Quantum computer architecture for solving quantum chemical problems

Abstract

A quantum computer architecture and a method for solving quantum chemical problems are provided, comprising: determining and storing (135) an approximate ground state for the Hamiltonian H using a classical computer (130); modeling the approximate ground state on a first quantum register (210) of a quantum computing unit QPU (240); modeling the time evolution operator (230) as a gate sequence of the QPU (240) and executing (145) the same; modeling a measurement operator x on one of the QPU (240); reading and storing (155) the measurement operator according to time evolution to obtain an approximation for the ground state value E0 (260) of H, wherein the determination of the approximate ground state is carried out using a Density Matrix Renormalization Group DMRG.

Description

The present invention relates to quantum computers, and more particularly to the use of a quantum computer to solve quantum chemistry issues.Many industrial chemical issues, such as fertilizer material production and battery research, can be considered in a quantum chemical approach. It is thus possible to develop potential new materials or even improved methods for obtaining specific materials. For example, new materials for battery cells can be found that are essential for the mobility of the future. The determination of the desired properties of the desired materials can only be carried out numerically, which, however, is also subject to certain limitations, especially with increasing complexity and size of the desired molecules, due to a very large computational effort. Accordingly, the development of new methods and computer architectures is a critical step in order to be able to operate advanced quantum chemistry.A very important property for characterizing molecules is the ground state | ψ gnd ≅and the ground state energy E gnd. The density matrix normalization group (DMRG) method has proven to be one of the best classical methods over a long time in order to solve problems of solid-state physics and thus also of quantum chemistry. The DMRG method is a variation algorithm which searches the state | ψ≅of any molecule by which the function E= ψ|H| ψ≅ / 〈 ψ| ψ≅is iteratively minimized.The method is very efficient because it uses matrix product states. The matrices occurring in this case are reduced in their dimension in a manner such that the result has a sufficiently high correctness. Let m be the maximum dimension of each matrix of the matrix product state. The larger m, the more accurate the result, but the slower the calculation.Alternatively, there are various approaches to "measure" a hamiltonian using a quantum computer and to determine the ground state in this way. Mention should be made here of the quantum phase estimation and the quantum measurement method. These methods have the potential to provide very accurate results for the ground state, with shorter runtimes than classical algorithms can offer.The DMRG method provides relatively precise results for the ground state in a short time, even for small maximum matrix dimensions m. However, these results are not precise enough with reasonable computational effort to be considered representative results. At the same time, the quantum algorithms are limited in that they require a "good" starting state (a state "close to" the base state) as input in order to be able to ascertain the precise results with high probability.Furthermore, U.S. Pat. No. 10,984,152 B2 describes a quantum simulation method comprising the generation of a set of models representing a quantum system. The set of models includes subsystem models representing respective fragments of the quantum system. The quantum system is simulated by operating the set of models on a computer system that includes a classical processor unit and multiple non-interleaved quantum processor units (QPUs), and that implement the respective subsystem models for the non-interleaved QPUs. In some examples, density matrix embedding theory (DMET) is used to calculate an approximate ground state energy for the quantum system.US 2020 / 0364601 A1 describes methods and devices for using a hybrid architecture of quantum and classical computers for calculating the quantum mechanical energy and / or electronic structure of a chemical system, as well as for identifying stable conformations of a chemical system (e.g. a molecule) and / or for carrying out an ab-initio molecular dynamics calculation or simulation of the chemical system.US 2020 / 0394549 A1 discloses a preparation of correlated Fermionic states on a quantum computer for determining a ground state of a correlated Fermionic system. In various embodiments, a quantum circuit is provided that includes a linear chain of qubits and a plurality of matching gates arranged in layers. Each matchgate is configured to perform a two-qubit rotation on adjacent qubits within the linear chain. An initial state is provided for each qubit in the linear chain. The quantum circuit is applied to the initial values and thus makes an approach to the linear chain of qubits, which approach corresponds to a Fermionic state.US 2021 / 0081804 A1 describes a machine learning-based method or system for identifying small, drug-like molecules, in which a tensor network representation of molecular quantum states of a data set of small, drug-like molecules is provided as input for a machine learning system, such as a neural network system. The machine learning method or system may itself be configured as a tensor network. A training dataset may be used to train the machine learning system, and the training dataset is a tensor network representation of the molecular quantum