A curated list of algorithm implementations on noisy, intermediate-scale quantum (NISQ) computers. Implemented algorithms are ordered chronologically and include architecture (e.g., superconducting), number of qubits, and references.
Please submit pull requests (or email rlarose (at) umich (dot) edu) with algorithm implementations not included below. Any and all corrections are welcome. References to open-access journals or the arXiv are preferred in all cases, if available. Markdown table generators such as https://www.tablesgenerator.com may be useful.
| Year | Month | Algorithm | Description | Qubit type | Computer | Number of Qubits | Reference |
|---|---|---|---|---|---|---|---|
| 1997 | Aug | ---- | Implemented gates (XOR, Toffoli), prepared entangled state | NMR | ---- | 1-3 | https://arxiv.org/abs/quant-ph/9709001 |
| 1997 | Oct | ---- | Implemented gates (Rotation, CNOT), prepared entangled state | NMR | ---- | 1-2 | |
| 1997 | Nov | Grover | Executed Grover's algorithm on two qubits. | NMR | ---- | 2 | Paper |
| 1998 | Jan | DJ | Executed DJ algorithm on NMR quantum computer | NMR | ---- | 2 | https://arxiv.org/abs/quant-ph/9801027 |
| 1998 | Feb | QEC | Implemented 3-bit code for phase errors in liquid state NMR | NMR | 3 | https://arxiv.org/abs/quant-ph/9802018 | |
| 1998 | Aug | DJ | Executed DJ algorithm on NMR quantum computer | NMR | ---- | 3 | https://arxiv.org/abs/quant-ph/9808039 |
| 2000 | Mar | DJ | Executed DJ algorithm on NMR quantum computer | NMR | ---- | 2-3 | https://journals.aps.org/pra/abstract/10.1103/PhysRevA.61.042306 |
| 2000 | Mar | Entanglement | Experimental entanglement of four particles | Trapped ion (9Be+) | ---- | 2-4 | |
| 2000 | Apr | Benchmark | Coherent manipulations of seven qubits | NMR | ---- | 7 | |
| 2000 | June | DJ | Executed DJ algorithm on NMR quantum computer | NMR | ---- | ?? | https://aip.scitation.org/doi/10.1063/1.482015 |
| 2000 | June | DJ | Executed DJ algorithm on NMR quantum computer | NMR | ---- | 4 | https://journals.aps.org/pra/abstract/10.1103/PhysRevA.62.012310 |
| 2000 | July | Order finding | Experimental realization of order finding | NMR | ---- | 5 | https://arxiv.org/abs/quant-ph/0007017 |
| 2000 | Dec | BV | Executed BV algorithm on an ensemble quantum computer | NMR | ---- | 2 | https://arxiv.org/abs/quant-ph/0012114 |
| 2001 | June | QEC | Experimental demonstration of five qubit code | NMR | ---- | 5 | https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.86.5811 |
| 2001 | Sep | BV | Executed BV algorithm | NMR | ---- | 2 | https://arxiv.org/abs/quant-ph/0012114 |
| 2001 | Dec | Shor | Factor 15 | NMR | 7 | https://arxiv.org/abs/quant-ph/0112176 | |
| 2003 | Jan | DJ/BV | Implement DJ and BV on | Linear optics | ---- | 3 | Paper |
| 2003 | Feb | DJ | Executed DJ on ion-trap quantum computer | Trapped ion (40Ca+) | ---- | 1 | Paper |
| 2004 | Dec | QEC | Demonstrates 3 qubit code for spin flip errors | Trapped ion (9Be+) | ---- | 3 | |
| 2005 | May | QFT | Semi-classical QFT | Trapped ion (9Be+) | ---- | 3 | https://science.sciencemag.org/content/308/5724/997 |
| 2005 | Sep | DJ/Grover | Implemented multiple algorithms on NMR quantum computer | NMR | ---- | ?? | https://arxiv.org/abs/quant-ph/0509046 |
| 2005 | Oct | Grover | Executed Grover's algorithm on two trapped ion qubits | Trapped ion (111Cd+) | |||
| 2007 | May | Shor | Factor 15 | Photonic | ---- | 4 | |
| 2007 | Apr | Shor | Factor 15 | Photonic | ---- | 4 | |
| 2009 | Mar | DJ/Grover | Executed Grover and DJ algorithm on superconducting processor | Superconducting | ---- | 2 | https://arxiv.org/abs/0903.2030 |
