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# How to Contribute

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202 changes: 202 additions & 0 deletions LICENSE
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93 changes: 93 additions & 0 deletions README.md
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# 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 $$2^n$$
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 $$g2^n$$, 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), 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).

## qsimh

qsimh is a hybrid Schrödinger-Feynman simulator
[[3]](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 $$m^k$$ paths. To simulate a circuit with
fidelity one, one needs to simulate all the $$=m^k$$ paths and sum the results.
The total runtime is proportional to $$(2^{n_1} + 2^{n_2})m^k$$, where $$n_1$$
and $$n_2$$ 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 $$F\approx 1/m^p$$ (for all the
prefix gates having the same Schmidt rank m). One needs to run $m^p$
simulations with different prefix paths and sum the results to get $$F = 1$$.

[[3]](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
aplications in [apps](apps) to meet their own needs. The usage of sample
applications is described in [docs](docs/usage.md).

### Input format

Circuit input format is described in [docs](docs/input_format.md).

### Sample Circuits

A number of sample circuits are provided in
circuits.

### Unit tests

Unit tests are located in [tests](tests). The Google test framework is used.
Paths to Google test include files and to Google test library files should be
edited in [tests/make.sh](tests/make.sh).

## Cirq Usage

[Cirq](https://github.com/quantumlib/cirq) is a framework for modeling and
invoking Noisy Intermediate Scale Quantum (NISQ) circuits.

To run qsim on Google Cirq circuits, or just to call the simulator from Python,
see [docs](docs/cirq_interface.md).

## Authors

Sergei Isakov (Google): qsim and qsimh simulators, Vamsi Krishna Devabathini
(Google): Cirq interface.

## Disclaimer

This is not an officially supported Google product.
21 changes: 21 additions & 0 deletions apps/make.sh
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# Copyright 2019 Google LLC. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

#!/bin/bash

g++ -O3 -mavx2 -mfma -fopenmp -lgomp -o qsim1 qsim1.cc
g++ -O3 -mavx2 -mfma -fopenmp -lgomp -o qsim2 qsim2.cc
g++ -O3 -mavx2 -mfma -fopenmp -lgomp -o qsim3 qsim3.cc
g++ -O3 -mavx2 -mfma -fopenmp -lgomp -o qsimh1 qsimh1.cc
g++ -O3 -mavx2 -mfma -fopenmp -lgomp -o qsimh2 qsimh2.cc
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