In 2023, a group of researchers at Oak Ridge National Laboratory ran a simulation of a 61-qubit quantum circuit on the Theta supercomputer. Storing its state vector would have required 32 exabytes of memory, more than the total capacity of all hard drives on the planet. But thanks to data compression, they fit it into 768 terabytes. That is what everyday work looks like for those trying to make classical machines play quantum music.

This music is structured in an unusual way. A quantum bit, or qubit, does not store just a zero or a one, but a quantum superposition: both values at once, with different weights. When you have two qubits, there are four states, all existing in parallel. Three qubits give eight states. Each new qubit doubles the number of possible combinations, and soon the orchestra is playing every conceivable melody at once. To describe that, a classical computer has to hold every note of this infinite score in memory.

Engineers have found several ways to lighten this burden. On CPUs, compressing the state vector lets you store only the significant numbers, discarding near-zero contributions. On GPUs, the cuQuantum library has accelerated tensor network compression, which are graphs of tensors representing the quantum circuit, by up to 547 times compared to a baseline approach. On FPGAs, precomputing matrices and streaming processing allow efficient complex-number operations even with limited resources. All these are different ways to make the hardware play faster without losing the melody.

Until recently, it was unclear which hardware accelerations were most effective and how to systematize them. Now it is clear: the key accelerations lie in data compression, reduced precision, memory access optimization, and parallelism, and the choice of platform, CPU, GPU, or FPGA, determines which techniques apply. Simulator developers can immediately pick the right optimizations, and researchers can see promising directions without re-analyzing the literature.

Ahead lie hybrid approaches that combine different accelerators and the adaptation of compression methods from machine learning. Already today, these techniques help test quantum algorithms faster without access to expensive quantum machines, bringing closer the day when a real quantum orchestra plays at full volume.