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https://github.com/quantumlib/qsim

Schrödinger and Schrödinger-Feynman simulators for quantum circuits.
https://github.com/quantumlib/qsim

nisq quantum-circuit-simulator quantum-computing quantum-simulator

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Schrödinger and Schrödinger-Feynman simulators for quantum circuits.

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README 

        
# qsim and qsimh



Quantum circuit simulators qsim and qsimh. These simulators were used for cross

entropy benchmarking in

[[1]](https://www.nature.com/articles/s41586-019-1666-5).



[[1]](https://www.nature.com/articles/s41586-019-1666-5), F. Arute et al,

"Quantum Supremacy Using a Programmable Superconducting Processor",

Nature 574, 505, (2019).



## qsim



qsim is a Schrödinger full state-vector simulator. It computes all the *2n*

amplitudes of the state vector, where *n* is the number of qubits.

Essentially, the simulator performs matrix-vector multiplications repeatedly.

One matrix-vector multiplication corresponds to applying one gate.

The total runtime is proportional to *g2n*, where *g* is the number of

2-qubit gates. To speed up the simulator, we use gate fusion

[[2]](https://arxiv.org/abs/1601.07195) [[3]](https://arxiv.org/abs/1704.01127),

single precision arithmetic, AVX/FMA instructions for vectorization and OpenMP

for multi-threading.



[[2]](https://arxiv.org/abs/1601.07195) M. Smelyanskiy, N. P. Sawaya,

A. Aspuru-Guzik, "qHiPSTER: The Quantum High Performance Software Testing

Environment", arXiv:1601.07195 (2016).



[[3]](https://arxiv.org/abs/1704.01127) T. Häner, D. S. Steiger,

"0.5 Petabyte Simulation of a 45-Qubit Quantum Circuit", arXiv:1704.01127

(2017).



## qsimh



qsimh is a hybrid Schrödinger-Feynman simulator

[[4]](https://arxiv.org/abs/1807.10749). The lattice is split into two parts

and the Schmidt decomposition is used to decompose 2-qubit gates on the

cut. If the Schmidt rank of each gate is *m* and the number of gates on

the cut is *k* then there are *mk* paths. To simulate a circuit with

fidelity one, one needs to simulate all the *mk* paths and sum the results.

  The total runtime is proportional to *(2n1 + 2n2)mk*, where *n1*

and *n2* are the qubit numbers in the first and second parts. Path

simulations are independent of each other and can be trivially parallelized

to run on supercomputers or in data centers. Note that one can run simulations

with fidelity *F < 1* just by summing over a fraction *F* of all the paths.



A two level checkpointing scheme is used to improve performance. Say, there

are *k* gates on the cut. We split those into three parts: *p+r+s=k*, where

*p* is the number of "prefix" gates, *r* is the number of "root" gates and

*s* is the number of "suffix" gates. The first checkpoint is executed after

applying all the gates up to and including the prefix gates and the second

checkpoint is executed after applying all the gates up to and including the

root gates. The full summation over all the paths for the root and suffix gates

is performed.



If *p>0* then one such simulation gives *F ≈ m-p* (for all the

prefix gates having the same Schmidt rank *m*). One needs to run *mp*

simulations with different prefix paths and sum the results to get *F = 1*.



[[4]](https://arxiv.org/abs/1807.10749) I. L. Markov, A. Fatima, S. V. Isakov,

S. Boixo, "Quantum Supremacy Is Both Closer and Farther than It Appears",

arXiv:1807.10749 (2018).



## C++ Usage



The code is basically designed as a library. The user can modify sample

applications in [apps](https://github.com/quantumlib/qsim/tree/master/apps)

to meet their own needs. The usage of sample applications is described in the

[docs](https://github.com/quantumlib/qsim/blob/master/docs/usage.md).



### Input format



The circuit input format is described in the

[docs](https://github.com/quantumlib/qsim/blob/master/docs/input_format.md).



NOTE: This format is deprecated, and no longer actively maintained.



### Sample Circuits



A number of sample circuits are provided in

[circuits](https://github.com/quantumlib/qsim/tree/master/circuits).



### Unit tests



Unit tests for C++ libraries use the Google test framework, and are

located in [tests](https://github.com/quantumlib/qsim/tree/master/tests).

Python tests use pytest, and are located in

[qsimcirq_tests](https://github.com/quantumlib/qsim/tree/master/qsimcirq_tests).



To build and run all tests, run:

```

make run-tests

```

This will compile all test binaries to files with `.x` extensions, and run each

test in series. Testing will stop early if a test fails. It will also run tests

of the `qsimcirq` python interface. To run C++ or python tests only, run

`make run-cxx-tests` or `make run-py-tests`, respectively.



To clean up generated test files, run `make clean` from the test directory.



## Cirq Usage



[Cirq](https://github.com/quantumlib/cirq) is a framework for modeling and

invoking Noisy Intermediate Scale Quantum (NISQ) circuits.



To get started simulating Google Cirq circuits with qsim, see the

[tutorial](https://github.com/quantumlib/qsim/blob/master/docs/tutorials/qsimcirq.ipynb).



More detailed information about the qsim-Cirq API can be found in the

[docs](https://github.com/quantumlib/qsim/blob/master/docs/cirq_interface.md).



## Disclaimer



This is not an officially supported Google product.



# How to cite qsim



Qsim is uploaded to Zenodo automatically. Click on this badge [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.4023103.svg)](https://doi.org/10.5281/zenodo.4023103) to see all the citation formats for all versions.



An equivalent BibTex format reference is below for all the versions:



```

@software{quantum_ai_team_and_collaborators_2020_4023103,

  author       = {Quantum AI team and collaborators},

  title        = {qsim},

  month        = Sep,

  year         = 2020,

  publisher    = {Zenodo},

  doi          = {10.5281/zenodo.4023103},

  url          = {https://doi.org/10.5281/zenodo.4023103}

}

```