EP4639428A1

EP4639428A1 - Method for generating overlap-guided compact ansatz for practical quantum chemistry, uses thereof and related computing systems

Info

Publication number: EP4639428A1
Application number: EP24701891.4A
Authority: EP
Inventors: Jean-Philip PIQUEMAL; Emmanuel GINER; Muhammad HASSAN; César FENIOU; Diata TRAORE; Yvon MADAY
Original assignee: Qubit Pharmaceuticals; Centre National de la Recherche Scientifique CNRS; Sorbonne Universite; Universite Paris Cite
Current assignee: Qubit Pharmaceuticals; Centre National de la Recherche Scientifique CNRS; Sorbonne Universite; Universite Paris Cite
Priority date: 2023-01-23
Filing date: 2024-01-23
Publication date: 2025-10-29
Also published as: WO2024156718A1

Abstract

The invention relates to a computer implemented method for the generation of an optimized quantum computing circuit from an current ansatz, preferably said computer comprising quantum computational means, said method comprising: - a step of selecting (150), preferably by the quantum computational means, among a pool of unitary operators (U(θ)), the unitary operator (Â _n(θ _n)) whose action on an current ansatz produce a new wave function with the largest overlap with respect to a target wave function (Ψtarget) according to non-energy based criteria, and - a step of appending (160) the selected unitary operator to the left of the current ansatz to generate a new ansatz (Ψ(m)).

