#naqa

Temple ruins of Naqa, Sudan.

While the quantum computing community waits on fault-tolerant hardware, a family of algorithms exploits near-term quantum device noise. Noise-Adaptive Quantum Algorithms (NAQAs) exploit quantum noise instead of suppressing it. We discuss NAQAs' nature, history, key works that have inspired the discipline, and prospective future directions in this article.

NAQA Meaning

Noise-Adaptive Quantum Algorithms (NAQAs) exploit near-term quantum devices' intrinsic noise. The quantum computing community is still waiting for fault-tolerant hardware, and NAQAs can use QPU noise.

A detailed description of NAQAs:

Fundamental Idea:

Real-world QPUs operate in noisy environments, unlike a noise-free quantum system that would yield a single, optimal low-energy solution. This noise may produce multiple low-energy solutions, and bitstring samples may not be suitable solutions when constraints are applied. NAQAs combine noisy outputs instead of removing them. This aggregation uses quantum correlation to alter the basic optimisation problem before committing to a single sample. This improves quantum system solutions. NAQAs rely on reusing noisy data.

Origins and Comparison

NAQAs resemble the Cross-Entropy Method conceptually. CEM simulates distributions without physical noise via candidate sampling and iterative refinement. CEM and NAQAs respond to noisy outputs to guide search.

One major difference between CEM and NAQAs is:

CEM evaluates sampled candidates using a noisy cost function, unlike NAQAs, which measure quantum bitstrings. CEM favours top performance by updating the sample distribution, while NAQAs find new attractor states and alter the cost Hamiltonian. NAQAs minimise cost under a modified Hamiltonian, while CEM maximises performance across a probability distribution. CEM averages across noise, unlike NAQAs, which discover attractor states using noise.

The reference's “Quantum-Assisted Greedy Algorithms” fixed variables based on consensus across numerous sample bitstrings and were tested on D-Wave's QPU. These concepts underpin NAQAs. The pioneering study citation introduced the term “Noise-Directed Adaptive Remapping” (NDAR), which underpins additional research.

In contrast to ADAPT Algorithms:

It's important to realise that NAQAs are different from ADAPT algorithms like ADAPT-VQE and ADAPT-QAOA. As the algorithm advances, ADAPT algorithms adapt to the issue structure by changing the search space exploration (e.g., by picking a different “mixing” Hamiltonian). These ADAPT approaches were not designed to use QPU noise and have mostly worked in noise-free simulations. Real, loud quantum gear is used to test the NAQA series.

The NAQA Framework

The general NAQA pseudocode uses an iterative procedure:

Create samples with a quantum programme. The sampling stage can employ “stochastic optimisation” instead of quantum systems and is modular. issue Adaptation: Adjust the optimisation issue based on the sampleset. Fixing variable values by studying sample correlations and establishing the attractor state or utilising a bit-flip gauge transformation are popular methods.

To lead the algorithm towards promising solutions without limiting the solution space, numerous noisy samples must be collected and aggregated. This is the most complicated part. Re-optimize: Fix the changed optimisation.

Repeat until the solution is satisfactory or stops improving.

Gate-based and annealing-based quantum computers can leverage this paradigm. Despite their longer runtime and higher processing complexity, NAQAs are helpful for short-term devices and often outperform vanilla QAOA in noisy environments.

Benefits:

Theoretically, the NAQA architecture is simple and modular.

Improved Solution Quality: NAQAs outperform vanilla QAOA in noisy environments, according to research.

Drawbacks:

Computational Overhead: These methods take a lot of processing power, and many major studies lack runtime information, which may affect performance. Step 2—changing the optimisation problem can be difficult, especially when eigenvalue decompositions or other operations are needed. Since operations scale cubically with sample count (O(n³)),

Limitations/Unknowns:

Transferability: NAQAs perform well on Sherrington-Kirkpatrick (SK) Ising models, but real-world settings often produce power-law degree distributions, making it uncertain how well they translate. Comparisons with other noise-aware algorithms are few. NAQAs may be compared to Q-CTRL's hardware-independent MaxCut solution for insights.

Future Paths:

The Nubian Temple of Apedemak in Naqa (or Naga’a), Khartoum, Sudan