From NISQ to small logical quantum circuits

After six years of huge interest in NISQ (noisy intermediate-scale quantum) circuits there are still no practical applications where a noisy quantum device can outperform the best classical methods. Noise is too detrimental, and classical methods are too powerful. Experts continue to argue that now is not the time for commercial applications: quantum error correction, hundreds of logical qubits, and millions of error-corrected gates are needed.

Then what's next? Circuits of a moderate size with some limited error correction capabilities. LISQ (logical intermediate-scale quantum) or something else, for short.

What can we expect from these up and coming small scale logical circuits?

First, a lot of the tools developed for the NISQ era will become obsolete. For example, variational quantum circuits involving continuously-parameterised quantum gates cannot be easily implemented in a fault-tolerant manner. Instead, post-variational hybrid quantum-classical algorithms for this era will need to offload the continuously-parameterised part of the algorithm to a classical computer, with the quantum circuit used to measure a set of (hopefully classically-intractable) observables that are used as inputs to the classical tunable model.

Second, the hardware, algorithms, and the error correcting code cannot be considered in isolation. Choosing the right error correcting code will be essential to get the most out of the current hardware. Examples of this can be seen in QuEra's logical circuit demonstration from late last year, where the use of a 3D quantum error correction code allowed them to perform random IQP circuit sampling with error detection, and Quantinuum's recent demonstration of repeated error correction. Similar to the NISQ era, different hardware platforms will have different strengths and limitations in what kinds of circuits they will be able to run.

Finally, the most valuable software tools in the NISQ era were for quantum control and state tomography, essential to get the most out of the noisy hardware. These tools will remain important, since fidelities at the physical qubit level directly affect the amount of quantum error correction overhead required. As we move to logical circuits, the new valuable quantum software will be in the form of compilers that will take all the hassle out of hardware and error code selection out of the end-user and translate a given logical circuit into simple, understandable hardware requirements.