EP-4736079-A1 - METHOD AND SYSTEM FOR SCALABLE QUANTUM CIRCUIT CONFIGURATION IN NOISY INTERMEDIATE-SCALE QUANTUM DEVICES

EP4736079A1EP 4736079 A1EP4736079 A1EP 4736079A1EP-4736079-A1

Abstract

The invention relates to methods and systems for generation of an optimized ansatz (Ψ(m)) wave-function, said computer implemented method comprising operating a system comprising quantum computational means and classical computational means, said method comprising: o Generating analytic functions of a parameter Θ from an objective function; o Selecting several angles values of the parameter Θ to generate, from the analytic functions of the parameter Θ; o On the quantum computational means, computing unknown operator expectation values of the objective function at the several selected angles values; o On the classical computational means, computing the objective function for any unitary operator (B), any angle of the parameter θ, o Appending the resulting locally optimal unitary operator to the left of the current ansatz wave-function |Ψ(curr)), preferably to generate an optimized ansatz (Ψ(m)) wave-function.

Inventors

FENIOU, César
CLAUDON, Baptiste
HASSAN, Muhammad
COURTAT, Axel
ADJOUA, Olivier
MADAY, Yvon
PIQUEMAL, Jean-Philip

Assignees

Qubit Pharmaceuticals
Sorbonne Université
Centre National de la Recherche Scientifique
Université Paris Cité

Dates

Publication Date: 20260506
Application Date: 20240701

Claims (20)

1 . A computer implemented method for the generation of an optimized ansatz (^(m)) wavefunction, said computer implemented method comprising operating a system comprising quantum computational means and classical computational means, said method comprising: o Generating analytic functions of a parameter 0 from an objective function implying a current ansatz, unitary operators and parameter; o Selecting several angles values of the parameter 0 to generate, from the analytic functions of the parameter 0, a system of equations minimizing the number of measurements to be done on quantum computational means; o On the quantum computational means, computing unknown operator expectation values of the objective function at the several selected angles values; o On the classical computational means, computing the objective function for any unitary operator (B), any angle of the parameter 0, and thereby obtain: • the locally, optimal unitary operator B m that should be added to the current ansatz | l 4 J (curr)> wave function, and • the optimal angle 0' m ; and o Appending the resulting locally optimal unitary operator to the left of the current ansatz wave-function | ’4 J (cu rr)>, preferably to generate an optimized ansatz (^(m)) wave-function.
2. A computer implemented method according to claim 1 , wherein for the step of generating analytic functions of the parameter 0 from an objective function is done using trigonometric transformations.
3. A computer implemented method according to claim 1 or 2, wherein for the step of computing unknown operator expectation values of the objective function at the several selected angles values is done employing a minimal measurement strategy that optimizes the sampling points based on the trigonometric properties of the objective function.
4. A computer implemented method according to any one of claim 1 to 3, wherein for the step of computing the objective function for any unitary operator (B), the optimal unitary operator B m is determined by a greedy, gradient-free optimization process, and the optimal angle 0'm is optimized through analytical methods to achieve minimal energy configuration.
5. The computer implemented method according to anyone of the preceding claims, wherein the step of computing the objective function, for example L(B,0, | ’(curr)», at the several selected angles, requires measuring at most ten quantum circuits for Hamiltonians of a given form, regardless of the number of qubits.
6. The computer implemented method according to anyone of the preceding claims, wherein the steps of Generating, Selecting, Computing on the quantum computational means, and Computing the objective on the classical computational means are repeated iteratively and wherein the objective function, for example L(B,0, |'4 J (curr)» , is computed on the classical computational means analytically for any unitary operator (B), any angle of the parameter 0, and any ansatz wave-function |’4 J (m-1 )> already appended to the ansatz wave-function.
7. The computer implemented method according to anyone of the preceding claims, wherein the quantum computational means comprise quantum hardware or classical hardware configured to simulate quantum computing, and preferably are selected among: quantum computers based on trapped ions, superconducting quantum computers, neutral atoms in optical lattices, quantum dot computer spin-based or spatial-based, Bose-Einstein condensate-based quantum computer, quantum wells computers, nuclear magnetic resonance quantum computer, cavity quantum electrodynamics, optical quantum computer, or diamond-based quantum computer.
8. The computer implemented method according to anyone of the preceding claims, wherein the classical computational means comprise CPU, GPU or ASIC, preferably configured to support the computational demands and parallel processing requirements of hybrid quantum-classical algorithms.
9. The computer implemented method according to anyone of the preceding claims, wherein the pool of unitary operators is selected among: Qubit Excitation-based Pool, Qubit Hardware-efficient Pool, and/or Minimal Hardware-efficient Pool.
10. The computer implemented method according to anyone of the preceding claims, wherein the pool of unitary operators includes single and double fermionic excitation operators, spin-complemented pairs of single and double fermionic excitation operators and/or individual Pauli chains, e.g. from the division of fermionic-ADAPT operators after a Jordan- Wine mapping.
1 1 . The computer implemented method according to anyone of the preceding claims, wherein the ansatz wave function comprises more than five parameters, preferably more than 10, 15, 20 parameters.
12. The computer implemented method according to anyone the preceding claims, wherein it comprises the use of 30 or less, preferably 20 or less, even more preferably 10 or less quantum circuit measurements for each iteration, advantageously this is regardless of the number of qubits and the size of the operator pool.
13. The computer implemented method according to anyone of the preceding claims, wherein the unitary operator selected is the one whose action on a current ansatz (Ψ (curr)) produce a new wave function with the largest orbital overlap with respect to a target wave function C+'target).
14. The computer implemented method according to anyone of the preceding claims, wherein the parameterized unitary operator (0 m B m ) is select so as that its action on the current ansatz |Y(curr) is likely to produce a new wave-function having the largest overlap with a target wave-function,
15. The computer implemented method according to anyone of the preceding claims, wherein the overlap is calculated according to a Compute-Uncompute method or an Hadamard SWAP-Test.
16. The computer implemented method according to anyone of the preceding claims, wherein it further comprises a step of computing the target ansatz wave function (| T ref)) , said computing being performed by binary computing means or by quantum computing means.
17. The computer implemented method according to claims 14 or 15, wherein the target wave function is with a tractable high accuracy approximation of a full-CI wave-function.
18. The computer implemented method according to claims 14 or 15, wherein the target wave function is an ADAPT-VQE ansatz, for example comprising more than five parameters, preferably more than 10, 15, 20 parameters.
19. The computer implemented method according to claims 14 or 15, wherein the target wave function is a Selected-Configuration Interaction ansatz, preferably computed according to the so-called Configuration Interaction perturbatively selected iteratively (Cl PSI).
20. A computer implemented method for simulating quantum many-body system using the optimized ansatz generated according to anyone of the preceding claims.

