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Quantum optimization techniques using a parametrically controlled nonlinear resonator array



Solving complex mathematical optimization problems is of crucial importance in fields such as physics, chemistry, biology, social sciences and in a growing number of industries. Many difficult optimization problems, such as protein folding or air flight planning, can be greatly improved by choosing a quantum approach.

The power of quantum computing could solve problems that are impossible to solve with classical computers, or suggest a considerable speed-up compared to the most well-known classical algorithms. Even with the most powerful computers available today, the time required to solve many of these problems exceeds the age of the universe. There is a lot of hope that quantum computers could actually lead to a significant speedup. Therefore, there is a lot of eagerness to build quantum optimizers, as evidenced by investments from companies such as D-Wave Systems, Google, IBM, NASA, Lockheed Martin and others.


The processor we propose here is designed to integrate a general Ising problem in continuously variable states, and to implement adiabatic quantum annealing to find the lowest energy configuration of Ising spins. There is no other continuous variable quantum annealing technology that is both fully programmable, fully connected, as well as scalable. Quantum annealing, based on adiabatic quantum computing (AQC), aims to find solutions to the Ising problem. Many difficult optimization problems can be associated with finding the global minimum (ground state) of the Ising model.

Our quantum processor consists of a network of nonlinear resonators in each of which a physical spin is encoded using a parametric reader. A set of other one-photon local drives, as well as local couplings, are provided to map the Ising problem. The frequency and forces of the drives are adjusted adiabatically in order to find the lowest energy configuration of the spins. In practice, there are errant couplings, and the resonators can lead to losses, causing the introduction of errors during the calculation. In this processor, drives and couplings are selected to minimize these effects and thus preserve the quantum characteristics. Therefore, the present invention addresses for the first time the practical problems of quantum integration and control for annealing on continuous variable systems.



  • Continuous variable quantum annealing technology: a processor that is scalable, fully connected and fully programmable.

  • Quantum fluctuations of the lowest-energy continuous-variable state (which is the optimal solution to the Ising problem) make it noise-stable, thus preserving the quantum effect longer.

  • Our processor dramatically simplifies current architectures for large-scale quantum optimization and promises significant speedups compared to their classical counterparts.

  • Resonators (instead of qubits) as Ising's spin mapping unit.

  • Inexpensive: the components to make this processor already exist.

  • Infinitely faster: will allow the resolution of certain optimization problems that would take the age of the Universe to solve with conventional computers.

  • Optimized Design: Minimizes noise effects and preserves desirable quantum effects.

  • Numerical simulations demonstrating that our processor is functional.


  • A processor that can efficiently find optimal solutions to very difficult optimization problems will be of tremendous benefit to the community, science, and business.

    • Companies that need to solve these problems are: airlines, biotech, security, AI and others.

  • In the short term: interest of academic institutions for the construction of small devices.

  • In the medium term: mid-size test devices – Google, NASA, Lockheed Martin, IARPA.

  • Long term: huge market for a large-scale device: defense industries, finance, medicine, airlines.


This continuous variable quantum processor can solve any optimization problem that can be mapped to an Ising Hamiltonian, such as:

  • protein folding.

  • Airline flight schedules.

  • Image recognition.

  • Artificial intelligence.

  • The problem of the traveling salesman.



  • TRL 3: A prototype of the processor, representing the Ising spin in a parametrically controlled nonlinear oscillator, was recently demonstrated experimentally.


  • Canadian patent no. 2,968,830, issued November 29, 2018.

  • US patent no. 10262276 B2, published on April 16, 2019.


  • Development partners.

  • Commercial Partners.

Project Director: François Nadeau

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