states of small drug-like molecules.US 2021 / 0232960 A1 describes a method comprising the provision of a Fermionic Hamiltonian, the transformation of the Fermionic Hamiltonian into qubit operators, the transformation of the Fermionic Hamiltonian into qubit operators in a mean field hamiltonian and the embedding of the Hamiltonian into a quantum computer. Such systems and methods can improve the existing methods for solving electronic structural problems on a computer by adapting the problem to the available hardware, reducing computing costs, and reducing the number of qubits required to solve the electronic structural problems for a larger number of atoms.US 2022 / 0012382 A1 describes techniques for enabling density functional theory determinations using a quantum computer system. An apparatus includes a first computing processor and a second computing processor. The first computational processor may generate a density functional theory determination. The second calculation processor may input a quantum density into the density functional theory determination. The first computing processor may be operatively coupled to the second computing processor. Further, the first computing processor may be a classical computer and the second computing processor may be a quantum computer.US 2023 / 0020166 A1 describes a method for simulating a quantum chemical system comprising the steps of: determining a Boson hardcore hamiltonian describing the quantum chemical system, wherein the model hamiltonian limits the electronic states to electron singlet state configurations; determining a paired-electron unitary coupled cluster with double excitation (pUCCD) approach, wherein the approach is limited to paired electron configurations; mapping the pUCCD approach to qubit operations of a quantum circuit comprising a set of qubits and gates to allow pairs of qubits to interact with each other; determining a trial state on the quantum circuit by applying the qubit operations defined by the mapped pUCCD approach to the qubits; and determining an energy of the quantum chemical system based on the trial state and the constrained Hamilton term, grouping the Hamilton terms into three sets of operators that can be measured simultaneously; and an error mitigation technique based on a post-selection of the quantum measurements with the known particle number.US 2023 / 0040584 A1 describes a computer implemented method for solving a hamiltonian comprising performing a lanczos method in a tensor network, contracting a plurality of tensors in the network, a lanczos method acting on the non-contracted tensors, the lanczos method including evaluating a recursive relationship of an equation including using the equation at least twice, forming a tridiagonal block matrix having a block size greater than one based on the recursive relationship, and diagonalizing the block tridiagonal matrix to obtain new tensors and energy levels of the tensor network, wherein at least one of the tensors of the network has an index for the group of excitations; and solving for the rest of the tensor network.US 2023 / 0081927 A1 describes a method and apparatus for estimating the ground state characteristics of molecules and materials with high accuracy on a hybrid quantum class computer using low depth quantum circuits. The ground state energy is estimated for a Hamilton's matrix characterizing a physical system. For an observed quantity, samples are taken on a parameterized Hadamard test circuit, the results evaluated, and the expected value of the observed quantity is estimated with respect to the baseline energy. A weighted expected value is estimated and the ground state property is calculated.US 2021 / 0042653 A1 describes a method for determining an energy level of a physical system using a quantum computer, wherein the energy level of the physical system is described by summing a plurality of summands. The method includes performing an energy estimation routine that includes preparing an approach trial condition and estimating an expected value for each summands. The estimating includes constructing an initial quantum circuit based on the array of quantum gates to operate in the approach trial state, and further includes performing a summands expectation value determination subroutine a plurality of times in an iterative process. The energy estimation routine further includes summing the expected value estimates of each summands to determine an estimate for the energy of the experimental condition. The method further comprises determining the energy level of the physical system by applying an optimization method to the energy estimation routine.US 2022 / 0019931 A1 discloses methods, systems and devices for simulating physical systems. In one aspect, a method includes the steps of: selecting a first set of basis functions for the simulation, the first set of basis functions including an active and a virtual set of orbitals; defining a set of expansion operators for the simulation, the expansion operators approximating Fermionic excitations in an active space spanned by the active set of orbitals; performing a plurality of quantum calculations to determine a matrix representation of a hamiltonian characterizing the system in a second set of basis functions; calculating eigenvalues and eigenvectors of the hamiltonian using the determined matrix representation of the hamiltonian; and determining characteristics of the physical system using the calculated eigenvalues and eigenvectors.It is the object of the present invention to provide a fast and effective solution for calculating the ground state characteristics of quantum systems.This object is solved in a first embodiment by a method for