| 2009 | Nov | Shor | Factor 15 | Photonic | ---- | 4 | https://arxiv.org/abs/0911.1242 |
| 2010 | Feb | DJ | Implemented DJ algorithm with single electronic spin in diamond | NV Center | ---- | 1 | https://arxiv.org/abs/1002.2465 |
| 2011 | May | QEC | Implements multiple QEC codes | Trapped ion | ---- | ?? | Abstract |
| 2011 | Sep | QEC | Realization of 3 qubit bit (phase) flip code | Superconducting | ---- | 3 | https://arxiv.org/abs/1109.4948 |
| 2011 | Nov | Shor | Factor 21 | Photonic | ---- | 2 | https://arxiv.org/abs/1111.4147 |
| 2012 | Feb | Benchmark | Perform quantum process tomography on universal gate set | Superconducting | ---- | 2 | https://arxiv.org/abs/1202.5344 |
| 2013 | Apr | VQE | Compute ground state energy of He-H+ | Photonic | ---- | 2 | https://arxiv.org/abs/1304.3061 |
| 2014 | Jan | ---- | Gate implementations and entangled state preparation | Trapped ion (171Yb+) | ---- | 5 | https://arxiv.org/abs/1401.1575 |
| 2015 | Jan | Benchmark | Randomized benchmarking of single qubit gates | Neutral atom | ---- | 49 | https://arxiv.org/abs/1501.02041 |
| 2015 | Feb | Sim | Quantum simulation of Heisenberg and Ising models. | Superconducting | ---- | 2 | https://arxiv.org/abs/1502.06778 |
| 2015 | Apr | QEC | Demonstration of quantum error detection protocol | Superconducting | ---- | 4 | https://www.nature.com/articles/ncomms7979 |
| 2015 | July | Shor | Factor 15 | Trapped ion (40Ca+) | ---- | 5 | https://arxiv.org/abs/1507.08852 |
| 2015 | Dec | VQE/QPE | Compute energy surface of molecular Hydrogen | Superconducting | ---- | 2/3 | https://arxiv.org/abs/1512.06860 |
| 2016 | Mar | Benchmark | Executes single and two-qubit gates | Trapped ion (9Be+) | ---- | 1-2 (?) | https://arxiv.org/abs/1604.00032 |
| 2016 | Mar | DJ/BV/QFT | Execute DJ, BV, and QFT algorithms | Trapped ion (171Yb+) | ---- | 3-5 | https://arxiv.org/abs/1603.04512 |
| 2016 | Mar | BV | Implements BV algorithm | Trapped ion (171Yb+) | ---- | 2-3 | https://arxiv.org/abs/1603.05672 |
| 2016 | May | Mermin inequalties | Experimental test of Mermin inequalities | Superconducting | IBM Q Experience | 1-5 | https://arxiv.org/abs/1605.04220 |
| 2016 | May | Multiple | Executes QEC, arithmetic, etc. | Superconducting | IBM Q Experience | 1-5 | https://arxiv.org/abs/1605.05709 |
| 2016 | Aug | QEC | Demonstrates a method to optimize encoding procedure for small error correction code | Ion trap (40Ca+) | ---- | 7 | https://arxiv.org/abs/1603.00402 |
| 2017 | May | QEC | Sampling from states prepared with the [[4, 2, 2]] code | Superconducting | IBMQX4 | 5 | https://arxiv.org/abs/1705.08957 |
| 2017 | May | QEC | Demonstrates fault-tolerant state preparation | Superconducting | 5 | https://arxiv.org/abs/1705.09259 | |
| 2017 | June | Benchmark | Multiple benchmarking circuits | Superconducting | IBMQX3 | 5 | https://arxiv.org/abs/1706.04341 |
| 2017 | Aug | QEC | Experimental realization of error correction for Bell and GHZ states | Superconducting | ?? | 5? | https://arxiv.org/abs/1708.02297 |
| 2017 | Sep | QEC | Repetition code of 15 qubits. | Superconducting | IBMQX3 | 15 | https://arxiv.org/abs/1709.00990 |
| 2018 | Jan | Benchmark | Demonstrates graph states on 8-16 qubits are fully entangled | Superconducting | IBMQX5 | 8-16 | https://arxiv.org/abs/1801.03782 |
| 2018 | Jan | VQE | Computes energy landscapes of deuteron | Superconducting | IBMQX5/Rigetti 19Q-Acorn | 2-3 | https://arxiv.org/abs/1801.03897 |
| 2018 | Feb | VQE/QSE | Compute ground/excited states of H2 | Superconducting | ---- | 2 | PRX PDF |
| 2018 | Mar | S.O. | Compute state overlap for one-qubit states | Superconducting | IBMQX4, Rigetti 19Q-Acorn | 2 | https://arxiv.org/abs/1803.04114 |
