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Expand Up @@ -38,38 +38,75 @@ below](#5_consider_multiple_compute_nodes).
### 2. Estimate your memory requirements

You can estimate your memory requirements with the following rule of thumb:
$ memory\ required = 8 \cdot 2^N bytes $ for an N-qubit circuit
${\rm memory\ required} = 8 \cdot 2^N \ {\rm bytes}$ for an N-qubit circuit

In addition to memory size, consider the bandwidth of your memory. qsim performs
best when it can use the maximum number of threads. Multi-threaded simulation
benefits from high-bandwidth memory (above 100GB/s).

### 3. Decide between CPUs and GPUs
### 3. Decide among CPUs, single GPUs, or multiple GPUs

* GPU hardware starts to outperform CPU hardware significantly (up to 15x
faster) for circuits with more than 20 qubits.
* The maximum number of qubits that you can simulate with a GPU is limited by
the memory of the GPU. Currently, for a noiseless simulation on an NVIDIA
A100 GPU (with 40GB of memory), the maximum number of qubits is 32.
* For noiseless simulations with 32-40 qubits, you can use CPUs. However, the
runtime time increases exponentially with the number of qubits, and runtimes
are long for simulations above 32 qubits.
the memory of the GPU. For example, for a noiseless simulation on an NVIDIA
A100 GPU with 40GB of memory, the maximum number of qubits is 32.
* However, if you have access to a device with multiple GPUs, you can
pool their memory. For example, with eight 80-GB NVIDIA A100 GPUs (640GB of
total GPU memory), you can simulate up to 36 qubits. Multi-GPU simulations
are supported by [NVIDIA's cuQuantum Appliance](https://catalog.ngc.nvidia.com/orgs/nvidia/containers/cuquantum-appliance),
which acts as a backend for qsim.

The following charts show the runtime for a random circuit run on
[Google Compute Engine](https://cloud.google.com/compute), using an NVidia A100
[Google Compute Engine](https://cloud.google.com/compute), using an NVIDIA A100
GPU, and a compute-optimized CPU (c2-standard-4). The first chart shows the
runtimes for the noiseless simulation. The second chart shows the runtimes for a
noisy simulation, using a phase damping channel (p=0.01). The charts use a log
scale.
scale. These benchmarks were all performed using qsim's native GPU and CPU
backends and do not involve sampling bitstrings (i.e. no measure gates).

![qsim runtime comparison on multipe processors: noiseless](images/qsim_runtime_comparison_noiseless.png)
![qsim runtime comparison on multipe processors: noisy](images/qsim_runtime_comparison_noisy.png)

### 4. Select a specific machine
### 4. If using GPUs, select a backend

For GPU-based simulations, you can either use qsim's native GPU backend
or the NVIDIA cuQuantum backend. While the native qsim GPU backend is performant
for extracting amplitudes of specific quantum states, it is not optimized for
sampling bitstrings, i.e. for simulating circuits that have measurement gates. For
that purpose, cuQuantum performs significantly better. cuQuantum is also needed
for multi-GPU support. More specifically, there are three options for GPU-based
simulations:
1. Native qsim. This option involves compiling qsim locally with the CUDA toolkit
installed, as described [here](tutorials/gcp_gpu).
2. NVIDIA cuQuantum SDK/cuStateVec. This option involves installing [NVIDIA's cuQuantum SDK](https://developer.nvidia.com/cuquantum-sdk)
(instructions [here](https://docs.nvidia.com/cuda/cuquantum/custatevec/getting_started.html#installation-and-compilation)),
setting the `CUQUANTUM_ROOT` environment variable and then compiling qsim locally.
See further instructions [here](tutorials/gcp_gpu#optional-use-the-nvidia-cuquantum-sdk).
This allows you to use the cuQuantum backend with the latest version of qsim.
However, it does not enable multi-GPU support.
3. For multi-GPU support, you will need to use [cuQuantum Appliance](https://catalog.ngc.nvidia.com/orgs/nvidia/containers/cuquantum-appliance),
which runs in a Docker container and contains a version of qsim that has been
slightly modified by NVIDIA. The versions of qsim and cirq in this container
may be out of date.

We recommend option 2 if you are not planning to run multi-GPU simulations
and option 3 if you are.

Note the settings in [`qsimcirq.QSimOptions`](https://quantumai.google/reference/python/qsimcirq/QSimOptions),
which allow you to specify the GPU backend as well as related settings. We find
that `max_fused_gate_size = 4` is usually optimal for larger circuits, although you may want to experiment yourself.
In cuQuantum Appliance, these settings are extended, as documented [here](https://docs.nvidia.com/cuda/cuquantum/appliance/cirq.html),
allowing you to specify how many and which GPUs to use.


### 5. Select a specific machine

After you decide whether you want to use CPUs or GPUs for your simulation,
choose a specific machine:

#### For CPU-based simulations:

1. Restrict your options to machines that meet your memory requirements. For
more information about memory requirements, see step 2.
2. Decide if performance (speed) or cost is more important to you:
Expand All @@ -87,7 +124,133 @@ choose a specific machine:
typically, f=4 is the best option).
* Simulating a **deep circuit** (depth 30+).