solving a quantum chemical problem with Hamiltonian H, comprising:determining an approximate ground state | ψ 0 ≅ to Hamiltonian H with the aid of a classic computer;modelling | ψ 0 ≅ on a first quantum register of a quantum computing unit QPU; modelling the time development operator U(t)=e -iHt as gate sequence of the QPU; modelling a measurement operator x on the gates of the QPU;Measuring 〈 Ψ 0| U -1 xU| Ψ 0 ≅to obtain an approximation for the base state value of H, wherein it is provided that the determination of | ψ 0 ≅takes place with the aid of a density matrix renormalization group, DMRG, so that | ψ 0 ≅is a matrix product state.The object is also achieved in a second embodiment by a system for solving quantum chemical questions with Hamiltonian H.According to the invention, the system according to the second embodiment includes a classical computer; a quantum computer including a first quantum register of N qubits and a second quantum register of r qubits, wherein the classical computer is configured to calculate, with the aid of a density matrix renormalization group, DMRG, an approximate ground state | Ψ 0 ≅ for the hamiltonian H of the quantum mechanical problem, and wherein the quantum computer is configured to model the state | ψ 0 ≅ in the first quantum register and model a pointer state |x=0≅ in the second quantum register, wherein the quantum computer is further configured to model the state | ψ ≅, the common state | Ψ 0 〉 ⊗ |x≅ of the two quantum registers with the aid of a unitary time evolution U(t)=exp(-itH 1 ⊗ p), wherein H 1 is the hamiltonian of the system modeled in the first quantum register and p is the pulse to x, wherein the quantum computer is furthermore configured to read out the final state ∑ j λ j| E j〉 ⊗ |x=tE j ≅ after a time t in order to determine the basic state energy of H.A third embodiment relates to a computer readable storage medium including instructions that allow a method according to the first embodiment to be executed on a system according to the second embodiment.A quantum computer network for solving quantum chemical problems can be constructed by the constituent elements 1st data input surface 2nd storage unit 3rd central processing unit (CPU) 4th quantum processing unit (QPU)The information which must be given to the architecture is a Hamiltonian (Hamiltonian) operator H, which represents the quantum-mechanical representation of the molecule to be investigated. In the first step, the CPU uses this data and provides an approximation for the basic state of the molecule with the aid of the density matrix renormalization group with matrix dimension m, DMRG(m). During the calculation, the best possible energy of the basic state E 0 and the corresponding state | ψ 0 ≅ are determined. This result is preferably stored in the memory unit.Subsequently, the best possible state | ψ 0 ≅ is used as a starting point for the control of the QPU. The QPU comprises a plurality of qubits, which are preferably divided into two qubit registers, as well as a plurality of executable quantum gates. Preferably, a few auxiliary qubits are also needed. These may be part of the first and second registers or may form a further register. The state | ψ 0 ≅ is prepared on a plurality of qubits of the first qubit register and, if appropriate, with addition of the auxiliary qubits. This can be carried out efficiently since | ψ 0 ≅ can be represented by a matrix product representation. The sequence of quantum gates given in this architecture acts on the plurality of qubits of both quantum registers. By means of a measurement process, after application of all quantum gates of the given quantum gate sequence, a new value for the ground state energy is determined, which is stored in the memory unit.The quantum gate sequence can be constructed in such a way that it corresponds to the already known quantum algorithm for measuring a hamiltonian H, the quantum measurement. A gate sequence of quantum phase estimation may also be used.In the architecture presented here, it is also possible to introduce a further operator x, the so-called pointer, which acts on the multiplicity of qubits of the second qubit register.To carry out an advantageous measuring method, a quantum gate sequence is also required which implements the unitary operation on the plurality of qubits of the two qubit registers, wherein H is 1 of the hamiltonian of the system modeled in the first quantum register and p is the pulse conjugated to x. Two important steps must be taken into account in this case. On the one hand, the quantum chemical hamiltonian does not contain Fermionic operators and a does not commutate j and the summands. The Fermionic operators are replaced by operators executable on a quantum computer through the Jordan-Wiener transformation. Using the Trotter decomposition or the linear combination of units (LCU), the summands can be implemented efficiently individually within the time development operator exp(-ihH 1 ⊗ p). These individual unitary operators can be implemented by a quantum gate sequence consisting of one- and two-qubit gates.Advantageously, the Hamiltonian H 1 is modeled on the first quantum register, wherein N describes the number of orbitals for modeling | ψ 0 ≅.Advantageously, the N orbitals of (1) are represented by N digital qubits, wherein the Fermionic generation and destruction operators have been transformed into by means of Jordan-Wigner transformation. Here, σ {+,-,z},k are the Pauli spin matrices or ascent and descent operators acting on the jth qubit:Here, furthermore, the crown product of two matrices A and B is generally produced, and furthermore, the crown product is generally produced via a sequence of matrices A 1 to A