In the world of quantum computing, building a full-scale error-corrected quantum computer is a huge task that will allow us to solve problems that classical computers cannot. Although we are still a few years away from achieving this goal, we are using our current noisy quantum processors for various quantum experiments.
Unlike error-corrected quantum computers, experiments on noisy quantum processors have limitations due to noise. We can only perform a few thousand quantum operations before the noise starts to degrade the quantum state. However, in 2019, we conducted an experiment called random circuit sampling on our quantum processor and showed that it outperformed classical supercomputers. While we have not yet reached beyond-classical capabilities, we have made significant discoveries and observed novel physical phenomena using our quantum processors.
Even in this noisy regime, we believe that there are computational applications where quantum processors can outperform classical supercomputers. However, comparing the computational cost of a quantum experiment to a classical application is challenging. In our recent publication, “Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments,” we introduce the concept of “effective quantum volume” as a measure of the computational cost of a quantum experiment.
We applied this framework to evaluate the computational cost of three recent experiments: random circuit sampling, measuring out of time order correlators (OTOCs), and a Floquet evolution experiment related to the Ising model. OTOCs, in particular, are promising candidates for computational applications because they provide a way to measure the effective quantum volume of a circuit, which is difficult for classical computers to estimate accurately.
When it comes to running a quantum circuit on a noisy quantum processor, there are two competing factors to consider. On one hand, we want to achieve something that is difficult to accomplish classically, which increases the computational cost. On the other hand, each quantum gate introduces errors, reducing the fidelity of the quantum circuit. Finding the right balance between these factors is crucial to maximize the “computational resource” of a quantum circuit.
We can see these competing considerations in action in the random circuit sampling experiment, where errors in any gate can make the experiment fail. While it outperforms classical supercomputers, it is not a particularly useful application. In contrast, experiments involving OTOCs and Floquet evolution have the potential to address open questions in quantum many-body physics, as they focus on specific local observables. The effective quantum volume of a local observable is determined by the spread of information within the system, making it harder to simulate classically.
In conclusion, our research aims to understand and measure the computational cost of quantum experiments on noisy quantum processors. By introducing the concept of effective quantum volume, we can evaluate the potential of different experiments and identify promising computational applications of quantum processors.