simcount

Quantum algorithms for the simulation of Hamiltonian dynamics.

This repository contains:

• Implementations of quantum algorithms for the simulation of Hamiltonian dynamics in the Quipper quantum programming language.

• Sample quantum circuits.

Explicit descriptions of the algorithms, implementation details, and original references can be found in the following paper.

• Andrew M. Childs, Dmitri Maslov, Yunseong Nam, Neil J. Ross, and Yuan Su. Toward the first quantum simulation with quantum speedup. November 2017. Available from https://arxiv.org/abs/1711.10980.

License

• The code is released under the Apache License. See the LICENSE and NOTICE files for more information.

Build

The modules require Quipper. See Quipper for download options and installation instructions.

Assuming that Quipper is installed, the main file can be compiled as follows.

quipper Main.hs

Usage

The main function can be used to generate quantum circuits and gather some statistics about them. The options are

• n, the size of the simulated system (a nonzero integer, default: 50)

• a, the algorithm to use (default: pf4com)

• g, the type of gates to use (default: cz)

• z, the number of rotations to approximate (a nonzero integer, default: 1)

• f, the output format for circuits (default: gatecount)

• m, the random seed to use in generating the Hamiltonian (default: 1)

• h, to print the usage info

Possible values for a are: pf1ana, pf1min, pf1com, pf1emp, pf2ana, pf2min, pf2com, pf2emp, pf4ana, pf4min, pf4com, pf4emp, pf6ana, pf6min, pf6emp, pf8ana, pf8min, pf8emp, ts, qsp, qspja, qspsegment, qspsegmentemp.

Possible values for g are: cz, cz2ct, ct.

Possible values for f are: eps, pdf, ps, postscript, ascii, preview, gatecount.

Restriction: If the chosen simulation algorithm is not qsp, qspja, qspsegment, or qspsegmentemp, then n can be any integer greater than 3. If the algorithm is one of qsp, qspja, qspsegment, or qspsegmentemp, then n must be one of 13, 16, 20, 25, 32, 40, 42, 44, 46, 48 50, 52, 54, 56, 58, 63, 79, or 100. Circuits for other system sizes using the latter algorithms can be obtained by computing the relevant parameters and adding them to the Parameters.hs module. This can be done using the Mathematica notebooks provided in the Mathematica folder.

Usage examples:

• Preview the pdf of the circuit for the simulation of a system of 10 spins using the 4th order PF algorithm with commutator bound over the Clifford+Rz gate set:

    ./Main -n 10 -a pf4com -g cz -f preview
  

• Show the gatecounts of the circuit for the simulation of a system of 40 spins using the TS algorithm over the Clifford+Rz gate set:

    ./Main -n 40 -a ts -g cz -f gatecount
  

• Show the gatecounts of the circuit for the simulation of a system of 50 spins using the segmented QSP algorithm over the Clifford+T gate set:

    ./Main -n 50 -a qspsegment -g ct -f gatecount -z 21237612
  

  Note that in the above command the number of z-rotations has to be precomputed before constructing the circuit which requires counting the number of z-rotations in the corresponding circuit over the Clifford+Rz gate set. This can be achieved by using the cz2ct argument for g which produces circuits over the Clifford+Rz gate set using only half of the allotted precision.

Samples

The compressed folder samples.tar.gz contains sample circuits for the simulation of Hamiltonian dynamics before and after optimization. The optimizations were carried out using the techniques detailed in the following paper.

• Yunseong Nam, Neil J. Ross, Yuan Su, Andrew M. Childs, and Dmitri Maslov. Automated optimization of large quantum circuits with continuous parameters. October 2017. Available from https://arxiv.org/abs/1710.07345.

The sample circuits are given in the ASCII format of the Quipper language. The circuits correspond to systems of size 13, 16, 20, 25, 32, 40, 50, 63, 79, and 100 and algorithms pf4ana, pf4min, pf4com, pf4emp, pf6emp, ts, qspja, and qspsegment.

Contributors

• Andrew M. Childs
• Dmitri Maslov
• Yunseong Nam
• Neil J. Ross
• Yuan Su

Contact

Questions and comments can be addressed to: [email protected]