OpenQC Algorithm Catalog — central index for all quantum algorithm repos

W state: symmetric 3-qubit entangled state (|001⟩ + |010⟩ + |100⟩)/√3.

Transmit 2 classical bits using 1 qubit and a pre-shared Bell pair (encodes message '11').

Find the ground-state energy of a Hamiltonian using a parameterized ansatz and classical optimizer. This minimal H2 example uses a single Ry rotation.

Simulate the Fermi-Hubbard model on a small lattice using VQE. The Hubbard model describes electron interactions in materials — fundamental to understanding superconductivity, magnetism, and strong…

Find the ground state energy of water (H2O) using VQE. Requires 8-12 qubits depending on basis set and orbital reduction. Full Hamiltonian needs Qiskit Nature for dynamic generation from molecular …

Scan ground state energy across multiple bond lengths to map the potential energy surface. Runs VQE at each geometry point and plots energy vs distance. Requires dynamic Hamiltonian generation at e…

Find the ground state energy of beryllium hydride (BeH2) using the Variational Quantum Eigensolver. Uses a 6-qubit parity-mapped Hamiltonian with 15 representative Pauli terms from the STO-3G basis…

Teleport the state of qubit 0 to qubit 2 using a pre-shared Bell pair and classical communication.

The rotated surface code on a 3x3 grid (distance 3). Uses 9 data qubits and 8 syndrome ancillas with nearest-neighbor connectivity. The dominant QEC code for superconducting hardware.

The simplest quantum error-correcting code. Encodes one logical qubit into 5 physical qubits (distance 3) with 4 syndrome ancillas to detect single bit-flip errors.

Approximate combinatorial optimization using alternating problem and mixer unitaries. This 4-qubit example targets a MaxCut problem on a 4-node ring graph with p=1.

Solve the Vehicle Routing Problem (VRP) via QAOA with QUBO encoding. Multiple vehicles serve customers from a depot, minimizing total distance. Generalization of TSP with capacity constraints. QUBO…

Solve the Travelling Salesman Problem using QAOA with QUBO penalty encoding. N cities are mapped to N^2 binary variables (x_{i,p} = city i at position p). Constraints enforce each city visited once…

Solve graph coloring using QAOA with QUBO penalty encoding. N nodes with K colors use N*K binary variables. One-hot constraint per node (exactly one color) plus penalty for same-color adjacent node…

Solve simplified protein folding using QUBO formulation on a coarse-grained lattice model. Maps amino acid sequences to lattice positions, minimizes energy via annealing. Research-grade problem — e…

Greenberger–Horne–Zeilinger (GHZ) state: maximally entangled 3-qubit state (|000⟩ + |111⟩)/√2.

Simulate the E91 QKD protocol (Ekert, 1991). Uses shared Bell pairs for key distribution. Alice and Bob measure in different bases — matching bases yield key bits, non-matching bases test the CHSH …

Estimate drug-target binding affinity using VQE for the interaction Hamiltonian between a small molecule and protein binding site. Requires quantum chemistry stack to compute molecular interaction …

Simulate quantum circuits classically using tensor network contraction. Handles 30-50 qubit circuits that are too large for statevector simulation but have limited entanglement depth. Uses quimb/co…

Preparation of the maximally entangled two-qubit Bell state |Φ⁺⟩ = (|00⟩ + |11⟩)/√2.

Simulate the B92 QKD protocol (Bennett, 1992). A simplified version of BB84 using only 2 non-orthogonal states (|0> and |+>) instead of 4. Bob's conclusive measurements yield key bits. Simpler but …

Solve MaxCut graph partitioning via quantum/simulated annealing. Same problem as qaoa-maxcut but uses annealing instead of gate-based QAOA. Compare results across paradigms: gate-based (QAOA) vs an…

Solve job-shop scheduling via annealing with QUBO encoding. Each job has ordered tasks assigned to machines with durations. Minimizes makespan (latest completion time). Real-world operations resear…

4-qubit hardware-efficient variational ansatz for VQE (Variational Quantum Eigensolver), 2-layer Ry-Rz-CNOT structure.

One first-order Trotter step simulating the 1D transverse-field Ising model on 4 qubits (J=1, h=0.5, dt=0.1).

Measure |⟨ψ|φ⟩|² between two quantum states using a Fredkin (controlled-SWAP) gate.

First CSS code: encodes 1 logical qubit in 7 physical qubits, corrects any single-qubit error using the classical Hamming [7,4] code.

Find the hidden period s='11' of a 2-to-1 function f(x) = f(x⊕s) with exponential quantum speedup.

Core period-finding subroutine of Shor's algorithm: find the period r of f(x) = 7^x mod 15.