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An ansatz inspired by quantum optimal control for variational quantum algorithms

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Technological advances in high-performance computing have enabled countless scientific discoveries and technical breakthroughs since the dawn of the computing age. These advances are largely the result of the miniaturization of processors and the availability of greater computing power, as predicted by Moore's Law. However, we are rapidly approaching the limits of transistor miniaturization and the need to find alternative technologies is crucial for continued progress.

By exploiting the intrinsic properties of quantum mechanics, quantum computers will bring exponential improvements to solve problems that classical computers cannot solve, or solve efficiently, such as optimization (travelling salesman, machine learning), number factorization first, the simulation of matter (materials, molecules and proteins) and the modeling of financial markets.

The appearance of new, increasingly powerful quantum devices is prompting research to find algorithms that are increasingly capable of exploiting the computing power of small quantum processors. Hybrid quantum-classical algorithms have been introduced for this purpose. Known as quantum variational algorithms (AQV), these methods use a quantum computer only for the most critical part of a program, while a more robust classical coprocessor serves as an optimizer that works in a loop with the quantum device - see figure 1. Here, the term "variational" refers to the fact that free parameters of the routine are iteratively adjusted to find the solution, and that this solution is the lowest value that the algorithm can find. The solution is therefore referred to as the ground state of the problem. AQVs exploit the use of a variational circuit, the Ansatz, which must be run on the quantum computer.

While it is still too early to predict which area will be most affected by future generations of quantum processors, the simulation of quantum matter is of particular interest to researchers in this field. Importantly, the latter has the potential to revolutionize fields such as medicine (design of drugs), engineering (design of materials), agriculture (fertilizers) and chemistry (design of chemical processes). Although current quantum devices are still modest in size and subject to ambient noise, we expect that future generations of quantum processors of increasing size and quality will ultimately be able to disrupt the state of the art in classical calculation.


This invention relates to the state of the art of ansatz of variational quantum algorithms for physics and chemistry. We introduce a new variational ansatz inspired by techniques from quantum optimal control theory. This leads to a variational search that breaks the symmetries of the Hamiltonian of the problem, allowing greater flexibility in the preparation of states. We call this ansatz "Quantum-Optimal-Control-inspired Ansatz", or QOCA. We compare the QOCA to the materially efficient (HEA) ansatz and the variational Hamiltonian (AHV) ansatz on a small instance of an extremely difficult problem in condensed matter physics, the Fermi model. -Hubbard. We find that in some cases, HEA and VHA fail to converge to the ground state, whereas QOCA accomplishes this task using fewer variational parameters. Due to the great flexibility of QOCA, this work opens the door to a multitude of applications of variational quantum algorithms.



  • The first VQA to introduce symmetry breaking terms into the VHA.

  • The method provides several routes to systems of increasing sizes.

  • Noise-resilient method due to its variational nature.

  • The flexibility of the method comes from the freedom one has for designing the variational form (the ansatz), with a plethora of choices applicable to different problems.


  • This invention is at the heart of a rapidly expanding field.  

    • The quantum computing software market is expected to grow from US$0.11 billion in 2021 to US$0.43 billion in 2026, growing at a CAGR of 30.5%! Source: Markets and Markets.


  • Quantum Computer Algorithms

    • A radical improvement in the construction of quantum programs.

    • Will eventually solve prototypical problems, larger than FermiHubbard, in condensed matter physics and quantum chemistry

    • Possibly allow to understand materials with exotic properties.



TRL 4-5

  • Extremely promising results were obtained: this new variational form QOCA solved the problem of simulating the FermiHubbard model with four and six sites. This model is central in research on quantum materials such as high temperature superconductors.


  • International patent application (WO2021/203202A1)


Licenses. Development partners

Project Director: François Nadeau

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