QAOA MaxCut on a 5-node ring

This record moves from primitives to a small optimization workload: the objective, circuit, sampling boundary, and acceptance metric stay visible together.

TakesNothingWhat joins here

No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.

Nothing in the Atlas meets this end.

ReturnsNothingWhat joins here

No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.

Nothing in the Atlas meets this end.

This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →

QAOA at depth $p=1$ prepares $|\gamma,\beta\rangle = e^{-i\beta H_M}e^{-i\gamma H_C}H^{\otimes n}|0\rangle^{\otimes n}$ , alternating a problem (cost) unitary and a mixer unitary. For MaxCut on a graph $G=(V,E)$ , the cost Hamiltonian is $H_C=\sum_{(j,k)\in E}\frac{1}{2}(I-Z_jZ_k)$ , whose expectation counts cut edges, and the mixer is $H_M=\sum_j X_j$ , whose exponential is a product of independent $X$ -rotations letting the state explore bitstrings. For this record's 5-node ring, $H_C$ sums five such terms around the cycle. The reported acceptance is empirical, not a matrix identity: the sampled 4096-shot distribution (seed 42) is compared with the reference simulator using total variation distance, giving $\mathrm{TVD}=0.0088$ against a $\delta\le0.05$ threshold — evidence that the sampled circuit matches its own noiseless simulation, not a claim that $p=1$ finds the graph's true maximum cut.

TakesNothingWhat joins here

No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.

Nothing in the Atlas meets this end.

ReturnsNothingWhat joins here

No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.

Nothing in the Atlas meets this end.

This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →

Qubits: 5
Depth: 14 gates
Shots: 4096
Graph: 5-node ring
QAOA depth: p = 1
Acceptance: TVD ≤ 0.05
Seed: 42

H×5 on q[0], q[1], q[2], q[3], q[4]
Cost on q[0], q[1]
Mixer on q[0], q[1], q[2], q[3], q[4]

Best cut family72%

Other bitstrings28%

Quantum vs classical

Classical baseline

Exact enumeration for the five-node fixture; Goemans–Williamson or MILP for larger MaxCut instances.

Quantum claim

The circuit samples candidate cuts; it does not replace the classical optimizer or certify a global optimum by itself.

How to compare

Report approximation ratio, success probability, optimizer cost, shots, and wall-clock time against the same instance and budget.

Nobody has reviewed this record for gaps yet.

FrameworkNative

qaoa_maxcut_ring.py

from qiskit import QuantumCircuit

qc = QuantumCircuit(5, 5)
qc.h(range(5))
# p=1 cost and mixer layers
for edge in ((0, 1), (1, 2), (2, 3), (3, 4), (4, 0)):
    qc.cx(*edge)
qc.measure(range(5), range(5))

FINAL_CIRCUIT = qc

The public snippet keeps the graph structure readable; the verified run stores the full parameterized circuit.

Where this sits

This record is named by the layer graph at:

Alternate a cost unitary with a mixer, p times Method
Takes An Ising or QUBO operator, diagonal in the computational basis, whose extremal eigenvector encodes the problem's solution — given, for QAOA, as a sum of clause terms $C(z) = \sum_{\alpha=1}^{m} C_\alpha(z)$ over $n$ bits and $m$ clauses; given, for adiabatic evolution, as the final Hamiltonian $H_P$ of an interpolation whose starting point $H_B$ has an easily-constructed ground state. Neither method is told how the operator was built, or by which encoding. Returns A bit string $z$ read off the computational basis — the assignment — together with the objective value it achieves, or, for the adiabatic route, the stated promise that this string is (with fidelity approaching 1, for a long enough evolution time) the true minimiser. Neither route returns an energy with an error bar; both return a string.

Related entries

Bell state measurement
Basic circuits
QFT resource screen
Algorithms

QAOA MaxCut on a 5-node ring

QAOA, p=1, MaxCut on a 4-cycle

Quantum vs classical

Classical baseline

Quantum claim

How to compare

Where this sits

Related entries

References