Description

Method and system for scalable quantum circuit configuration in noisy intermediate-scale quantum devices. Field of the invention The present invention relates to the field of quantum computers. De|cription of Related Art Quantum computing is a rapidly improving technology that employs the laws of quantum mechanics to solve specific problems which are too complex for classical computers. In the past three decades, quantum computing has gathered significant attention due to its potential to solve computational problems that are not adapted for classical computers. Among the most promising approaches in this domain is the use of hybrid quantum-classical systems, which integrate quantum and classical computing elements. A notable example of such systems is the Variational Quantum Eigensolver (VQE), designed primarily for simulating quantum many-body systems. VQEs operate by constructing a parameterized wave-function, which is optimized to minimize the expectation value of a given Hamiltonian. However, the practical implementation of these algorithms faces significant challenges, especially within the noisy intermediate-scale quantum (NISQ) era. NISQ devices, characterized by their limited qubit count and inherent noise, impose substantial restrictions on quantum algorithm performance. The primary difficulties involve the noisy evaluation of the wave-functions and the polynomial scaling in the number of observables needed for effective operation. These issues often result in suboptimal performance and limited scalability of VQE algorithms, necessitating a significant number of quantum circuit evaluations, which can be resource-intensive. Recent developments have attempted to address these challenges through various adaptations of the VQE framework. Techniques such as the adaptation of quantum circuits based on dynamic selection of operators from a predefined pool have been explored to enhance the efficiency and accuracy of these algorithms. Nonetheless, these methods still contend with the fundamental issue of noise and the extensive computational overhead linked to iterative optimization procedures. In particular, the challenge of optimizing high-dimensional cost functions on NISQ devices remains a significant challenge. The need to balance quantum resource utilization with algorithmic performance under noisy conditions continues to drive research in this area. Thus, there is still a need for new methods and quantum circuit focusing on addressing the constraints of noise and limited qubit coherence times, optimize the use of quantum resources, and improve the scalability and accuracy of quantum computations in practical applications, in particular when Variational Quantum Eigensolver is concerned. Summary of the invention The following sets forth a simplified summary of selected aspects, embodiments and examples of the present invention for the purpose of providing a basic understanding of the invention. However, the summary does not constitute an extensive overview of all the aspects, embodiments and examples of the invention. The sole purpose of the summary is to present selected aspects, embodiments and examples of the invention in a concise form as an introduction to the more detailed description of the aspects, embodiments and examples of the invention that follow the summary. In one aspect, the invention relates to a computer implemented method for the generation of an optimized ansatz (ψ(m)) wave-function, said computer implemented method comprising operating a system comprising quantum computational means and classical computational means, said method comprising: o Generating analytic functions of a parameter 0 from an objective function implying a current ansatz, unitary operators and parameter; o Selecting several angles values of the parameter 0 to generate, from the analytic functions of the parameter 0, a system of equations minimizing the number of measurements to be done on quantum computational means; o On the quantum computational means, computing unknown operator expectation values of the objective function at the several selected angles values, o On the classical computational means, computing the objective function for any unitary operator (B), any angle of the parameter 0, and thereby obtain: • the locally, optimal unitary operator Bm that should be added to the current ansatz | ψ-1 (curr)> wave function, and • the optimal angle 0'm; and o Appending the resulting locally optimal unitary operator to the left of the current ansatz wave-function |ψ (curr)>, preferably to generate an optimized ansatz (ψ(m)) wave-function. The invention introduces a novel implementation of a method of generation of an optimized ansatz (MJ(m)) wave-function, such as a Variational Quantum Eigensolver (VQE), optimized for noisy quantum devices. It implements an adaptive, quasi-greedy optimization development that reduces dependency on gradient calculations. This approach enables more efficient quantum computation