Description

Method for generating overlap-guided compact ansatz for practical quantum chemistry, uses thereof and related computing systems Field of the invention [0001] The present invention relates to the field of quantum computers. In particular, the invention relates to the field of parametrizing and using computing devices for simulating complex quantum systems with accuracy. Description of Related Art [0002] 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. [0003] Simulating complex quantum systems is among the main promising applications of quantum computing devices. Indeed, the computational cost of approximating the ground state energy of an N-electron molecular system on classical computing architectures typically grows exponentially in N. As Quantum computers allow for the encoding of the exponentially scaling underlying Hilbert space using only O(N) qubits, they are therefore likely to outperform classical devices on a range of chemical simulations. In particular, in this field, one of the main challenges is to be able to calculate properties of complex molecules with a chemical accuracy (defined as < 10^-3 Hartree). Currently, this is a task that is out of reach for large-scale systems using classical approaches. [0004] Despite promises of exponential speedups from recent research results, quantum algorithms and in particular quantum chemistry algorithms require optimization to achieve an advantage over their classical counterparts on state-of-the-art supercomputers for problems of interest. [0005] This is the case both with the Noisy Intermediate-Scale Quantum devices, where coherence times in quantum devices prohibit all but the shortest experiments to be performed, and in first-generation fault-tolerant devices, where a single non-Cliford rotation requires thousands of additional qubits and hundreds of error correcting cycles. [0006] In the field of digital quantum simulation, the variational quantum eigensolver (VQE) has emerged as a competitive class of algorithms for generating approximate ground states of quantum systems on Noisy Intermediate Scale Quantum (NISQ) devices (Peruzzo, A.; McClean, J.; Shadbolt, P.; Yung, M.-H.; Zhou, X.-Q.; Love, P. J.; Aspuru- Guzik, A.; O’brien, J. L. A variational eigenvalue solver on a photonic quantum processor. Nature communications 2014, 5, 1–7 and McClean, J. R.; Romero, J.; Babbush, R.; Aspuru-Guzik, A. The theory of variational hybrid quantum-classical algorithms. New Journal of Physics 2016, 18, 023023), due to its relatively low circuit length. [0007] In the VQE approach, a parameterized wave-function is generated and variationally tuned to minimize the expectation value of the molecular electronic Hamiltonian. A variety of different parameterized wave-functions have been proposed, including the Trotterised Unitary Coupled Cluster (tUCC) ansatz (Bartlett, R. J. Coupled- cluster approach to molecular structure and spectra: a step toward predictive quantum chemistry. The Journal of Physical Chemistry 1989, 93,1697–1708 and Romero, J.; Babbush, R.; McClean, J. R.; Hempel, C.; Love, P. J.; Aspuru-Guzik, A. Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz. Quantum Science and Technology 2018, 4, 014008) which consists of a sequence of exponential, unitary operators acting on a judiciously chosen reference state. While the tUCC approach includes electronic correlation and has, in principle, a rather simple quantum circuit structure, the excessive depth of these quantum circuits makes them ill- suited for applications in the NISQ regime. This issue has led to the proposal that ansatz wave-functions be constructed through the action of a selective subset of possible unitary operators, i.e., only those operators whose inclusion in the ansatz can potentially lead to the largest decrease in the expectation value of the molecular electronic Hamiltonian. In this context, the Adaptive Derivative-Assembled Pseudo-Trotter VQE (ADAPT-VQE) has emerged as the gold standard for generating highly accurate and compact ansatz wave- functions. In ADAPT-VQE, the ansatz is grown iteratively by appending a sequence of unitary operators to the reference Hartee-Fock state. At each iteration, the unitary operator to be applied is chosen according to a simple criterion based on the gradient of the expectation value of the Hamiltonian. [0008] Moreover, the ADAPT-VQE algorithm attempts to alleviate these problems by avoiding the inclusion of unitary operators in the ansatz wave-function that are not expected to lead to a lowering of the resulting energy. Numerical evidence suggests that ADAPT-VQE is indeed resource-saving and the energy-gradient criterion employed by ADAPT-VQE leads to much more accurate wave-functions than conventional VQE algorithms while preserving moderate circuit depth. [0009] In spite of this comparative advantage, such an energy gradient guided procedure has a tendency to fall into local minima of the energy landscape. Exiting from such minima comes at the expense of adding and optimizing operators through multiple ADAPT iterations (Grimsley, H. R.; Barron, G. S.; Barnes, E.; Economou, S. E.; Mayhall, N. J. ADAPT-VQE is insensitive to rough parameter landscapes and barren plateaus. arXiv preprint arXiv:2204.071792022), and leads to over-parameterized wave-functions. In practice, this is associated with an unnecessary increase of the quantum circuit depth required for the representation of the ansatz wave-function coupled to an increasingly difficult optimization. Therefore, simulating strongly correlated systems on existing NISQ devices is simply too demanding to accomplish with ADAPT-VQE. [0010] Moreover, as in classical methods of quantum chemistry, the choice of the ansatz for the molecular wave function is a crucial step in VQE implementations since it determines the accuracy of the obtained ground state energy. [0011] Hence, there is a need for solutions capable of simulating complex quantum systems and capable to calculate properties of complex molecules with a chemical accuracy (defined as < 10^-3 Hartree). In particular, the fundamental challenge in implementing the VQE methodology on NISQ devices is thus to construct an ansatz wave-function that can capture the most important contributions to the electronic correlation energy and, at the same time, is capable of being represented on rather shallow quantum circuits. A necessary condition to achieve the latter is that the chosen ansatz wave-function be parameterized with a relatively small number of optimization parameters. Summary of the invention [0012] 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. [0013] In one aspect, the invention relates to a computer implemented method, said computer comprising quantum computational means, said method comprising: - a step of selecting on the quantum computational means, among a pool of unitary operators, the unitary operator whose action on a current ansatz produce a new wave function with the largest overlap with respect to a target wave function, and - a step of growing the ansatz by appending the selected unitary operator to the left of the current ansatz to generate a new ansatz. [0014] In particular, the invention relates to a computer implemented method for the generation of an optimized quantum computing circuit from a current ansatz, preferably said computer comprising quantum computational means, said method comprising: - a step of selecting, preferably by the quantum computational means, among a pool of unitary operators, the unitary operator whose action on the current ansatz produce a new wave function with the largest overlap with respect to a target wave function according to non-energy-based criteria, and - a step of growing the ansatz by appending the selected unitary operator to the left of the current ansatz to generate a new ansatz; and - a step of parametrization of the new ansatz, said parametrized new ansatz defining the optimized quantum computing circuit. [0015] Preferably, the invention relates to a computer implemented method for the generation of an optimized quantum computing circuit from a current ansatz, the current ansatz being a current quantum state of a quantum system, preferably said computer comprising quantum computational means, said method comprising: - a step of selecting, preferably by the quantum computational means, among a pool of unitary operators, the unitary operator whose action on the current ansatz produce a new wave function with the largest overlap with respect to a target wave function according to non-energy based criteria, said step comprising a selection of the unitary operator, whose addition to the current ansatz maximize the overlap between a new wave-function and the target wave-function; and - a step of growing the ansatz by appending the selected unitary operator to the left of the current ansatz to generate a new ansatz; and - a step of optimizing the parameters of the new ansatz, said parametrization corresponding to the generation of the optimized quantum computing circuit. [0016] The invention aims to overcome the disadvantages of the prior art. In particular, the invention proposes a solution capable of simulating complex quantum systems and capable to calculate properties of complex molecules with a chemical accuracy (defined as < 10^-3 Hartree). Moreover, as it will be illustrated in examples the solution can be used to overcome the challenges of energy plateaus faced by the classical methods. [0017] This method is a new method of constructing an ansatz of a system, such as a physical system, in particular a chemical system. Rather than attempting to minimize the energy of the ansatz at each iteration, and potentially encountering local minima, the ansatz is grown using operators that maximize its overlap, preferably orbital overlap, with a target wave function that preferably already captures some electronic correlation of the system, i.e. chemical system. Such a target wave-function is used as a guide to construct an ansatz in the right direction and to catch the bulk of electronic correlation. The invention is of particular interest in hybrid quantum classical simulations of quantum chemical systems. Indeed, it generate a new ansatz (which can be described as compact or ultra-compact) suitable for high-accuracy (i.e. chemical accuracy) initialization for a new ADAPT procedure. As it will be illustrated, this produces massive savings in circuit depth and number of optimization parameters. [0018] According to other optional features of the method according to the invention, it can optionally include one or more of the following characteristics alone or in combination: - It further comprises a step of initializing a quantum reference state of the quantum computing means so as to allow them to behave like the current ansatz; - It further comprises a step of implementing the optimized quantum computing circuit on quantum computational means. The optimized quantum computing circuit is preferably implemented with 1 and 2 qubit gates on quantum computational means as the parametrized unitary operators can be decomposed into 1 or 2 qubit gates. - the unitary operator selected is the one whose action on a current ansatz produce a new wave function with the largest orbital overlap with respect to a target wave function. - It further comprises a step of defining, preferably by a classical computing hardware, the pool of unitary operators. - the pool of unitary operators includes any operators which can be parameterized, in particular it includes any operators with parameters that can be decomposed into 1 or 2 qubit gates. - the pool of unitary operators includes single and double fermionic excitation operators. - the step of defining the pool of parameterized unitary operators comprises the use of a qubit excitation operators. - the pool of unitary operators comprises spin-complemented pairs of single and double fermionic excitation operators. - the pool of unitary operators comprises individual Pauli chains, e.g. from the division of fermionic-ADAPT operators after a Jordan-Wine mapping. - It further comprises a step of computing the target ansatz wave function, said computing being performed by binary computing means or by quantum computing means. - the step of computing the target ansatz wave function is realized by binary computing means and preferably the target ansatz wave function has been built according to a selective configuration interaction method, more preferably by a CIPSI. - the target wave function is a tractable high accuracy approximation of the ground state of a target Hamiltonian. This can be used to provide a suitable initial state in quantum computing. - the target wave function is a full-CI wave-function, for example computed in a minimal basis set. - the target wave function is with a tractable high accuracy approximation of a full-CI wave-function. - the target wave function is an ADAPT-VQE ansatz, for example comprising more than five parameters, preferably more than 10, 15, 20 parameters. - the target wave function is a Selected- Configuration Interaction ansatz, preferably computed according to the so-called Configuration Interaction perturbatively selected iteratively (CIPSI). - It further comprises a step of measuring overlap gradients, said computing being performed by binary computing means or by quantum computing means. - at the step of measuring overlap gradients, when the norm of the lower overlap gradient is inferior to a threshold value, the steps of selecting and growing are not carried out and the step of optimizing the parameters is directly initiated as a convergence have been reached. - the overlap gradients being expressed in terms of commutators involving the molecular Hamiltonian acting on the current ansatz wave-function. - the step of selecting the unitary operator, e.g. parameterized unitary operator, comprises a selection of the unitary operator, e.g. parameterized unitary operator, among the pool of unitary operators, e.g. parameterized unitary operator, whose addition to the current ansatz will maximize the overlap between a new wave-function and the target wave-function. - it further comprises a step of optimizing all parameters in the new ansatz wave- function to generate an optimized ansatz with a wave-function whose overlap, preferably orbital overlap, with the target wave-function is maximized. - it further comprises a step of reiterating from the step of measuring using the optimized ansatz wave function as the current ansatz wave-function. - each operator added to the current ansatz corresponds to an