n.Preferably, the unitary transformation exp(-iθσ {+,-,z},i σ {+,-,z},j) is performed by a sequence of 1-qubit and 2-qubit operations.Advantageously, the 2-qubit operation is a controlled NOT, cNOT, and the 1-qubit operations include at least two elements from the following list: rotations about the x-axis R x, rotations about the y-axis R y rotations about the z-axis R z, phase rotations of the excited state T, and Hadamard gate H.Advantageously, the time development operator U(t) can be generated with the aid of the Trotter decomposition.Alternatively, the time development operator can advantageously be generated with the aid of a Linear Combination of Unitary Operators, LCUO, as set out, for example, in Children and Wiebe, arXiv:1202.5822.Advantageously, as shown in Childs et al., arXiv:quant-ph / 0204013, the quantum system is an extended system | Ψ 〉 | x 〉 consisting of the modeled system | Ψ ≅ on the first quantum register and an auxiliary system | x ≅ on a second quantum register, wherein the measurement operator x acts on states of the second register, and wherein the time evolution operator is given by U(t) = exp(-itH 1 ⊗ p), wherein H 1 represents the hamiltonian of the system modeled in the first quantum register and p represents the pulse conjugate to x.Advantageously, this time evolution is performed by a sequence of 1-qubit and 2-qubit operations.Advantageously, the time development U(t) is applied to a starting state | Ψ 0 ≅ ⊗ |x=0≅ and leads, after a measurement of the quantum system, to a final state, wherein the λ i are the weights of the individual energy eigenstates in the state | Ψ 0 ≅ so that the basic state value E 0 of H can be determined from a measurement of the auxiliary system |x≅ with probability |λ 0|2.Preferably, the auxiliary system |x≅is so large that the measured state is essentially an intrinsic state of the auxiliary system and thus an intrinsic state of energy of H.Advantageously, the time t is selected in such a way that the influence of excited states is minimized.Advantageously, the measurement operator x is represented by r describing the number of qubits of the second register.Preferably, the quantum computer is a digital quantum computer which passes the Fermionic generation and destruction operators of the hamiltonian H by Jordan-Wigner transformation on the first register.Model the pointer state x on the second register, where σ {+,-,z},k are the Pauli spin matrices acting on the jth qubit of the respective register.Advantageously, the quantum computer is configured to perform 1-qubit and 2-qubit operations on the qubits of the two quantum registers, and wherein the classic computer is configured to represent the time evolution U(t) by a sequence of these 1-qubit and 2-qubit operations and to instruct the quantum computer to perform this sequence.Before the translation into a gate sequence, the time development U(t) can advantageously be broken down into smaller time pieces with the aid of a Trotter break-down or a Linear Combination of Unitary Operators, LCUO, or Linear Combination of Units, LCU.Advantageously, the 2-qubit operation is a controlled NOT, cNOT, and the 1-qubit operations include at least two elements from the following list: rotations about the x-axis R x, rotations about the y-axis R y rotations about the z-axis R z, phase rotations of the excited state T, and Hadamard gate H.Advantageously, the measurement time t is chosen such that the influence of excited states is minimized.Advantageously, the calculated ground state properties can be used for one or more of the following areas: energy storage, in particular battery design, thermal energy storage, fuel cell design and design and optimization of renewable energy technology; agricultural chemistry, in particular development of pesticides and herbicides, development of fertilizers, development of crop protection strategies, reduction of pesticide residues; catalyst design, in particular for the synthesis of fine chemicals, for petrochemicals, fuel production, polymerization and refining of crude oil; food industry, in particular preservation of foods; electronics, in particular design of semiconductors, design of display technology, design and development of printed circuits; Molecular electronics, in particular design and synthesis of molecular materials, development and production of molecular components (diodes, transistors, etc.), representation of molecular properties and integration of molecular components; aeronautical industry, in particular fuel development, material design and corrosion protection; medical industry, in particular medicament discovery and development, medicament formulation, safety rating of medicaments and medical devices (sensors, biocompatible materials, etc.); construction industry, in particular safety and durability rating, rating of the ecological influence of materials, design of construction materials and optimization of buildings; traffic, in particular optimization of combustion and optimization of exhaust gas catalysts; cosmetics industry, in particular optimization of cosmetic formulations and rating of cosmetic effectiveness; Oil industry, in particular fuel cell design, refinery process optimization, product quality optimization, process safety optimization, catalyst development and reaction kinetics optimization; chemical process optimization, in particular distillation and absorption process design and optimization, product quality optimization, process safety optimization and reaction kinetics optimization; paints and lacquers, in particular optimization of the formulations of paints and lacquers and development and optimization of pigments; packaging materials, in particular the optimization