Blocking qubits in multiple GPUs

[QuantumFran]

Hi,

I am currently working on a distributed quantum computing simulator, using qiskit-aer and GPUs. We are performing different tests and we have doubts about how to calculate the blocking qubits for our use case. According to the official documentation, the formula to calculate blocking qubits with GPUs is the following:

sizeof(complex) * 2^(blocking_qubits+4) < size of the smallest memory space in bytes.

From this formula we understand that:

1. sizeof(complex) is equal to 8 since we are using single precision.
2. “size of the smallest memory space in bytes”, we understand that it is the main memory dedicated to the GPU.
3. The value of blocking qubits is independent of the number of qubits we want to simulate.

From the formula we do not understand if the 4 that we add to the value of the blocking qubits is a constant value or it varies depending on the number of GPUs used for the simulation. If it is constant, why do we add 4?

As I mentioned, we have done several tests on AWS, distributing the simulation between different g5.xlarge instances (24 GiB dedicated RAM for GPU and 16 GiB Host RAM). According to the formula, the maximum value for blocking qubits should be 27. However, we have run 35 and 36 qubit circuits distributing between 16 and 32 g5.xlarge instances with a blocking qubit value of 29 and it worked, so we have assumed that the “size of the smallest memory space in bytes” has to be multiplied by the number of instances.

In the case of a 36 qubit circuit with single precision distributed over 32 instances, the “size of the smallest memory space in bytes” would be:

24 GiB = 25,770,000,000,000 Bytes
25,770,000,000,000 Bytes * 32 instances = 824,640,000,000,000 bytes

If we try a value of 30 for blocking qubits it should work.

8 (single precision) * 2^(30 blocking qubits +4) = 137.438.953.472
137.438.953.472 < 824.640.000.000

However, it returns the following error:

Simulation failed and returned the following error message:
ERROR:  [Experiment 0] std::bad_alloc

Could you help us understand the formula and find the optimal value for blocking qubits?

Thank you in advance.

Best regards.