additional layer of quantum gates in the quantum circuit and an additional parameter in the ansatz. - it further comprises introducing a machine-learning framework incorporating a trainable quantum circuit. - it utilizes classical data obtained through standard computational chemistry methods for training a machine learning model. The machine-learning framework can be used to further iteratively refine the current ansatz. - it further comprises a step of a second order perturbation theory correction. [0019] According to another aspect, the invention can also relate to a computer implemented method for the generation of an optimized quantum computing circuit from a new ansatz generated according to the invention, said method comprising the use of the new ansatz as an initial state in an ADAPT-VQE procedure. For example, the use of the new ansatz (Ψ(m)) can comprise initializing a reference state (|Ψref^) based on the new ansatz (Ψ(m)). [0020] According to another aspect, the invention can also relate to a quantum computing means for quantum simulations characterized in that it comprises an optimized quantum computing circuit obtainable, preferably obtained, by a method according to the present invention. [0021] According to other optional features of the quantum computing means for quantum simulations according to the invention, a quantum circuit corresponding to an ansatz of a molecule comprising at least three atoms, said ansatz comprising no more than 20 parameters per atom and has a chemical accuracy threshold of 10^-3 Hartree or less, at bond length of 3 Angstrom or more. [0022] According to another aspect, the invention can also relate a quantum circuit for quantum chemical simulation characterized in that it comprises an ansatz of a molecule comprising at least three atoms, said ansatz comprising no more than 20 parameters per atom and has a chemical accuracy threshold of 10^-3 Hartree or less, at bond length of 3 Angstrom or more. Brief description of the drawings [0023] The foregoing and other objects, features and advantages of the present invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which: FIG.1 is a schematic view of a computer implemented method according to an embodiment of the present invention. FIG.2 is a schematic view of a computer implemented method according to an embodiment of the present invention. FIG.3 are comparisons of the Full-CI Overlap Guided ADAPT-VQE and the ADAPT- VQE for the ground state of BeH₂ (FIG.3A) and linear H₆ chain (FIG.3B) with an interatomic distance of 3 Angstrom for both. The plots represent the energy convergence as a function of the number of parameters in the ansatz. The grey area indicates chemical accuracy at 10⁻³ Hartree. FIG.4 are comparisons of the Overlap-ADAPT-VQE and the ADAPT-VQE for the ground state of linear BeH₂ at equilibrium (FIG.4A) and stretched geometry (FIG.4B). The plot represents the energy convergence as a function of the number of parameters in the ansatz. The right-pointing triangles denotes the start of an ADAPT-VQE procedure. The left-pointing triangle denotes the end of an adapt procedure at which point the resulting wave-function can be taken as target for an Overlap-Guided adaptive procedure. The dotted line in Fig.4B corresponds to the previous FCI- Overlap-ADAPT-VQE. The grey area indicates chemical accuracy at 10⁻³ Hartree. FIG.5 is comparison of the Overlap-ADAPT-VQE and the ADAPT-VQE for the ground state of linear N₂ at stretched geometry. The plot represents the energy convergence as a function of the number of parameters in the ansatz. The right-pointing triangles denotes the start of an ADAPT-VQE procedure. The left-pointing triangle denotes the end of an adapt procedure at which point the resulting wave-function can be taken as target for an Overlap-Guided adaptive procedure. The dotted line correspond to the p_{revious FCI-Overlap-ADAPT-VQE. The grey area indicates chemical accuracy at 10} ⁻³ Hartree. FIG.6 is a comparison of the CIPSI-Overlap-ADAPT-VQE and the ADAPT-VQE for t^{he ground state of linear H} ₆ ^{chain with an interatomic distance of 3 Angstrom. The} plot represents the energy convergence as a function of the number of parameters in the ansatz. The CIPSI-Overlap-ADAPT ansatz is grown up to 20 parameters and then used as the initial state for an ADAPT-VQE process, denoted by the top-pointing triangle. The horizontal dotted line corresponds to the energy error of the initial C_{IPSI target wave-function. The grey area indicates chemical accuracy at 10} ⁻³ _Hartree. FIG.7 are comparisons of the CIPSI-Overlap-ADAPT-VQE and the ADAPT-VQE for t^{he ground state of linear BeH} ₂ ^{molecule with an interatomic distance of 3 Angstrom. The} plots represent the energy convergence as a function of the number of parameters in the ansatz for two CIPSI initial wavefunction. The CIPSI-Overlap ansatz is grown up to 10 parameters (FIG.7A) for the poor, or 25 parameters (FIG.7B) for the acceptably, accurate CIPSI initial wavefunction and then used as the initial state for an ADAPT- VQE process, denoted by the top-pointing triangle. The horizontal dotted line corresponds to the energy error of the initial CIPSI target wave- function. The grey area i_{ndicates chemical accuracy at 10} ⁻³ _Hartree. FIG.8 represent a schematic illustration of a computer system according to an embodiment of the invention. FIG.9 represent a quantum computing circuit according to an embodiment of the invention. FIG.10 illustrate a method according to an embodiment of the invention. [0024] Several aspects of the present invention are disclosed with reference to flow diagrams and/or block diagrams of methods, devices and computer program products according to embodiments of the invention. [0025] On the figures, the flow diagrams and/or block diagrams show the architecture, the functionality and possible implementation of devices or systems or methods and computer program products, according to several embodiments of the invention. [0026] For this purpose, each box in the flow diagrams or block diagrams may represent a system, a device, a module or code which comprises several executable instructions for implementing the specified logical function(s). [0027] In some implementations, the functions associated with the box may appear in a different order than indicated in the drawings. [0028] For example, two boxes successively shown, may be executed substantially simultaneously, or boxes may sometimes be executed in the reverse order, depending on the functionality involved. [0029] Each box of flow diagrams or block diagrams and combinations of boxes in flow diagrams or block diagrams may be implemented by special systems that perform the specified functions or actions or perform combinations of special equipment and computer instructions. Detailed description [0030] Hereinafter, we describe the vocabulary associated with the invention, before presenting the drawbacks of the prior art, and then finally showing in greater detail how the invention remedies them. [0031] Conventional computers operate on binary digits that store or represent information in the form of binary states to perform computational and information processing functions. In contrast, quantum computing devices operate on quantum bits (or qubits) that store or represent information as both binary states and superpositions of binary states. A distinction between a quantum and classical computer is that the quantum computer is probabilistic, thus measurements of algorithmic outputs provide a proper solution within a confidence interval. The computation is then repeated until a satisfactory probable certainty of solution can be achieved. A quantum computation uses a qubit as its essential unit instead of a classical computing bit. The qubit (e.g., quantum binary digit) is the quantum-mechanical analog of the classical bit. Whereas classical bits can employ on only one of two basis states (e.g., 0 or 1), qubits can employ superpositions of those basis states, allowing a number of qubits to theoretically hold exponentially more information than a same number of classical bits. General quantum programs require coordination of quantum and classical parts of a computation. One way to think about general quantum programs is to identify processes and abstractions involved in specifying a quantum algorithm, transforming the algorithm into executable form, running an experiment or simulation, and analyzing the results. [0032] A “quantum circuit” denotes a sequence of gates that can be implemented on a quantum computing mean to formally realize a unitary operator that acts on a given initial quantum state and produces a final quantum state. Circuits can be parametrized via gate parameters such as one or more angles of a single qubit rotation gate. A “gate” denotes an operation on a quantum system that transforms a quantum state. A quantum computing mean can be either on a hardware exploiting quantum physics phenomena for the generation of physical Qubit or on a classical hardware simulating Qubit. [0033] A “Variational Quantum Eigensolver” (VQE) denotes a near term quantum algorithm that can find a ground state of a Hamiltonian on a quantum computing device. A VQE can be based on a variational principle. A VQE can be successful when a cost function to be minimized reaches an optimal value. [0034] By “Hamiltonian” (H) or “molecular Hamiltonian” can mean, within the meaning of the invention, an operator that fully defines a quantum system. The lowest eigenstate of such operators can be called a ground state that can be the target of quantum chemistry calculations. A Hamiltonian, written in a computational basis state, can be different for each molecule. “Energy” denotes an expectation value of a Hamiltonian on a given normalized quantum state. Energy can be minimized when the state is the ground state. [0035] By “wavefunction” (^) can mean, within the meaning of the invention, a function which represents the probability density of finding a particle at a given location, preferably on Hilbert space. A target wave function can be an approximation of the ground state of an Hamiltonian. [0036] By "ansatz" or "ansatz wavefunction" can mean, within the meaning of the invention, a subroutine consisting of a sequence of gates applied to specific wires. An ansatz wavefunction can capture the most important contributions to the electronic correlation energy and, at the same time, is capable of being represented on rather shallow quantum circuits. The initial ansatz can also be called the current ansatz which is the ansatz which will be grown by appending the selected operators. As the process is preferably iterative, the process begin with an initial ansatz while after at least an iteration a current ansatz (the current ansatz can generally be the new ansatz of the previous iteration) is used. [0037] By “process”, “compute“, “determine”, “display”, “extract”, “compare” or more broadly “executable operation” can mean, within the meaning of the invention, an action performed by a computing device or a processor unless the context indicates otherwise. In this regard, the operations relate to actions and/or processes of a data processing system, for example a computing system or an electronic computing device, which manipulates and transforms the data represented as physical (electronic) quantities in the memories of the computing system or other devices for storing, transmitting or displaying information. In particular, calculation operations are carried out by the processor of the device, the produced data are entered in a corresponding field in a data memory and this field or these fields can be returned to a user for example through a Human Machine Interface formatting such data. These operations may be based on applications or software. [0038] The terms or expressions “application”, “software”, “program code”, and “executable code” mean any expression, code or notation, of a set of instructions intended to cause a data processing to perform a particular function directly or indirectly (for example after a conversion operation into another code). Exemplary program codes may include, but are not limited to, a subprogram, a function, an executable application, a source code, an object code, a library and/or any other sequence of instructions designed for being performed on a computing system. [0039] By “processor” is meant, within the meaning of the invention, at least one hardware circuit configured to perform operations according to instructions contained in a code. The hardware circuit may be an integrated circuit. Examples of a processor include, but are not limited to, a central processing unit, a graphics processor, an application- specific integrated circuit (“ASIC” according to Anglo-Saxon terminology), and a programmable logic circuit. A single processor or several other units may be used to implement the invention. [0040] By “coupled” is meant, within the meaning of the invention, connected, directly or indirectly, with one or more intermediate elements. Two elements may be coupled mechanically, electrically or linked by a communication channel. [0041] The expression “human-machine interface”, within the meaning of the invention, corresponds to any element allowing a human being to communicate with a computer, in particular and without that list being exhaustive, a keyboard and means allowing in response to the commands entered on the keyboard to perform displays and optionally to select with the mouse or a touchpad item displayed on the screen. Another embodiment is a touch screen for selecting directly on the screen the elements touched by the finger or an object and optionally with the possibility of displaying a virtual keyboard. [0042] When interested in the analysis of chemical systems at chemical accuracy, the ADAPT-VQE process as such, which is not the invention and will be described hereafter, is capable of approximating the ground state Full-CI energy to a very high accuracy. Unfortunately, attaining a suitably accurate approximation to the sought-after energy may require a large number of ADAPT iterations which results both in deep quantum circuits that cannot be implemented on the current generation of NISQ devices as well as an increasingly computationally expensive optimization procedure. This problem is particularly apparent in strongly correlated systems for which the ADAPT process frequently encounters energy plateaus prior to achieving the chemical accuracy threshold of 10⁻³ Hartree. [0043] Since quantum chemists are primarily interested in numerical