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A curated list of NISQ implementations.
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README.md Added arXiv papers for week of August 19-23, 2019. Aug 26, 2019

README.md

NISQ Implementations

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.

Contributions

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.

Chronological ordering

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 PDF
2000 Apr Benchmark Coherent manipulations of seven qubits NMR ---- 7 PDF
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 PDF
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 PDF
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

Algorithm keys (Alphabetical)

  • 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.
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