into n qubits as amplitudes √p, exactly, with one uniformly controlled RY rotation per qubit.
A ground-state preparation method that projects non-unitary imaginary-time evolution onto a parameterized quantum circuit.
The thermal (Gibbs) state of a single qubit in a longitudinal field, prepared exactly via a one-ancilla purification circuit.
A hybrid chemistry workflow that compares a quantum expectation loop with classical eigensolvers.
The three-qubit W state, an equal superposition of every single-excitation basis string that survives the loss of one qubit better than GHZ.
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