of packaging materials and structures and the optimization of the sustainability of packaging materials; solar cell design, in particular boundary layer design, solar cell structure optimization and solar cell material design and optimization; Waste management, in particular optimization of waste treatment processes and avoidance or containment of dirt; magnetic materials, in particular design and optimization of magnetic materials, development of spintronic components and optimization of magnetic data memories; and climate technology, in particular design and optimization of carbon capture and storage, CCS, systems and for evaluating the effects of climate conversion.An embodiment of the invention will be explained below with reference to the drawings.The following are shown: FIG. 1 is a schematic illustration of an architecture according to an embodiment of the invention FIG. 2 is a schematic illustration of a quantum measurement method according to an embodiment of the invention; and FIGS. 3a-3c are schematic representations of gate sequences for the representation of Fermionic operators used in Hamiltonian. FIG. 3d shows a further schematic illustration of the gate sequence for illustrating Fermionic operators. FIG. 3e shows a schematic illustration of a gate sequence for generating the unitary time development.The figures are described in more detail below:FIG. 1 shows a schematic diagram of a system 100 according to an embodiment of the invention. This consists of a data input 110 for inputting 115 the desired molecular hamiltonian H into a storage unit 120. This memory unit is accessed in an access step 125 by a classic CPU 130 to perform a DMRG, the result of which is an approximate ground state | Ψ 0 ≅ and an approximate ground state energy E gnd. These are stored in the memory unit in a further step 135. Furthermore, the CPU 130 is configured to control a quantum computing unit, QPU 140, having a correspondingly constructed gate sequence in a step 145 to perform a quantum measurement method with the hamiltonian H and the ground state | ψ 0 ≅ in order to generate a value for the ground state energy E gnd. This value is then read out in a step 155 and is likewise stored in the memory unit 120.FIG. 2 shows a diagram of a quantum measurement method 200. A first quantum register 210 of the QPU 140 is prepared in the ground state | Ψ 0 ≅ obtained from the DMRG, and a second quantum register 220 encodes a pointer state |x). Since the DMRG baseline state | ψ 0 ≅ is a matrix product state, it may be set on the first quantum register 210 by a corresponding sequence of 1-qubit and 2-qubit operations calculated by the CPU 130. The two quantum registers are propagated together with a time evolution U(t)=exp(-itH 1 ⊗ p) 230. This time evolution is also provided by the CPU 130 through a sequence of 1-qubit and 2-qubit operations calculated accordingly, preferably with the aid of a Trotter decomposition or a Linear Combination of Unitary Operators, LCUO. The second quantum register 220 finally passes through an inverse quantum Fourier transform 240. A final measurement of the two quantum registers 210 and 220 places the system in one of the pointer's eigenstates 250 corresponding to one of the eigenstates of H. In this eigenvalue basis, the state | ψ 0 ≅ can be represented as ∑ j λ j| E j ≅. Thus, the measured value of |x≅with a probability of |λ j|2 corresponds to the value tE j,, i.e. with a probability 260 of |λ 0|2 corresponds to the sought basic state.FIG. 3 shows the representation of Fermionic operators by a gate sequence of a quantum computer.FIGS. 3a to 3d show the representation of different excitation operators in second quantization as a sequence of 1-qubit and 2-qubit operations, in particular of rotation (T, Y, R z( θ))-Hadamard H and cNOT gates.In particular, FIG. 3 ashows the representation of the particle number operator as rotation T(θ) on the qubit q, wherein T(θ)|0≅=|0≅, T(θ)|1≅=e -iθ|1 ≅and the angle θ is a function of the prefactor h pp.FIG. 3 bshows the representation of an excitation operator as a sequence of cNOT (represented by ≅), Hadamard gates (H) and rotations about the Z-axis, R z( θ) and Y=R z( π / 2).Figure 3c shows a representation of the coulomb and exchange interaction term through the same gates as in Figure 3b and an additional global phase G(θ).FIG. 3 dis a diagram of the multiple cNOT used in the gate sequence of FIGS. 3 band 3 c, and thus a schematic diagram of equations (2) and (3).Figure 3e shows an exemplary representation of a unitary time evolution for a system with four qubits in the first register and one qubit (first row) in the second register through a sequence of 1-qubit and 2-qubit operations as introduced in Figures 3b to 3c. In particular, it is shown how the time t to be propagated was broken down into four trotter steps by trotter decomposition.List of reference characters100 System 110 Data input 115 Store 120 Store 125 Access to molecular data 130 CPU 135 Store ψ 0 and E 140 QPU 145 Quantum algorithm execute 155 Read-out and store the measured value for the ground state energy E 0200 Quantum measurement method 210 First quantum register 220 Second quantum register 230 Unitary Time Evolution 240 Inverse Fourier Transformation 250 System state energy measured on the basis of the measurement operator 260 itselfReferences included in the specificationThis list of documents cited by the applicant has been produced in an automated manner and is only included for the better information of the reader. The list is not part of the German patent application or utility model application. The DPMA does not take any adhesion for any faults or omissions.Patent Literature citedU.S. Pat. No. 10,984,152 B2

