Benchmark Algorithm | Description |
---|---|

Amplitude Estimation (AE) | AE aims to find an estimation for the amplitude of a certain quantum state. |

Deutsch-Jozsa | This algorithms determines, whether an unknown oracle mapping input values either to 0 or 1 is constant (always output 1 or always 0) or balanced (both outputs are equally likely). |

GHZ State | The Greenberger-Horne-Zeilinger state is an entangled quantum state with a certain type of entanglement. |

Graph State | Graph states in quantum computing represent a graph with vertices and edges through a quantum circuit. |

Ground State | A famous application of quantum computing and specifically of VQE algorithms is the ground state estimation of molecules. Here, we provide two different molecules, H2 ("small") and LiH ("medium"), and estimate their ground state using VQE with a TwoLocal ansatz. The source code for the algorithmic level originates from this page. |

Grover's (no ancilla) | One of the most famous quantum algorithm known so far, Grover's algorithm finds a certain goal quantum state determined by an oracle. In our case, the oracle is implemented by a multi-controlled Toffoli gate over all input qubits. In this no ancilla version, no ancilla qubits are used during its realization. |

Grover's (v-chain) | Similar to the algorithm above with the difference, that the ancillary mode is a v-chain in this algorithm. |

Portfolio Optimization with QAOA | This algorithms solves the mean-variance portfolio optimization problem for different assets. In this case, a QAOA algorithm instance is used. The source code for the algorithmic level originates from this page. |

Portfolio Optimization with VQE | This algorithms solves the mean-variance portfolio optimization problem for different assets. In this case, a VQE algorithm instance is used. The source code for the algorithmic level originates from this page. |

Pricing Call Option | This algorithm estimates the fair price of a european call option using iterative amplitude estimation. The source code for the algorithmic level originates from this page. |

Pricing Put Option | This algorithm estimates the fair price of a european put option using iterative amplitude estimation. The source code for the algorithmic level originates from this page. |

Quantum Approximation Optimization Algorithm (QAOA) | One of the most famous algorithm from the algorithmic class of variational quantum algorithms. It is a parameterizable quantum algorithms to solve optimization problems. Here, it solves a max-cut problem instance. |

Quantum Fourier Transformation (QFT) | QFT embodies the quantum equivalent of the discrete Fourier transform and is a very important building block in many quantum algorithms. |

Entangled QFT | Applies regular QFT to entangled qubits. |

Quantum Neural Network (QNN) | This algorithm class is the quantum equivalent to classical Neural Network. The source code for the algorithmic level originates from this page. |

Quantum Phase Estimation (QPE) exact | QPE estimates the phase of a quantum operation and is a very important building block in many quantum algorithms. In the exact case, the applied phase is exactly representable by the number of qubits. |

Quantum Phase Estimation (QPE) inexact | Similar to QPE exact with the difference, that the applied phase is not exactly representable by the number of qubits. |

Quantum Walk (no ancilla) | Quantum walks are the quantum equivalent to classical random walks. In this no ancilla version, no ancilla qubits are used during its realization. |

Quantum Walk (v-chain) | Similar to the algorithm above with the difference, that the ancillary mode is a v-chain in this algorithm. |

Random Circuit | This benchmark represents a random circuit which is twice as deep as wide. It considers random quantum gates with up to four qubits. |

Routing | This problem is similar to the travelling salesman problem with the difference, that more than one vehicle may be used to travel between those to be visited points, such that each point is visited at least once. The source code for the algorithmic level originates from this page. |

Shor's | This algorithm is one of the most famous quantum algorithms and used to find prime factors of integers. Here, we provide quantum algorithms solving this problem for the integers 9, 15, and 821. The filename, e.g., shor_821_4_t-indep_42.qasm includes also the to be factorized number (821) and the period used, namely 4. |

Travelling Salesman | The travelling salesman problem is a very prominent optimization problem of calculation the shortest path of a number of to be visited points. Here, this is formulated as a quadratic problem and solved using VQE with a TwoLocal ansatz. The source code for the algorithmic level originates from this page. |

Variational Quantum Eigensolver (VQE) | VQE is also one of the most famous algorithm from the class of variational quantum algorithms. It is a parameterizable quantum algorithms with different possible choices of an ansatz function. Here, a TwoLocal ansatz is chosen and applied to the same max-cut problem instance as in QAOA. |

Efficient SU2 ansatz with Random Parameters | VQE ansatz with randomly initialized values. Detailed information can be found on this page. |

Real Amplitudes ansatz with Random Parameters | VQE ansatz with randomly initialized values. Detailed information can be found on this page. |

Two Local ansatz with random parameters | VQE ansatz with randomly initialized values. Detailed information can be found on this page. |

W-State | The W state is an entangled quantum state with a certain type of entanglement. |