*By Amara Grap*s

The most astonishing feature of the quantum computing field to newcomers is the variety of methods (‘modalities’) to make a qubit. With the state-of-the-art today, what evidence, if any, is there for particular applications that are better suited to particular quantum computing modalities? GQI’s Doug Finke says in a recent Laser Focus article :

We aren’t at the point yet where we can definitely say which quantum applications will be able to provide commercially useful results on which machines. But the one thing that makes us optimistic is the diversity of innovative approaches and rapid advances organizations are making in both hardware and software to get us to the point where the systems can be used for quantum production for useful applications.

We know the answer in a general sense: from quantum hardware that is gate-based**,** versus annealing**,** versus bosonic (photonic). Gates refers to logic gates using the computational method we are familiar from classical computing. Quantum annealers use adiabatic models as a paradigm in the device’s quantum fluctuations to find the global minimum of a given objective function. Gaussian boson sampling (GBS) is how photonic quantum devices sample from the output distribution of a specific linear optical circuit.

In today’s NISQ era, we can also learn which hybrid quantum technology modality is suited for which problem in an algorithm sense, by the choice of ansatz to solve the problem. Ansatz (from German Ansätze): the first guess or initial condition, in quantum computing, refers to a trial wavefunction or trial state used as a starting point for approximations or optimizations. We introduced the use of ansatzes in Part 3 of The Many Faces of Hybrid Classical-Quantum Computing. In GQI’s Quantum Algorithms Framework, the ansatzes fit inside the *Notable Early NISQ Heuristics* and *Variable Quantum Algorithm* labels in the next figure, inside the red rectangle.

**Figure**. Slide from Presentation *GQI Quantum Software State of Play* showing GQI’s own Algorithm Framework that incorporates algorithmic themes for different hardware eras. *If you are interested to learn more, please don’t hesitate to contact **info@global-qi.com**.*

**Ansatz Research**

Ansatzes are a key to answer this application | modality question. The answer will become clear in the near future as the hybrid quantum-classical Use Cases continue to be developed. Today I will show you the zoo of ansatz research, where a quick search of ArXiv for all years returns ~400 ansatz research papers, with ~360 of those research articles in the last five years.

The best education I’ve found so far for clarity to understand the ansatz zoo is Sophia Economou’s May 7, 2021, 30 min. presentation for the Quantum Research Seminars Toronto : How to create a good ansatz for variational quantum algorithms She presents three different classes of ansatzes, with a theme of problem focus. see the next figure. In the left side of the arrow in red are the Hardware-Efficient Ansatzes (HEA), which are agnostic for the problem, and towards the right, is the highest degree of problem-tailoring. In her seminar, she explains the forms of the ansatz function and how further to develop them while customizing it for the problem at hand..

**Figure**. Schematic for classes of ansatz development from Sophia Economou’s May 7, 2021, 30 min. presentation for the Quantum Research Seminars Toronto: How to create a good ansatz for variational quantum algorithms

**The Ansatz Library, circa 2019**

Cao et al, 2019’s 194-pg tome Quantum Chemistry in the Age of Quantum Computing includes a table (Table 5) that identified particular chemistry problems with their ansatzes and quantum computing architecture (i.e. modality). This was the paper which inspired my thinking that we have some evidence for preferences for quantum hardware modalities to particular hybrid problems. The readable research article maps chemistry Hamiltonians to qubit Hamiltonians and describes in 25p a handful of ansatzes for state preparation in chemistry problems.

**The Ansatz Library, circa 2022**

Several years later, Tilley et al, 2022 in their 156-pg tome: The Variational Quantum Eigensolver: a review of methods and best practices provided a VQE Survey with practical advice and descriptions of the ansätzes, indicating a good growth of the field. The ‘Fixed Structure’ classification in Tilley’s work would lie on the left of Economou’s figure Arrow as ‘Problem Agnostic’ and the ‘Adaptative structure’ would lie in the middle of her figure Arrow.

**Fixed structure ansatz**

- Hardware-efficient ansatz
- The Unitary Coupled Cluster (UCC)
- Symmetry-preserving methods
- Hamiltonian Variational Ansatz

**Adaptative structure ansatz**

- Iterative ansatz growth methods (ADAPT-VQE and extensions)
- Iterative Hamiltonian dressing (iterative Qubit Coupled Cluster (iQCC) and extensions)

**The Ansatz Library, circa 2024**

In 2024, the ansatz zoo expanded significantly. Blekos, et a.l, 2024 in *A review on Quantum Approximate Optimization Algorithm and its variants** *provide at least 14 different classes, where the Hardware-efficient (now called Hardware-specific) is one of the 14. It’s a detailed 67-pg review with 10-pgs of ansatz descriptions plus practical advice, including this Section 6.1: *Which QAOA Ansatz Variant Should I Use for My Problem?* For quantum computer scientists today, who are implementing real Use Cases on hybrid quantum-classical hardware, this might be one of your most valuable papers to have in your library.

As we’ve just scratched the surface of this deep topic, we’ll be returning to the topic again in the future.

September 6, 2024