[0007] US 2020 / 0364601 A1

[0008] US 2020 / 0394549 A1

[0009] US 2021 / 0081804 A1

[0010] US 2021 / 0232960 A1

[0011] US 2022 / 0012382 A1

[0012] US 2023 / 0020166 A1

[0013] US 2023 / 0040584 A1

[0014] US 2023 / 0081927 A1

[0015] US 2021 / 0042653 A1

[0016] US 2022 / 0019931 A1

[0017]

Claims

A method for solving a quantum chemical problem with Hamiltonian H, comprising: determining and storing (135) an approximate ground state | ψ 0 ≅ to the Hamiltonian H with the aid of a classical computer (130); modelling | ψ 0 ≅ on a first quantum register (210) of a quantum computing unit QPU (140); modelling the time evolution operator U(t)=e -iHt(230) as gate sequence of the QPU (140) and executing (145) the same; modelling a measurement operator x on the gates of the QPU (140); Reading and storing (155) 〈 Ψ 0| U -1 xU| Ψ 0 ≅ in order to obtain an approximation for the basic state value E 0(260) of H, characterized in that the determination (135) of | ψ 0 ≅ is carried out with the aid of a density matrix renormalization group, DMRG, such that | ψ 0 ≅ is a matrix product state.The method of claim 1, wherein the hamiltonian H on the first quantum register is modeled by H 1 = ∑ i, j = 1 N h i, j a i a j + ∑ i, j, k, l h i, j, k, l a i a j a k a l where N describes the number of orbitals for modeling | ψ 0 ≅.The method of claim 2, wherein the N orbitals are represented by N digital qubits, wherein the Fermionic generation and destruction operators a j †, a j have been transformed by means of Jordan-Wigner transformation into a j = ⊗ k = 1 j - 1 k ⊗ σ +, j ⊗ k = j + 1 N σ z, k and a j = ⊗ k = 1 j - 1 1 k ⊗ σ -, j ⊗ k = j + 1 N σ z, k where σ {+,-,z},k are Pauli spin matrices acting on the jth qubit.The method of claim 3, wherein the unitary time evolution exp(-iθσ {+,-,z},i σ {+,-,z},j) (230) is performed by a sequence of 1-qubit and 2-qubit operations.The method of claim 4, wherein the 2-qubit operation is a controlled NOT, cNOT, and the 1-qubit operations include at least two elements from the following list: rotations about the x-axis R x, rotations about the y-axis R y rotations about the z-axis R z, phase rotations of the excited state T, and Hadamard gate H.The method of any one of claims 1 to 5, wherein U(t) (230) is generated using the Trotter decomposition U ( t ) = e - i H t ≈ ∏ k t / Δ t e - i H Δ t.The method of any of claims 2 to 6, wherein the quantum system is an extended system | Ψ 〉 | x ≅ consisting of the modeled system | Ψ 〉 the first quantum register (210) and an auxiliary system | x ≅ on a second quantum register (220), wherein the measurement operator x represents a state of the auxiliary system, and wherein the unitary time evolution (230) is given by U(t) = exp(-itH 1 ⊗ p), wherein p is the pulse conjugated to x.Method according to claim 7, wherein the time development U(t) (230) is applied to a starting state | Ψ 0 〉 |x = 0 ≅ and leads to a final state (250) ∑ j λ j| E j 〉 |x = tE j ≅, wherein the λ i are the weights of the individual energy eigenstates in the state | Ψ 0 ≅ so that the basic state value E 0(260) of H can be determined from a measurement