results in the regime 10⁻³ to 10⁻⁴ Hartree, i.e., slightly below the chemical accuracy threshold, it is natural to ask if the ADAPT-VQE procedure could be modified so as to avoid these initial energy plateau slowdowns and achieve the required accuracy using an ansatz compact-enough to be implementable on current NISQ devices. [0044] As it will be described in the example, the invention relates to a new method which can overcome the challenges of energy plateaus faced by the classical methods. Hence, this method can be used to generate compact ansatz capable of chemical accuracy with shallow quantum circuit even for complex chemical system. Moreover, as it will be also described in example, this new method can be used to further compact ansatz generated through another methods like SCI or ADAPT-VQE. As the ansatz is grown using operators that maximize its overlap with a target wave function that preferably already captures some electronic correlation of the system, i.e. chemical system. Such a target wave- function is used as a guide to construct an ansatz in the right direction and to catch the bulk of electronic correlation. [0045] Hence, according to a first aspect, the invention relates to computer- implemented method. [0046] Preferably, said computer comprising quantum computational means. The computer can be a Hybrid Quantum / classical computing means. Also, the computer implementing the method of the invention can comprise hardware equipment that are physically distant but connected by a communication network. [0047] The quantum computational means can be quantum hardware or classical hardware configured to simulate quantum computing. [0048] The quantum hardware can for example be 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. [0049] The computer-implemented method can be used for compressing an existing ansatz such as a ADAPT-VQE ansatz by taking as guide the existing ansatz and achieving a near accuracy ansatz with fewer operators. Hence, the invention allows the creation of a new ansatz that is free of any unnecessary operators that have accumulated during the ADAPT-VQE processing of the guide and then proceed the iterations of VQE. [0050] To anticipate applications on noisy quantum machines of such procedures and ansatz, the inventors developed a method to minimize both circuit depth and the number of evaluations simultaneously. The Overlap-Guided (OG) Adaptive procedure allows to grow wave-functions by maximizing their overlap with any intermediate target wave- function that already captures some electronic correlation. By avoiding building the ansatz in the energy landscape strewn with local minima, the OG-Algorithm produces ultra- compact ansatz suitable for high-accuracy initializations of a new ADAPT procedure. Spectacular advantages over ADAPT- VQE are observed for strongly correlated systems including massive savings in circuit depth. Since this compression strategy can also be initialized with accurate Selected- Configuration Interaction (SCI) classical target wave- functions, it paves the way to chemically accurate simulations of larger systems, and strengthens the promise of decisively surpassing classical quantum chemistry through the power of quantum computing. [0051] Rather than contructing an ansatz wave-function through an energy minimisation procedure and potentially encountering local minima, we grow the ansatz wave-function through a process that maximizes its overlap with a – potentially intermediate – target wave function that already captures some electronic correlation of the system. We thus use such a target wave-function as a guide to help us build our ansatz in the right direction so as to catch the bulk of electronic correlation. [0052] As illustrated in figure 1, in an embodiment, the computer-implemented method comprises the following steps: - Set the initialization to a reference state, for example the Hartree-Fock reference state; - Identify the exponential one-body or two-body Qubit excitation/de-excitation operator whose action on the current ansatz will produce a new wave-function with the largest overlap with respect to the target wave-function; and - Append the selected operator to the left of the current ansatz and optimize all parameters in the new ansatz wave-function so as to maximize the overlap of the target wave-function with the updated ansatz wave-function. [0053] Moreover, the computer-implemented method can comprise a step of comparing the total number of operators in the updated ansatz with p and exit the iterative process when the total number of operators in the updated ansatz is greater than p. [0054] In another embodiment, a computer implemented method according to the invention comprise: - a step of selecting, preferably by the quantum computational means, among a pool of unitary operators, the unitary operator Â_m(θ_m) whose action on a current ansatz Ψ(m−1) produce a new wave function with the largest overlap with respect to a target wave function Ψtarget according to non-energy-based criteria, and - a step of growing the ansatz by appending the selected unitary operator to the left of the current ansatz Ψ(m−1) to generate a new ansatz Ψ(m). [0055] As illustrated in figure 2, in another embodiment, the computer-implemented method comprises the following steps: selecting 150 the unitary operator (Âm(θm)) whose action on an initial ansatz Ψ(0) or current ansatz produce a new wave function with the largest overlap with respect to a target wave function Ψtarget according to non-energy based criteria; and growing 160 the ansatz. [0056] Further, this method can comprise a step of parametrization 170 of the new ansatz Ψ(m), said parametrized new ansatz Ψ(m) defining the optimized quantum computing circuit. The parametrization 170 can comprise an optimization of the parameters and an update of the new ansatz. [0057] As illustrated in figure 2, a computer-implemented method according to the invention can comprise the following steps: - Initialize 110 a Hartree-Fock reference state |Ψ_HF^, - Define 120 an operators Pool (e.g. Â_i(θ_i), i ∈ [1,N]), - Compute 130 a target ansatz wave function |Ψtarg ^, - Set 131 a target wavefunction |Ψtarg ^, - Measure 140 overlap gradients, and/or - Implement 190 the optimized quantum computing circuit. [0058] As shown in figure 1, a method according to the invention can comprise a step of initializing 110 a reference state |Ψ_REF^, preferably a Hartree-Fock reference state |Ψ_HF^. This step can be designed to initialize a quantum reference state of the quantum computing means so as to allow them to behave like the initial ansatz (Ψ(0)). [0059] In particular, this step can also comprise a mapping, preferably by a classical computing hardware, of a molecular Hamiltonian into a qubit representation. This is designed to create a reference state on which will be built the new ansatz. [0060] As shown in figure 1, a method according to the invention can comprise a step of defining 120 a pool of operators (e.g. Â_i(θ_i), i ∈ [1,N]), also called pool of unitary operators. These unitary operators can be parameterized unitary operators. This step can preferably be done on classical computer. [0061] An advantage of the present invention is that with the proposed solution convergence in overlaps can be achieved more quickly by incorporating a wider range of operators, such as generalized excitations or symmetry breaking operators, into the pool of operators used. [0062] The step of defining 120 the pool of unitary operators can comprise the use of a qubit excitation operators. It can also comprise dividing fermionic-ADAPT operators after a Jordan-Wigner mapping and selecting the individual Pauli strings as operators of the pool. [0063] Generally, the pool of unitary operators can include single and double fermionic excitation operators, spin-complemented pairs of single and double fermionic excitation operators, and/or individual Pauli chains (for example from the division of fermionic- ADAPT operators after a Jordan-Wine mapping). [0064] For example, the pool of unitary operators can be defined according to the instructions already described in the following methods: Fermionic-ADAPT-VQE, Qubit- ADAPT-VQE, or Qubit-Excitation-Based-ADAPT-VQE. [0065] As shown in figure 2, a method according to the invention can comprise a step of computing 130 a target ansatz wave function |Ψtarg ^. [0066] This step allows in particular to combine classical selected-CI approaches and quantum computing. It can be used to take a highly relevant CIPSI wave-function as target for the overlapping according to the invention. [0067] An advantage of the present invention is that the proposed solution can compute by quantum computing means or classical computing means a target ansatz wave function that will be used to grown an ansatz with an reduced number of operators and parameters. [0068] This step is particularly designed to be performed by binary computing means or by quantum computing means. Preferably, the step of computing 130 the target ansatz wave function |Ψref^ is realized by binary computing means (CPU, GPU... classical computer). [0069] The target wave function is a full-CI wave-function, for example computed in a minimal basis set. [0070] Preferably, the target wave function is with a tractable high accuracy approximation of a full-CI wave-function. However, the present invention can bring significant gains in terms of quantum circuit complexity, even with a potentially intermediate target wave function that already captures some electronic correlation of the system, e.g. chemical system to be studied. [0071] More preferably, in an embodiment, the target ansatz wave function is built according to a selective configuration interaction method (SCI), more preferably by a Configuration Interaction Perturbatively Selected Iteratively (CIPSI). [0072] In another embodiment, the target ansatz wave function has been computed on quantum computing means. More preferably, the target ansatz wave function is an ADAPT-VQE ansatz computed iterative steps, for example comprising more than five parameters, preferably more than 10, 15, 20 parameters. [0073] The method can also comprise a step of setting 131 the target wavefunction |Ψtarg^. [0074] As shown in figure 2, a method according to the invention can comprise a step of measuring 140 overlap gradients. [0075] An advantage of the present invention is that the step of measuring 140 overlap gradients can be performed on classical computing means or quantum computing means. Hence, this step can be implemented with computing being performed by binary computing means or by quantum computing means. [0076] In particular, depending on whether the target wavefunction is in a quantum or a classical representation, the screening (such as a gradient screening) and the overlap measurements can be performed using either a quantum or a classical device. In particular, if the targeted wave-function is classically computed, then no additional quantum resources are required or measurements are required to compute the overlaps. [0077] Preferably, the overlap gradients being expressed in terms of commutators involving the molecular Hamiltonian acting on the current ansatz wave-function. [0078] The process can comprise a step of verifying 145 the convergence. For example, at the step of measuring 140 overlap gradients, when the norm of the lower overlap gradient is inferior to a threshold value, the steps of selecting 150 and growing 160 are not carried out and the step of optimizing 170 the parameters is directly initiated as a convergence have been reached. [0079] As shown in figure 2, a method according to the invention can comprise a step of selecting 150 a unitary operator. [0080] This step is in particular designed to select the unitary operator (Âm(θm)) whose action on a current ansatz (Ψ(m−1) produce a new wave function with the largest overlap with respect to a target wave function. Moreover, this selection is done according to non- energy-based criteria. Preferably, the selection is done according to an orbital overlapping. [0081] This step can be implemented with binary computing means or with quantum computing means. The selection is preferably performed by quantum computational means. [0082] The method according to the invention advantageously iteratively generates a compact approximation of a target wave function through a procedure that maximises, at each iteration, the overlap of the current iterate with the target. This is achieved by adding on-the-fly, the most relevant unitary operator from a finite-size pool of admissible operators, with a selection criterion based on the gradient of the overlap of the ansatz with the target. Whether the ansatz evolves within the symmetry-relevant subspace of the target depends on the choice of the operator pool. For example, pools made of fermionic operators adhere to all the desired symmetries, which facilitates the convergence to the target state but comes at the expense of requiring more quantum gates per operator. Conversely, Qubit-Excitation-Based, Qubit, or Minimal ZY pools may respect only a subset of these symmetries or none at all, but they are more resource-efficient. [0083] The unitary operator is selected among a pool of unitary operators (U(θ)). The pool of unitary operators can comprise preferably at least 50, preferably 75, more preferably 100 unitary operators. [0084] In particular, this step of selecting 150 can comprise a selection of the unitary operator with the largest overlap gradient, preferably the largest orbital overlap gradient with the target wave function. [0085] Preferably, the step of selecting 150 the parameterized unitary operator comprises a selection of the parameterized unitary operator among the pool of parameterized unitary operators whose addition to the current ansatz will maximize the overlap between a new wave-function and the target wave-function. ^{[0086] For example, at the mth iteration the method have current ansatz wave-function} a_{s well as a target wave-function |Ψref^. To identify the parameterized} exponential qubit excitation evolution operator Â_m (θ_m) whose action on the current ansatz will produce a new wave-function with the largest overlap with respect to the target wave-function, the overlap gradient expression give by the following equation can be used: [0087] Any parameterized qubit excitation evolution operator Â_m(θ_m) can be of the form [0088] where Bm is a sum of so-called Pauli strings involving X and Y single qubit Pauli gates. Using the chain rule, we therefore deduce that: [0089] We have thus reduced the problem of computing the sought-after overlap gradients _{at the Overlap-ADAPT iteration to one of measuring the overlap between the target} _{wave-function |Ψref^ and an intermediate wave-function |iBmΨ} ^m−1 _{^ where Bm is a sum} of so-called Pauli strings involving X and Y single qubit Pauli gates. Let us emphasize here that our overlap operator identification process is based on finding qubit excitation evolution operator that maximizes the magnitude of the above computed gradient (and not the value of the gradient itself). [0090] For classically represented target wave-functions (such as CIPSI wave-functions), such overlaps can be readily computed on classical architecture by making use of the usual determinant-based expansion of wave-functions. [0091] In order to evaluate this equation on quantum architecture, we can proceed as follows. Using a direct calculation based on the Taylor series together with the commutation relations of Pauli matrices, it can first be deduced that : [0092] Each of the terms on the right-hand side of the above expression is now measurable on a quantum computer using the usual methods. Consequently, the sought-after overlap gradient can be computed at the cost of four measurements of the overlap ^Ψ_ref| AÂ _m(θ i.e., one for each as well as knowledge of the overlap from the previous iteration, i.e., | ^Ψ_ref|Ψ^m−1^|. [0093] Since only four overlap evaluations are required to evaluate a single overlap gradient, the process according to the invention is very sober in terms of quantum resources. Indeed, computing a single expectation value of the Hamiltonian (or one energy gradient) can necessitate measuring nearly each Pauli string in the Jordan-Wigner encoding of the Hamiltonian, which represents O(N⁴) function evaluations. [0094] As shown in figure 2, a method according to the invention can comprise a step of growing 160 the initial ansatz or current ansatz. [0095] In particular, growing 160 the initial ansatz can comprise appending 160 the selected unitary operator to the left of the initial ansatz (Ψ(0)) or current ansatz (Ψ(m-1)) to generate a new ansatz (Ψ(m)). [0096] This step can be implemented with binary computing means or with quantum computing means. [0097] As shown in figure 2, a method according to the invention can comprise a step of parametrization 170 the new ansatz. This step can also be considered as comprising a step of optimizing the parameters of the new ansatz (Ψ(m)). [0098] This step is in particular designed to generate parametrized new ansatz defining an optimized quantum computing circuit. It generally comprises an optimization of the parameters in the new ansatz wave function so as to minimize the expectation value of the molecular Hamiltonian. [0099] This step can be implemented with binary computing means or with quantum computing means. In particular, the output of the previous step is fed into a classical optimization algorithm which calculates the optimal set of parameters that minimizes the expectation value of the Hamiltonian H. [0100] In this approach, a parameterized wave-function is generated and is preferably variationally tuned to minimize the expectation value of the molecular electronic Hamiltonian. A variety of different parameterized wave-functions have been proposed, including the Trotterised Unitary Coupled Cluster (tUCC) ansatz which consists of a sequence of exponential, unitary operators acting on a judiciously chosen reference state. [0101] In order to limit the number of integrated operators to those with the most impact on the overlap, the method can comprise a step 175 of comparing the gradient norm to a threshold value and exit the iterative process if the gradient norm is smaller than said threshold value. [0102] A computer implemented method according to the invention wherein it further comprises a step of optimizing 170 all parameters in the new ansatz wave-function to generate an optimized ansatz with a wave-function whose overlap, preferably orbital overlap, with the target wave-function is maximized. [0103] Also, the method can comprise a comparison of the number of operators in the new ansatz and a step of iterating 180 is the number of operators is below a predetermined threshold. [0104] As shown in figure 2, a method according to the invention can comprise a step of reiterating 180 from the step of measuring 140 using the optimized ansatz wave function as the initial ansatz wave-function. [0105] Indeed, the method according to the invention preferably comprises an iterative process in order to the unitary operators maximizing the overlap with the target overlap. [0106] This step is particularly designed to be performed by binary computing means or by quantum computing means. [0107] In order to limit the number of integrated operators to those with the most impact on the overlap, the method can comprise a step 175 of comparing the total number of operators in the new ansatz to a threshold value and exit the iterative process if the total number of operators in the new ansatz is greater than said threshold value. [0108] The method according to the invention not only delivers a precise initial state but presents it in the structure of a parameterized quantum circuit. This circuit can be fine- tuned on the quantum computer, offering adapt-ability based on the desired post- treatment. This feature proves especially advantageous in the realm of VQE, where flexibility in the ansatz is sought. [0109] By generating a compact quantum circuit that encodes the best classically-derived wave function, the invention secure an initial quantum state with strong overlap with the sought-after ground state of the system. This initial state preparation will greatly facilitate a following quantum post-treatment, such as QPE, which offers asymptotic advantage in determining the ground state energy compared to classical approaches. [0110] The key takeaway is that, even for chemical systems of prime hardness, quantum state preparation of accurate initial state has proven seamless with the invention coupled to a classical ground state approximation procedure. The resulting quantum circuits exhibits an insignificant circuit depth in the context of early-fault-tolerant era. The invention may therefore offer a practical approach for any such algorithm involving classical data loading by allowing the use of an operator pool tailored to the target state’s characteristics. [0111] As shown in figure 2, a method according to the invention can comprise a step of implementing 190 the optimized quantum computing circuit. This step is particularly designed to be performed by quantum computing means. [0112] In particular, the method can comprise a step of parametrizing the quantum state of the quantum computing means so as to allow them to behave like the parametrized new ansatz. [0113] The figure 10 illustrates a preferred embodiment of the present invention. [0114] In another aspect, the invention relates to a computer implemented method to build system-adapted ansatz, said method comprising the use of the new ansatz (Ψ(m)) produced according to the invention, as the reference state in a method comprising a measure of the energy of the Hamiltonian with respect to a proposed ansatz wave- function. In particular, the method can comprise a step of parametrizing the quantum state of the quantum computing means so as to allow them to behave like the parametrized new ansatz. [0115] In particular, the invention relates to a computer implemented method to build system-adapted ansatz, said method comprising the use of the new ansatz (Ψ(m)) produced according to the invention, as an initial state in an ADAPT-VQE procedure. [0116] In particular, this computer implemented method to build system-adapted ansatz can comprise initializing a reference state |Ψref^, for example in ADAPT-VQE procedure, based on the new ansatz (Ψ(m)). [0117] The computing system is configured to process the one or more computing tasks including at least one combinatorial optimization task using a Variational Quantum Eigensolver (VQE) algorithm implemented by using one or more Ansätze circuit and a cost function arrangement to generate the one or more quantum circuits. The computing system is configured to apply iteratively a filtering operator to the cost function arrangement to generate a corresponding filtered cost function arrangement of a Filtering Variation Quantum Eigensolver (F-VQE) algorithm that excludes one or more energy states of the cost function arrangement that exceed an energy threshold and retains one or more energy states of the cost function arrangement that are below the energy threshold, wherein the filtered cost function arrangement is used in the one or more quantum circuits to generate the output results. [0118] the computing system is configured to process the one or more computing tasks including at least one combinatorial optimization task using a Variational Quantum Elgensolver (VQE) algorithm implemented by using one or more Ansatze circuit and a cost function arrangement to generate the one or more quantum circuit [0119] In another aspect, the invention relates to a quantum circuit 10 for quantum chemical simulation. [0120] In particular, the invention relates to a quantum circuit 10 for quantum chemical simulation obtainable, preferably obtained, by a method according to the invention. [0121] Preferably, the invention relates to a quantum circuit 10 for quantum chemical simulation according to the invention which is characterized in that its structure is defined by the new ansatz obtained by the method according to the invention. [0122] Preferably, a quantum circuit for quantum chemical simulation according to the invention is characterized in that its structure is defined by an ansatz of at least three interacting atoms (e.g. molecule comprising at least three atoms), said ansatz having a chemical accuracy threshold of 10^-3 Hartree or less, at bond length of 3 Angstrom or more. [0123] Preferably, the quantum circuit 10 has a base structure defined by a layered gate ansatz, or an alternating operator ansatz. [0124] Preferably, the ansatz defining the quantum circuit comprises at most 20 parameters per atom (i.e. interacting atoms). More preferably, the ansatz defining the quantum circuit comprises at most 15 parameters per atom (i.e. interacting atoms). Even more preferably, the ansatz defining the quantum circuit comprises at most 12 parameters per atom (i.e. interacting atoms). [0125] Preferably, the ansatz defining the quantum circuit comprises at most 20 operators per atom (i.e. interacting atoms). More preferably, the ansatz defining the quantum circuit comprises at most 15 operators per atom (i.e. interacting atoms). Even more preferably, the ansatz defining the quantum circuit comprises at most 12 operators per atom (i.e. interacting atoms). [0126] In particular, each operator added to the initial ansatz can correspond to an additional layer of quantum gates in the quantum circuit and/or an additional parameter in the ansatz. [0127] In another aspect, the invention relates to quantum computing means 10 for quantum chemical simulations. In particular, the quantum computing means comprise a quantum circuit 11 for quantum chemical simulation obtainable, preferably obtained, by a method according to the invention. [0128] Preferably, the quantum computing means for quantum chemical simulations according to the invention comprises a quantum circuit 11 corresponding to an ansatz of a molecule comprising at least three atoms, said ansatz comprising at most 20 parameters per atom and has a chemical accuracy threshold of 10^-3 Hartree or less, at bond length of 3 Angstrom or more. Preferably, the ansatz comprises at most 15 parameters per atom, more preferably at most 12 parameters per atom, even more preferably at most 9 parameters per atom. For example, the ansatz can comprise from 15 to 20 parameters per atom of the molecule. [0129] The invention quantum computing means 11 can be integrated in a computing system 1 as described hereafter. Also, the computer implemented methods according to the invention can be implemented on a computing system. [0130] The computing system can include one or more classical binary computers coupled to one or more quantum computers. The one or more classical binary computers can be configured to receive one or more computing tasks via an input port and to output corresponding computational results via an output port. [0131] The one or more quantum computers can be configured to execute one or more quantum circuits that are generated from the one or more tasks to generate corresponding output results for the one or more classical binary computers to use to generate the corresponding computational results. [0132] The figure 7 is a schematic block diagram illustrating various hardware components that may be utilized a computing system according to the invention. [0133] In particular, as illustrated in figure 7, the computing system 1 can comprises: one or more quantum computing mean, one or more memory components 20, one or more communication interfaces 30; one or more processors 40; and/or one or more user interfaces 50. [0134] The memory component 20 may comprise any computer readable medium known in the art including, for example, a volatile memory, such as a static random access memory (SRAM) and a dynamic random-access memory (DRAM), and / or a non-volatile memory, such as read-only memory, flash memories, hard disks, optical disks and magnetic tapes. The memory component 20 may include a plurality of instructions or modules or applications for performing various functions. Thus, the memory component 10 can implement routines, programs, or matrix-type data structures. Preferably, the memory component 20 may comprise a medium readable by a computing system in the form of a volatile memory, such as a random-access memory (RAM) and / or a cache memory. The memory component 20, like the other modules, can for example be connected with the other components of the computing system 1 via a communication bus and one or more data carrier interfaces. [0135] Furthermore, the computing system 1 can also comprise a communication interface 30. The communication interface 30 is preferably configured to transmit data on at least one communication network and may implement a wired or wireless communication. The computing system 1 can communicate with other devices or computing systems and in particular with clients thanks to the communication interface 30. A communication interface 30 according