nLab measurement-based quantum computation

Idea

What has come to be known as measurement based quantum computation is a scheme for quantum computation in which quantum gates are implemented by partial quantum measurement on entangle states (Bell states).

Due to wavefunction collapse upon quantum measurement, such processes are not reversible on the total quantum state space — conversely, each such measurement-based gate operation “uses up the entanglement-resource” in order to implement (reversible) quantum gates on a computational subspace. Therefore one also speaks of “one-way quantum computation” [Raussendorf &Briegel (2001)].

Related concepts

• quantum measurement

• quantum teleportation

• quantum computation

  • adiabatic quantum computation

  • topological quantum computation

References

The original articles:

• Daniel Gottesman, Isaac L. Chuang, Quantum Teleportation is a Universal Computational Primitive, Nature 402 (1999) 390-393 [doi:10.1038/46503, arXiv:quant-ph/9908010]

• Emanuel Knill, Raymond Laflamme, Gerard J. Milburn, A scheme for efficient quantum computation with linear optics, Nature 409 (2001) 46–52 [doi:10.1038/35051009]

• Robert Raussendorf, Hans J. Briegel, A One-Way Quantum Computer, Phys. Rev. Lett. 86 (2001) 5188 [doi:10.1103/PhysRevLett.86.5188]

• Michael Nielsen, Quantum computation by measurement and quantum memory, Physics Letters A 308 (2003) 96–100 [doi:10.1016/S0375-9601(02)01803-0]

• Debbie W. Leung, Quantum computation by measurements, International Journal of Quantum Information 02 01 (2004) 33-43 [arXiv:quant-ph/0310189, doi:10.1142/S0219749904000055]

Review:

• Hans J. Briegel, Dan E. Browne, Wolfgang Dür, Robert Raussendorf, Maarten Van den Nest, Measurement-based quantum computation, Nature Physics 5 1 (2009) 19-26 [arXiv:0910.1116, doi:10.1038/nphys1157]

• Tzu-Chieh Wei, Measurement-Based Quantum Computation, Oxford Research Encyclopedia of Physics (2021) [arXiv:2109.10111, doi:10.1093/acrefore/9780190871994.013.31]

Towards formalizing measurement-based quantum protocols:

• Vincent Danos, Elham Kashefi, Prakash Panangaden, The Measurement Calculus, Journal of the ACM, 54 2 (2007) [arXiv:0704.1263, doi:10.1145/1219092.1219096]

Using (motivating) the ZX-calculus for formalizing measurement-based quantum protocols:

• Ross Duncan, Simon Perdrix, Rewriting Measurement-Based Quantum Computations with Generalised Flow, in: Automata, Languages and Programming. ICALP 2010, Lecture Notes in Computer Science 6199, Springer (2010) [doi:10.1007/978-3-642-14162-1_24]

• Ross Duncan, A graphical approach to measurement-based quantum computing [arXiv:1203.6242 video exposition:YT]

Concerning measurement-based quantum gates on Majorana zero modes:

• Torsten Karzig, Yuval Oreg, Gil Refael, Michael H. Freedman: Robust Majorana magic gates via measurements, Phys. Rev. B 99 (2019) 144521 [doi:10.1103/PhysRevB.99.144521, arXiv:1812.10498]

Proposed relation to gauge theory:

• Gabriel Wong, Robert Raussendorf, Bartlomiej Czech: The Gauge Theory of Measurement-Based Quantum Computation, Quantum 8 1397 (2024) [arXiv:2207.10098, doi:10.22331/q-2024-07-04-1397]