LIQ𝑈𝑖|⟩ is a simulation platform developed by the Quantum Architectures and Computation team at Microsoft Research to aid in the exploration of quantum computation. LIQ𝑈𝑖|⟩ stands for “Language Integrated Quantum Operations”.
A quantum operation is usually referred to as a unitary operator (U) applied to a column state vector (also known as a ket: |> ). The “i” is just a constant scaling factor, hence the acronym.

LIQ𝑈𝑖|⟩ includes three simulators:

• A full state vector simulator that tracks the detailed evolution of the quantum state
• A stabilizer simulator based on CHP (Aaronson and Gottesman, http://arXiv.org/abs/quant-ph/0406196)
• A highly-optimized full state vector simulator for fermionic Hamiltonians

LIQ𝑈𝑖|⟩ is available under a Microsoft Research license.

See the Microsoft Research project page on LIQ𝑈𝑖|⟩ and the paper, LIQ𝑈𝑖|⟩: A Software Design Architecture and Domain-Specific Language for Quantum Computing.

To stay up to date on what we're doing with LIQ𝑈𝑖|⟩, please watch our repository and sign up for the LIQ𝑈𝑖|⟩ email list. To sign up, send an email to [email protected] with a one-line body reading:

SUB Liquid-news FirstName LastName

Replacing FirstName and LastName with your first and last names. If you prefer to remain anonymous, you may instead send an email containing:

SUB Liquid-news anonymous

If you use LIQ𝑈𝑖|⟩ in your research, please cite it as follows:

• bibTex:

@misc{1402.4467,
  author = {Dave Wecker and Krysta M.~Svore},
  title = {{LIQU}i|>: {A} {S}oftware {D}esign {A}rchitecture and {D}omain-{S}pecific 
            {L}anguage for {Q}uantum {C}omputing},
  year = {2014},
  eprint = {1402.4467},
  url = {arXiv:1402.4467v1}
}

• Text:

D. Wecker and K. M. Svore, “LIQ𝑈𝑖|⟩: A Software Design Architecure and Domain-Specific 
    Language for Quantum Computing,” (2014), arXiv:1402.4467v1 [quant-ph], 
    http://arxiv.org/abs/1402.4467.

You can use LIQ𝑈𝑖|⟩ to define quantum circuits, render them into a variety of graphical formats, and execute them using an appropriate simulator.

Some of the specific algorithms you can simulate with LIQ𝑈𝑖|⟩ are:

• Simple quantum teleportation
• Shor's factoring algorithm
• Quantum chemistry: computing the ground state energy of a molecule
• Quantum error correction
• Quantum associative memory (Ventura and Martinez, http://arxiv.org/abs/quant-ph/9807053)
• Quantum linear algebra (Harrow, Hassidim, and Lloyd, http://arxiv.org/abs/0811.3171)

All of these algorithms, and many more, are included as samples with LIQ𝑈𝑖|⟩.

You can download the LIQ𝑈𝑖|⟩ executable, libraries, sample scripts, and documentation from this site.

See the Getting Started page for directions on how to download, register, and start using LIQ𝑈𝑖|⟩.

If you don't have access to a Windows environment, you can use LIQ𝑈𝑖|⟩ on a Windows virtual machine. See the Using LIQ𝑈𝑖|⟩ on Microsoft Azure page for directions.

See the users' guide and the full help documentation. The help may also be downloaded as a single file, if desired. There is also a tutorial video available that will take you through the basics.

Note that this version of LIQ𝑈𝑖|⟩ is limited to a maximum of 23 physical qubits for full state vector simulation.

If you run into a problem or have a question, you can post an issue. If you have other feedback, you can contact the LIQ𝑈𝑖|⟩ team at [email protected].