to the invention is in particular configured to exchange data with third-party devices or systems. [0136] A computing system 1 may comprise one or more processors 40. A processor 40 may be operably coupled to the memory component 20 to execute instructions, encoded in programs, for carrying out the presently disclosed techniques, more particularly to perform the method according to the invention. [0137] The encoded instructions may be stored in any suitable article of manufacture (such as the memory component 20) that includes at least one tangible non-transitory, computer- readable medium that at least collectively stores these instructions or routines. In this manner, the memory component 20 may contain a set of instructions that, when executed by the processor 40, performs the method of the invention. [0138] The memory component 20 may include any number of databases or similar storage media that can be queried from the processor 40 as needed to perform the method of the invention. [0139] These different modules or components are separated in Figure 7, but the invention may provide various types of arrangement, for example a single module cumulating all the functions described here. Similarly, these modules or components may be divided into several electronic boards or gathered on a single electronic board. A computing system 1 according to the invention can be incorporated into a computing system and able to communicate with one or several external devices such as a keyboard, a pointer device, a display, or any device allowing a user to interact with the system 1. [0140] The computing system 1 may also be configured to communicate with or via a human-machine-interface. Thus, in one embodiment of the present invention, the computing system 1 can be coupled to a human interface machine (HMI). The HMI may be used to allow the transmission of parameters to the devices or conversely make available to the user the values of the data measured or calculated by the device. [0141] In general, the HMI is communicatively coupled to a processor and includes a user output interface and a user input interface. The user output interface may include an audio and display output interface and various indicators such as visual indicators, audible indicators and haptic indicators. The user input interface may include a keyboard, a mouse, or another navigation module such as a touch screen, a touchpad, a stylus input interface, and a microphone for inputting audible signals such as a user speech, data and commands that can be recognized by the processor. [0142] Thus, in another aspect, the invention relates to one or more computer- readable media storing computer-readable instructions that when executed by one or more quantum computing mean 10 and/or one or more processors 40 cause the one or more processors to perform a method according to the invention. Preferably, the computer-readable media is a tangible non-transitory computer-readable media. [0143] For the purposes of this disclosure, computer-readable media may include any instrumentality or aggregation of instrumentalities that may retain data and/or instructions for a period of time. Computer-readable media may include, for example, without limitation, storage media such as a direct access storage device (e.g. a hard disk drive or floppy disk drive), a sequential access storage device (e.g. a tape disk drive), compact disk, CD-ROM, DVD, RAM, ROM, electrically erasable programmable read-only memory (EEPROM), and/or flash memory; as well as communications media such as wires, optical fibers, microwaves, radio waves, and other electromagnetic and/or optical carriers; and/or any combination of the foregoing. [0144] In particular, any combination of one or more computer-readable media may be used. In the context of this document, a computer-readable medium may be any tangible medium that may contain, or store, a program for use by or in connection with an instruction execution system, apparatus, or device. A computer-readable medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared or semiconductor system, apparatus or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium would include: a hard disk, a random-access memory (RAM). [0145] Computer program code for performing operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object-oriented programming language such as Java, C ++, or similar, the programming language "C" or similar programming languages, a scripting language such as Perl, or similar languages, and / or functional languages such as Meta Language. Program code can run entirely on a user's computer, partly on a user's computer, and partly on a remote computer or entirely on the computer or remote server. In the latter scenario, the remote computer can be connected to a user's computer by any type of network, including a local area network (LAN) or a wide area network (WAN). [0146] These computer program instructions may be stored on a computer readable medium that can direct a computing device (i.e. computer, server ...), so that the instructions stored in the computer-readable medium produce a computing device configured to implement the invention. [0147] For example, a computing device may be a personal computer, a network storage device, or any other suitable device and may vary in size, shape, performance, functionality, and price. The computing device may include random access memory (RAM), one or more processing resources such as a central processing unit (CPU) or hardware or software control logic, ROM, and/or other types of nonvolatile memory. Additional components of the computing device may include one or more disk drives, one or more network ports for communication with external devices as well as various input and output (I/O) devices, such as a keyboard, a mouse, and a video display. The computing device may also include one or more buses operable to transmit communications between the various hardware components. EXAMPLE [0148] The invention is further described in detail by reference to the following experimental examples. These examples are provided for purposes of illustration only and are not intended to be limiting unless otherwise specified. Thus, the invention should in no way be construed as being limited to the following examples, but rather, should be construed to encompass any and all variations which become evident as a result of the teaching provided herein. [0149] Without further description, it is believed that one of ordinary skill in the art can, using the preceding description and the following illustrative examples, make and utilize the quantum circuit and ansatz of the present invention and practice the methods of the invention. The following working examples therefore, specifically point out the preferred embodiments of the present invention, and are not to be construed as limiting in any way the remainder of the disclosure. [0150] High-Performance State-Vector Emulator [0151] A quantum computing state-vector emulator package dedicated to quantum chemistry can be used. Classical hardware, massively parallel thanks to an efficient multi- GPU (GPU=Graphics Processing Unit) implementation, can be used to implement the invention. High performance is ensured by an ensemble of fast custom CUDA sparse linear algebra libraries, which act on the native quantum chemistry algorithms to accelerate exact/noiseless simulations. For example, using a single DGX-A100 node (8 X A100 GPUs, 40Gb of memory/GPU), we have been able to carry out a 28 qubits Overlap- ADAPT-VQE simulation producing over 600 iterations within 8 days. Overlap-Guided Adaptative Algorithm [0152] As described, the inventors developed a new computer implemented method for generation of an optimized circuit for quantum computing, in particular for chemical simulation with quantum computing. ^{[0153] A set W} _{p of all wave-functions, for any integer p, that can be represented by the} product of exactly p exponential one-body and two-body Qubit excitation/de-excitation operators acting on the Hartree-Fock reference state can be introduced as: Where W_p is the set of all wave-functions θ_k is the parameters of the operators Q_Pk and Q^† P_k are Qubit excitation/de-excitation operators |Ψ_HF^ is the Hartree-Fock wave function [0154] For any natural number p, the best approximation of the full-CI wave-function of a chemical system in the set Wp can be defined as: where ||·|| denotes a suitable norm on the space of all wave-functions. |Ψ^ is the trial ansatz wav wave function |Ψ_ref^ is the reference wave function is the best approximation of the full-CI wave-function [0155] At this step the usual L² and H¹ norms can be used with the L² norm being particularly amenable to practical computations. [0156] In other words, |Ψ_p∗^ is the best approximation of the full-CI wave-function using a product of exactly p exponential one-body and two-body Qubit excitation/de-excitation operators acting on the Hartree-Fock reference state. [0157] An adaptive, iterative procedure that generates an approximate solution to the optimization problem can be defined as follows: - Set the initialisation to the Hartree-Fock reference state, set the target wave function, and set a pool of operators; preferably also states a maximum number p of operators to be included in the ansatz: - Identify the exponential one-body or two-body Qubit excitation/de-excitation operator Â_m(θ_m), whose action on the current ansatz |Ψ_m−1^ will produce a new wave-function with the largest overlap with respect to the target wave-function. This identification can be done by computing the following gradient involving the current ansatz wave-function preferably at θ = 0: - Append the selected operator Â_m(_θm) to the left of the current ansatz |Ψ_m−1^; e.g. defines: - Optimize all parameters θ_m, θ_m−1,… in the new ansatz wave-function so as to maximise the overlap of the target wave-function with the updated ansatz wave- function; e.g. solve And - Define the new ansatz wave-function |Ψ_m^ using the newly optimized parameters, e.g. define These optimized values are not necessarily the same as those used to define |Ψ_m−1^ [0158] If the total number of operators in the updated ansatz is greater than p, exit the iterative process. Otherwise go to the step of identification with the updated ansatz wave- function. [0159] This adaptive procedure is referred in the present invention as the Overlap-Guided (OG) adaptive procedure. Using Full-CI wave-function as the target wave-function [0160] The performance of the OG adaptive procedure has been compared with that of QEB-ADAPT VQE. To do so, we compute the energy of the OG-approximation of the Full- CI wave-function (as the target wave-function) and plot this energy in comparison to the energy obtained using QEB-ADAPT-VQE (Figures 3A & 3B). [0161] The figure 3A illustrate the result for a stretched BeH₂ molecule. The most striking feature of this energy plot is that the orbital overlap optimization procedure of the present invention is able to avoid the initial energy plateaus afflicting the ADAPT procedure. Indeed, whereas the QEB-ADAPT VQE procedure presents between the twentieth and the fiftieth parameter a succession of plateaus in staircase, the method according to the invention makes it possible to reach values of chemical accuracy without presence of plateau. This suggests the potential for creating a more condensed ansatz than ADAPT- VQE and sidesteps the issue of energy plateaus. [0162] The figure 3B illustrate the results for a stretched linear H₆ chain in a minimal basis set at 3 Angstrom. According to this energy plot, the procedure of the invention is able to avoid the energy plateaus afflicting the ADAPT procedure and preventing it to obtain a chemical accuracy with less than 50 parameters. Indeed, whereas the QEB- ADAPT VQE procedure presents a plateau from the twentieth parameter the method according to the invention makes it possible to improve by an order of magnitude the accuracy within 50 parameters compared to the QEB-ADAPT VQE procedure. This suggests the potential for creating a more condensed ansatz than ADAPT-VQE for complex systems. Using ADAPT-VQE produced wave-function as the target wave-function, Application of OG for compactification of ADAPT-VQE Ansatz [0163] From this first procedure, a practical VQE based on orbital overlap optimization can be developed by replacing the targeted full-CI wave-function, with a tractable high accuracy approximation thereof. [0164] For this section, we take as guide an ADAPT-VQE ansatz after a certain number of iterations. OG-ADAPT-VQE is then an attempt to compress this ADAPT-VQE ansatz by achieving a near accuracy ansatz with fewer operators. The objective is to create a new ansatz that is free of any unnecessary operators that have accumulated during the ADAPT-VQE processing of the guide and then proceed the iterations of VQE. [0165] As a test of its effectiveness, we apply the overlap-guided adaptive algorithm to a target wave-function provided by an existing QEB-ADAPT-VQE procedure and then use the result as a high-accuracy initialisation for a new QEB-ADAPT-VQE procedure. Essentially, this first set of numerical experiments is meant to model the situation where we have a strong constraint on the circuit depth (represented by the number of optimisation parameter in the ansatz wave-function), and we wanted to illustrate that it is possible to use the OG procedure according to the invention to compactify the ADAPT- VQE ansatz thereby obtaining a higher accuracy wave-function that respects the constraint on the circuit depth. [0166] The following classical numerical simulations have been carried out using Openfermion- PySCF module for integral computations and OpenFermion for second quantization and Jordan-Wigner mapping. The calculations are performed within the minimal STO-3G basis set without considering frozen orbitals unless otherwise specified. [0167] All optimization routines use the BFGS algorithm implemented on the SCIPY Python module. A pool of non spin-complemented restricted single- and double-qubit excitations evolutions has been used. Only excitations from occupied orbitals have been considered to empty ones in the Hartree-Fock determinant. Using fewer operators in the pool will make the gradient screening process faster and easier to handle, but it can result in a less effective ansatz construction. However, to ensure fair comparisons, this same pool will be used for both the Overlap-Guided Ansatz and ADAPT-VQE. [0168] The benchmark molecule used in this section is the