| 2018 | Apr | Multiple | Grover, BV, Shor, HHL, persistent homology, ... (cont. below) | Superconducting | IBMQX4/5 | 1-5 | https://arxiv.org/abs/1804.03719 |
| 2018 | Apr | Multiple | Min. spanning tree, QAOA, qPCA, qSVM, Schrodinger's eqn. simulation, state preparation, state tomography | Superconducting | IBMQX4/5 | 1-5 | https://arxiv.org/abs/1804.03719 |
| 2018 | Apr | SVM | Classify two-dimensional data | Superconducting | ---- | 2 | https://arxiv.org/abs/1804.11326 |
| 2018 | June | Benchmark | Randomized benchmarking | Superconducting | IBMQX4/5, Rigetti 8Q-Agave/19Q-Acorn | 5-19 | https://arxiv.org/abs/1806.02736 |
| 2018 | June | Scrambling | Application of quantum scrambling in Rydberg atom | Superconducting | IBMQX4 | 5? | https://arxiv.org/abs/1806.00781 |
| 2018 | June | QEC | Randomized benchmarking on [4, 2, 2] code | Superconducting | IBMQX5 | 4 | https://arxiv.org/abs/1806.02359 |
| 2018 | July | QAQC | Compile quantum algorithms | Superconducting | Rigetti 8Q-Agave, IBMQX1/2 | 2 | https://arxiv.org/abs/1807.00800 |
| 2018 | July | QEC | Quantum error detection for (2n + 1)-qubit entangled states | Superconducting | IBMQX5 | 13 | https://arxiv.org/abs/1807.02883 |
| 2018 | July | Sim | Simulates spin-boson model | Superconducting | IBMQX4 | 5 | https://arxiv.org/abs/1807.00323 |
| 2018 | Sep | DJ/BV/QFT | Implemented DJ, BV, QFT, and Grover on three qubits | Superconducting | Trimon | 3 | https://arxiv.org/abs/1809.00668 |
| 2018 | Oct | VQSD | Diagonalize a 2x2 matrix | Superconducting | Rigetti 8Q-Agave | 1 | https://arxiv.org/abs/1810.10506 |
| 2018 | Nov | Benchmark | Introduces and computes quantum volume on several computers | Superconducting | IBMQ | 4-16? | https://arxiv.org/abs/1811.12926 |
| 2019 | Jan | QITE/QLanczos | Compute ground state energy of TFIM using two novel algorithms | Superconducting | Rigetti Aspen QPU | 2 | https://arxiv.org/abs/1901.07653 |
| 2019 | Feb | VQE | Compute ground state energy of H20 | Trapped ion (171Yb+) | IonQ | 10-11 | https://arxiv.org/abs/1902.10171 |
| 2019 | Mar | BV/HS | Execute BV and HS algorithms | Ion trap (171Yb+) | ---- | 11 | https://arxiv.org/abs/1905.09294 |
| 2019 | Mar | Benchmark | Executes randomized benchmarking with "error-aware" compiling | Superconducting | IBMQ16 | 16 | https://arxiv.org/abs/1903.10963v1 |
| 2019 | May | ---- | Demonstrates protocol for simultaneous entanglement generation of arbitrary qubit pairs | Ion trap (171Yb+) | IonQ | 11 | https://arxiv.org/abs/1905.09294 |
| 2019 | June | Sim. | Hamiltonian simulation for many-body dynamics | Superconducting | IBM 20Q | 6-10 | https://arxiv.org/abs/1906.06343 |
| 2019 | Aug | ---- | Entanglement generation in two-dimensional neutral atom qubit array; benchmark | Neutral atom | ---- | ?? | https://arxiv.org/abs/1908.06103 |
| 2019 | Aug | ---- | Parallel implementation of multi-qubit gates; benchmark | Neutral atom | ---- | 10? | https://arxiv.org/abs/1908.06101 |
| 2019 | Aug | Sim. | Simulates SU(2) non-abelian gauge field theory in one dimension | Superconducting | IBM 20Q | 4 | https://arxiv.org/abs/1908.06935 |
| 2019 | Aug | QML | Solves small optimization problems | Superconducting | Rigetti Aspen QPU | <= 10 | https://arxiv.org/abs/1908.08054 |
- BV: Bernstein-Vazirani.
- DJ: Deustch-Jozsa.
- HS: Hidden shift.
- QAQC: Quantum-assisted quantum compiling.
- QFT: Quantum Fourier Transform.
- QPE: Quantum phase estimation.
- QSE: Quantum subspace expansion.
- Sim: (Quantum) simulation.
- S.O.: State overlap.
- VQE: Variational quantum eigensolver.
- VQSD: Variational quantum state diagonalization.