of the auxiliary system |x ≅ with probability |λ 0|2.The method of claim 7 or 8, wherein the measurement operator x is represented by x = ∑ j = 1 r 2 - j 1 σ z, j 2 where r describes the number of qubits of the second quantum register.A system (100) for solving a quantum mechanical problem with Hamiltonian H, comprising: a classical computer (130); a quantum computer (140) comprising a first quantum register (210) of N qubits and a second quantum register (220) of r qubits, characterized in that the classical computer (130) is configured to calculate, by means of a density matrix renormalization group, DMRG, an approximate base state | Ψ 0 〉 for the Hamiltonian H of the quantum mechanical problem, and in that the quantum computer (140) is configured to calculate, modelling the state | ψ 0 ≅ in the first quantum register (210) and modelling a pointer state |x=0≅ in the second quantum register (220), wherein the quantum computer is further configured to propagate the common state | ψ 0 ≅ ⊗ |x≅ of the two quantum registers with the aid of a unitary time development U(t)=exp(-itH 1 ⊗ p) (230), wherein H 1 is the modelling of H onto the first quantum register and p is the pulse to x, wherein the quantum computer is further configured, the final state (250) ∑ j λ j| E f ≅ ⊗ |x = tE j ≅ after a time t to determine an approximate value for the ground state energy E 0(260) of H.The system (100) of claim 10, wherein the quantum computer (140) is a digital quantum computer configured to generate and destroy the Fermionic generation and destruction operators a j of the hamiltonian H by Jordan-Wigner transformation on the first quantum register (210) by a j = ⊗ k = 1 j - 1 k ⊗ σ +, j ⊗ k = j + 1 N σ z, k a j = ⊗ k = 1 j - 1 k ⊗ σ -, j ⊗ k = j + 1 N σ z, k and the pointer state x on the second quantum register (220) by x = ∑ j = 1 r 2 - j 1 - σ z, j 2 where σ {+,-,z},k are the Pauli spin matrices acting on the jth qubit of the respective register.The system (100) of claim 11, wherein the quantum computer (140) is configured to perform 1-qubit and 2-qubit operations on the two quantum registers (210, 220), and wherein the classic computer (130) is configured to represent the time evolution U(t) (230), preferably by means of a Trotter decomposition, by a sequence of these 1-qubit and 2-qubit operations and to instruct the quantum computer (140) to perform this sequence.The system (100) of claim 12, wherein the 2-qubit operation is a controlled NOT, cNOT, and the 1-qubit operations include at least two elements from the following list: rotations about the x-axis R x, rotations about the y-axis R y rotations about the z-axis R z, phase rotations of the excited state T, and Hadamard gate H.The system according to any of claims 10 to 13, wherein the measurement time t is chosen to minimize the influence of excited states.A computer readable storage medium including instructions which, when executed on the classical computer (130) of the system (100) according to claims 10 to 14, implement the method according to any of claims 1 to 9.

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