Beryllium Hydride (BeH₂) Molecule considered in the original ADAPT-VQE articles. The BeH₂ molecule has been considered both at its equilibrium geometry (bond length of 1.3264 Angstrom) and at a stretched geometry (bond length of 3.0 Angstrom), which is meant to model a more strongly correlated system. [0169] To address both the circuit depth and the number of evaluations constraints, the energy convergence as a function of the number of operators present in the ansatz has been evaluate. [0170] As shown in Figure 4A, the present invention achieves a higher performance than a classical Qubit-Adapt-VQE procedure even for low-complexity system such as the BeH₂ molecule with bond lengths of 1.3264 Angstrom. [0171] However, the advantage of the present invention is particularly notable for more complex systems such as the BeH₂ molecule with bond lengths of 3 Angstrom as illustrated in the figure 4B. Indeed, using an ADAPT-VQE ansatz as a target wave- function for the OG procedure of the invention, a chemical accuracy can be obtained with less than 40 parameters. Moreover, this results illustrated that the results obtained when using an ADAPT-VQE ansatz as a target wave-function are better than the ones using the FCI ansatz as a target wave-function. [0172] A further test of the Overlap adaptive algorithm applied to a target QEB-ADAPT- VQE wave-function is carried out for the diatomic Nitrogen (N₂) molecule at equilibrium and stretched geometries (Figure 5). Although the minimal basis set for N₂ is quite large, a tractable computation can be carried out using an active space approach where the eight core electrons of the N₂ molecule are frozen and the ground state energy of the system is computed using the resulting frozen core effective Hamiltonian an approach commonly referred as CAS. In this case, the Overlap-ADAPT procedure does not further compactify the QEB-ADAPT-VQE wave-function at equilibrium (results not shown). Nevertheless, we once again observe a huge gain in accuracy for the stretched geometry where the Overlap-QEB-ADAPT-VQE energy is an order of magnitude more accurate than the classical QEB-ADAPT-VQE energy. As a rule of thumb, for all these simulations, the Overlap-ADAPT algorithm is used to construct an approximate wave-function using a number of operators equal to about 40%-50% of the maximal operator count. If the maximal operator count is more flexible, then as a general rule we observe that the ADAPT-VQE ansatz taken immediately after the ADAPT process has exited an energy plateau, serves as an effective choice of target wave-function for an overlap-guided adaptive procedure, i.e., the Overlap-ADAPT-VQE can produce a more compact wave- function with comparable energy to that of the target ADAPT wavefunction. [0173] On the other hand, taking ADAPT-VQE ansatz wave-function from the middle of an energy plateau seems as the overlap-guided target seems to be a less effective strategy. Hence preferably, a method according to the invention use a target wave function from an ADAPT-VQE ansatz taken immediately after the ADAPT process has exited an energy plateau. Using SCI produced wave-function as the target wave-function [0174] The Linear H₆ Molecule system has already been extensively studied (Yordanov, Y. S.; Armaos, V.; Barnes, C. H.; Arvidsson-Shukur, D. R. Qubit-excitation-based adaptive variational quantum eigensolver. Communications Physics 2021, 4, 1–11) and it turned out that achieving chemical accuracy with ADAPT-VQE required more than 150 operators from a generalized pool of both fermionic- and qubit-excitations. It goes without saying that resources of this kind will never be accessible on NISQ devices, so it is necessary to improve the method for simulating this type of system. [0175] The key idea of SCI (Selected-Configured Interaction) is used to build a compact representation of the reference wavefunction by selecting on-the-fly the most relevant Slater determinants thanks to an importance criterion based on perturbation theory. Thanks to this smart selection of the Slater determinants, the variational energy of the reference wave function converges rapidly towards the Full-CI energy. [0176] Although the recent revival of SCI approaches has allowed to significantly pushed further the limit of the systems for which near FCI quality energies can be obtained (typically a few tens of correlated electrons in typically two hundreds of orbitals) the scaling of SCI is intrinsically exponential with the number of correlated electrons and orbitals. The reason for this exponential scaling is directly linked to the linear parametrization which implies that the intrinsic exponential structure of the wave function must be built explicitly by adding more and more determinants in the reference wave function. This necessarily leads to size consistency errors which manifest through an underestimation of the coefficients of the reference and perturbative wave functions and therefore of the correlation energy. Because the size consistency error grows with the total (absolute) value of the correlation energy, SCI struggle more and more as the number of correlated electrons increases and/or the strength of correlation increases. Attempt to cure this problem have been recently proposed with a selection of the individual excitation operators in a single-reference CC approach (Xu, E.; Uejima, M.; Ten-no, S. L. Towards Near-Exact Solutions of Molecular Electronic Structure: Full Coupled-Cluster Reduction with a Second-Order Perturbative Correction. J Phys Chem Lett 2020, 11, 9775–9780. Gururangan, K.; Deustua, J. E.; Shen, J.; Piecuch, P. High-level coupled-cluster energetics by merging moment expansions with selected configuration interaction. J Chem Phys 2021, 155, 174114). [0177] Another aspect of the present invention is to combine the robust and linear parametrization of SCI with the intrinsic exponential parametrization of the ansatz used in QC computation to overcome these limitations. [0178] Hence, as illustrated hereafter, the invention can comprise the use a SCI approach to generate the target wave functions. [0179] Starting from that SCI target wavefunction, the OG-ADAPT-VQE ansatz would allow for a size consistent optimization of the wave function in order to reach chemical accuracy with a minimal number of operators. [0180] We performed CIPSI calculations through the open-source quantum chemistry environment Quantum Package for the different molecular systems. As a reminder, the CIPSI wavefunction is used as an initial guide for our Ansatz and need not be extremely accurate. [0181] The figure 6 illustrate the energy convergence of the the two different ADAPT-VQE protocols on the stretched linear H6 system. We observe a significant difference in the results, with chemical accuracy being achieved using only 40 parameters when the QEB- ADAPT-VQE procedure is initialized with the overlap-guided-CIPSI intermediate wave- function whereas while the classical ADAPT-VQE ansatz is nearly 15 times less accurate despite using 50 parameters. In particular, for Figure 6, the CIPSI-OG ansatz (circle dots) is grown up to 20 parameters and then used as the initial state for an ADAPT-VQE process. The figure 6 shows the energy convergence plot of the two different ADAPT-VQE protocols on the stretched linear H6 system. We observe a significant difference in the results, where chemical accuracy is achieved using less than 50 parameters when the ansatz was initially guided by the CIPSI wave-function, whereas the original ADAPT-VQE ansatz was unable to achieve the same level of accuracy, despite using a much larger number of parameters. Additional calculations revealed that with the classical QEB- ADAPT-VQE protocol requires more than 150 parameters to achieve chemical accuracy. This massive performance gap demonstrates that the CIPSI wave-function initialization guides the ansatz construction in a manner that avoids a massive energy plateau which impedes the progress of classical QEB-ADAPT-VQE. [0182] Let us emphasize here that the initial CIPSI wave-function was composed of only 50 determinants and had an accuracy of less than 10−2 Hartree, which suggests that even alow accuracy classically computed target wave-function for the overlap-guided algorithm is enough to improve the convergence of the subsequent QEB-ADAPT-VQE procedure. This observation is particularly important since it highlights the potential of applying this CIPSI-Overlap- ADAPT procedure to much larger systems with strong correlation where CIPSI approaches are not particular effective and are simply unable to achieve chemical accuracy. [0183] For such systems, we can envision computing a CIPSI wave-function at the limit of classical computational resources, using this non-chemically accurate CIPSI wave- function as a target for the overlap-guided adaptive algorithm, and initialising a subsequent QEB-ADAPT-VQE procedure on a quantum computer in order to obtain a final result with chemical accuracy. On the accuracy of the initial SCI wave function used [0184] To further test the effectiveness of this CIPSI-Overlap-ADAPT approach, we return to the stretched BeH₂ molecule considered in the previous subsection. We employ two different CIPSI wave-functions as targets for the overlap-guided adaptive algorithm and use the approximate wave-functions obtained as high accuracy initializations for QEB- ADAPTVQE procedures. [0185] To check how the convergence criteria affects our OG procedure, we have run the adapt procedure twice on our OG-ansatz, once with a small number of parameters and a poor overlap with the target (Figure 6A), and again with an increased overlap and a higher number of parameters (Figure 6B). Hence, the stretched BeH₂ molecule have been tackled with two different CIPSI wave- functions as target wave function used in our OG growing ansatz procedure. [0186] Our results are displayed in Figure 7 and demonstrate that the CIPSI-Overlap- ADAPT produces a significantly more compact ansatz than the classical QEB-ADAPT- VQE procedure for both choices of CIPSI wave-functions. In both cases, the final accuracy of the wave-function with a maximal operator count of 50 operators is nearly an order of magnitude more than that of QEB-ADAPT-VQE. Furthermore, as noted in the case of the H6 molecule, the choice of a low accuracy CIPSI wave-function as the initial target for the Overlap-ADAPT-VQE does not meaningfully degrade the final accuracy. [0187] Hence, our OG-ADAPT ansatz is more compact than the ADAPT ansatz for both the CIPSI target wave-functions, regardless of their accuracy, and the number of parameters in the initial state grown with CIPSI-OG algorithm. [0188] As illustrated in these examples, the invention, through the Overlap-Guided (OG) procedure, allows one to create ansatz that are more compact than the popular ADAPT- VQE at chemical accuracy for usual small molecular systems. [0189] In this OG procedure, the ansatz is grown using operators that increase its overlap with a target wave-function rather than operators that lower its energy. The OG- ansatz, noticeably guided by the target wave-function, avoid most local traps that are typically encountered when starting from the Hartree-Fock state in standard ADAPT- VQE. [0190] Moreover, we combined classical selected-CI approaches and quantum computing by taking a CIPSI wave-function as target to the OG-ansatz. The aforementioned method resulted in a massive improvement over ADAPT-VQE, where the chemical accuracy is reached with substantially less operators. [0191] Hence, within the present invention, the hybrid Selected-CI - OG procedure has the potential to bring a quantum advantage over classical quantum chemistry methods by following this procedure: - pushing the classical computation of a complex molecular system to its limits to create the target wave function, then - generating the corresponding ansatz in a quantum computer using the OG adaptative procedure, - further improve this ansatz, for example through ADAPT-VQE, and - potentially further OG-compression steps. [0192] Moreover, as illustrated, this OG-ansatz can be used as initialization for a usual ADAPT-VQE procedure. Hence, the OG ansatz can be used as a state preparation procedure within a VQE framework that will be further optimized through the ADAPT process. [0193] We finally used the state of an ADAPT-VQE iteration as target and built an ansatz that achieves the same accuracy with significantly less operators. We have also shown that this compression process can be carried out multiple times and leads to an even more compact ansatz. Sparse Quantum State Preparation for Strongly Correlated Systems [0194] Quantum Computing allows, in principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register, offering a promising solution to overcome the limitations of traditional quantum chemistry methods. An essential requirement for ground state quantum algorithms to be practical is the initialisation of the qubits to a high-quality approximation of the sought-after ground state. Quantum state preparation enables the generation of approximate eigenstates derived from classical computations, but it is frequently treated as an oracle in quantum information. In this study, we investigate the quantum state preparation of prototypical strongly correlated systems’ ground state, up to 28 qubits, using GPU-accelerated state- vector emulator. Our results indicate that the recently developed technology offers the most advantageous performance for near-term applications. [0195] Finally, this OG procedure is, by design, able to integrate seamlessly with the recent improvements made to ADAPT-VQE, (Sapova, M. D.; Fedorov, A. K. Variational quantum eigensolver techniques for simulating carbon monoxide oxidation. Communications Physics 2022, 5, 1–13.) sharing the same structure and adaptive property while still leveraging its own unique approach to operator selection and many combinations with ADAPT variants can now be studied. [0196] The invention can be the subject of numerous variants and applications other than those described above. In particular, unless otherwise indicated, the different structural and functional characteristics of each of the implementations described above should not be considered as combined and / or closely and / or inextricably linked to each other, but on the contrary as simple juxtapositions. In addition, the structural and / or functional characteristics of the various embodiments described above may be the subject in whole or in part of any different juxtaposition or any different combination.