### 5. Consider multiple compute nodes
#### For GPU-based simulations:

For GPU simulations, you may follow the instructions in [this](tutorials/gcp_gpu)
guide to set up a virtual machine (VM) on Google Cloud Platform (GCP).
Alternatively, you can use your own hardware.
Note the [hardware requirements](https://docs.nvidia.com/cuda/cuquantum/getting_started.html#custatevec)
for NVIDIA's cuQuantum when picking a GPU; in particular, it must have
CUDA Compute Capability 7.0 or higher.
At the time of writing, the following compatable GPUs are available on GCP:
* [NVIDIA T4](https://www.techpowerup.com/gpu-specs/tesla-t4.c3316).
This is the least expensive compatable GPU on GCP.
It has 16GB of memory and can therefore simulate up to 30 qubits.
It is not compatible with multi-GPU simulations.
* [NVIDIA V100](https://www.techpowerup.com/gpu-specs/tesla-v100-pcie-16-gb.c2957).
Like the NVIDIA T4, this GPU has 16GB of RAM and
therefore supports up to 30 qubits. It is faster than the T4.
Further, it is compatible with multi-GPU simulations. With 8 NVIDIA V100s (128GB),
you can simulate up to 33 qubits.
* [NVIDIA L4](https://www.techpowerup.com/gpu-specs/l4.c4091). This GPU has 24GB
of RAM and can therefore simulate up to 31 qubits. With eight of them (192GB), you can simulate
up to 34 qubits.
* [NVIDIA A100 (40GB)](https://www.techpowerup.com/gpu-specs/a100-pcie-40-gb.c3623).
Can simulate 32 qubits with a single GPU or 36 qubits with 16 GPUS (640GB).
* [NVIDIA A100 (80GB)](https://www.techpowerup.com/gpu-specs/a100-pcie-80-gb.c3821).
Can simulate 33 qubits with a single GPU or 36 with 8 GPUs (640GB).

If you are using GCP, pay attention to the hourly cost, which you can see when creating a VM. To estimate
your total cost, you need to know how long your simulation will take to run. Here
are our benchmarks of the various GPUs (except the L4, which was added after we performed
the benchmarks). We report the time in seconds to run a noiseless depth-N circuit on N qubits and
sample 100,000 N-bit bitstrings, all benchmarked using cuQuantum with `max_fused_gate_size = 4`.

<table>
<thead>
<tr>
<th rowspan=2>GPU</th>
<th rowspan=2>number of GPUs</th>
<th colspan=6>
Runtime using cuQuantum (seconds)
</th>
</tr>
<tr>
<th>N=26</th>
<th>N=28</th>
<th>N=30</th>
<th>N=32</th>
<th>N=34</th>
<th>N=36</th>
</tr>
</thead>
<tbody>
<tr>
<td>NVIDIA T4</td>
<td>1</td>
<td>1.25</td>
<td>3.5</td>
<td>13.4</td>
<td>insufficient RAM</td>
<td>insufficient RAM</td>
<td>insufficient RAM</td>
</tr>
<tr>
<td>NVIDIA V100</td>
<td>1</td>
<td>0.91</td>
<td>1.55</td>
<td>4.4</td>
<td>insufficient RAM</td>
<td>insufficient RAM</td>
<td>insufficient RAM</td>
</tr>
<tr>
<td>NVIDIA V100</td>
<td>2</td>
<td>1.0</td>
<td>1.3</td>
<td>2.5</td>
<td>insufficient RAM</td>
<td>insufficient RAM</td>
<td>insufficient RAM</td>
</tr>
<tr>
<td>NVIDIA A100 (40GB)</td>
<td>1</td>
<td>0.89</td>
<td>1.23</td>
<td>2.95</td>
<td>11.1</td>
<td>insufficient RAM</td>
<td>insufficient RAM</td>
</tr>
<tr>
<td>NVIDIA A100 (40GB)</td>
<td>2</td>
<td>1.04</td>
<td>1.24</td>
<td>1.88</td>
<td>4.85</td>
<td>insufficient RAM</td>
<td>insufficient RAM</td>
</tr>
<tr>
<td>NVIDIA A100 (80GB)</td>
<td>2</td>
<td>1.04</td>
<td>1.21</td>
<td>1.75</td>
<td>4.06</td>
<td>14.6</td>
<td>insufficient RAM</td>
</tr>
</tr>
<tr>
<td>NVIDIA A100 (80GB)</td>
<td>8</td>
<td>1.31</td>
<td>1.38</td>
<td>1.55</td>
<td>2.23</td>
<td>5.09</td>
<td>17.6</td>
</tr>
</tbody>
</table>


### 6. Consider multiple compute nodes

Simulating in multinode mode is useful when your simulation can be parallelized.
In a noisy simulation, the trajectories (also known as repetitions, iterations)
Expand All @@ -103,11 +266,11 @@ simulation using HTCondor on Google Cloud](/qsim/tutorials/multinode).
Runtime grows exponentially with the number of qubits, and linearly with circuit
depth beyond 20 qubits.

* For noiseless simulations, runtime grows at a rate of $ 2^N $ for an N-qubit
* For noiseless simulations, runtime grows at a rate of $2^N$ for an N-qubit
circuit. For more information about runtimes for small circuits, see
[Additional notes for advanced users](#additional_notes_for_advanced_users)
below).
* For noisy simulations, runtime grows at a rate of $ 2^N $ multiplied by the
* For noisy simulations, runtime grows at a rate of $2^N$ multiplied by the
number of iterations for an N-qubit circuit.

## Additional notes for advanced users
Expand Down Expand Up @@ -147,10 +310,13 @@ depth beyond 20 qubits.
addition to this, qsim is not optimized for small circuits.
* The total small circuits runtime overhead for an N qubit circuit
depends on the circuit depth and on N. The overhead can be large enough to
conceal the $ 2^N $ growth in runtime.
conceal the $2^N$ growth in runtime.

## Sample benchmarks

The following benchmarks are all run using qsim's native CPU and GPU backends
and do not involve sampling bitstrings.

**Noiseless simulation benchmarks data sheet**

For a random circuit, depth=20, f=3, max threads.
Expand Down
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