Claims

Claims 1. A computer implemented method for the generation of an optimized quantum computing circuit from a current ansatz (Ψ(m-1)), the current ansatz being a current quantum state of a quantum system, preferably said computer comprising quantum computational means, said method comprising: - a step of selecting (150), preferably by the quantum computational means, among a pool of unitary operators, the unitary operator (Â_m(θ_m)) whose action on the current ansatz (Ψ(m-1)) produce a new wave function with the largest overlap with respect to a target wave function (Ψtarget) according to non- energy based criteria, said step comprising a selection of the unitary operator, whose addition to the current ansatz maximize the overlap between a new wave-function and the target wave-function; and - a step of growing (160) the ansatz by appending the selected unitary operator to the left of the current ansatz (Ψ(m-1)) to generate a new ansatz (Ψ(m)); and - a step of optimizing (170) the parameters of the new ansatz (Ψ(m)), said parametrization corresponding to the generation of the optimized quantum computing circuit.

2. The computer implemented method according to the preceding claim, further comprising a step of implementing (190) the optimized quantum computing circuit on quantum computational means.

3. The computer implemented method according to any of the preceding claims, wherein the unitary operator (Â_m(θ_m)) selected is the one whose action on a current ansatz (Ψ(m)) produce a new wave function with the largest orbital overlap with respect to the target wave function (Ψtarget).

4. The computer implemented method according to any of the preceding claims, wherein the pool of unitary operators includes single and double fermionic excitation operators.

5. The computer implemented method according to any of the preceding claims, wherein the pool of unitary operators comprises spin-complemented pairs of single and double fermionic excitation operators.

6. The computer implemented method according to any of the preceding claims, wherein the pool of unitary operators comprises individual Pauli chains, e.g. from the division of fermionic-ADAPT operators after a Jordan-Wine mapping.

7. The computer implemented method according to any of the preceding claims, wherein it further comprises a step of computing (130) the target ansatz wave function (|Ψref^), said computing being performed by binary computing means or by quantum computing means.

8. The computer implemented method according to any of the preceding claims, wherein the target wave function is with a tractable high accuracy approximation of a full-CI wave-function.

9. The computer implemented method according to any of the preceding claims, wherein the target wave function is an ADAPT-VQE ansatz, for example comprising more than five parameters, preferably more than 10, 15, 20 parameters.

10. The computer implemented method according to any of the preceding claims, wherein the target wave function is a Selected-Configuration Interaction ansatz, preferably computed according to the so-called Configuration Interaction perturbatively selected iteratively (CIPSI).

11. The computer implemented method according to any of the preceding claims, wherein it further comprises a step of measuring (140) overlap gradients, said computing being performed by binary computing means or by quantum computing means.

12. The computer implemented method according to any of the preceding claims, wherein it further comprises a step of reiterating (180) from the step of measuring (140) using the optimized ansatz wave function as the current ansatz wave- function.

13. The computer implemented method according to any of the preceding claims, wherein it further comprises introducing a machine-learning framework incorporating a trainable quantum circuit.

14. A computer implemented method for the generation of an optimized quantum computing circuit from a new ansatz (Ψ(m)) generated according to any of the preceding claims, said method comprising the use of the new ansatz (Ψ(m)) as an initial state in an ADAPT-VQE procedure.

15. Quantum computing means for quantum simulations characterized in that it comprises an optimized quantum computing circuit obtainable, preferably obtained, by a method according to any of the preceding claims.

16. Quantum computing means for quantum chemical simulations characterized in that it comprises an optimized quantum computing circuit obtainable, preferably obtained, by a method according to any one of the claims 1 to 14.

17. The quantum computing means for quantum chemical simulations according to the preceding claim, characterized in that it comprises a quantum circuit corresponding to an ansatz of a molecule comprising at least three atoms, said ansatz comprising no more than 20 parameters per atom and has a chemical accuracy threshold of 10^-3 Hartree or less, at bond length of 3 Angstrom or more.