Methods for solving optimization problems on a quantum computer by using local energy detuning

Abstract

This invention is based on the idea of ​​solving an NP-complete optimization problem using a quantum computer by modeling the function to be optimized using the Hamiltonian of a quantum system and then driving the system into its ground state. The assignment of the ground state then solves the optimization problem. To solve the problem underlying the invention, a method for solving an optimization problem on a graph using Rydberg states is proposed, the method comprising the steps of: modeling the optimization problem by a graph with N nodes and K edges, encoding the N nodes of the graph by providing a system of N atoms numbered i ∈ {1, ..., N}, and encoding the K edges of the graph, wherein an edge K i,j between atoms (i,j) through interactions with interaction energy V i,jbetween the atoms (i,j) is encoded, setting energy imbalances Δ i0 of the individual atoms i, such that the ground state of the system of N atoms solves the optimization problem on the graph, driving the system of N atoms into the ground state and reading it out, whereby it is provided that the energy imbalances Δ i0 The respective atoms can be individually adjusted.

Description

[0001] The invention relates to the field of atomic quantum computers. In particular, the invention relates to a method for solving an optimization problem on a graph using Rydberg states. Technological background

[0002] One such method is known, for example, from US patent 2021 / 0279631 A1. This patent describes systems and methods relating to the selective arrangement of a large number of qubits in a spatial structure for encoding a quantum computing problem. Exemplary arrangement techniques can be used to encode various quantum computing problems. The large number of qubits can be brought into a final state using different control techniques. The final state can be measured to identify an exact or approximate solution to the quantum computing problem.

[0003] Also known from EP 4 141 752 A1 is a method for optimizing a function with respect to a group of elements, wherein the method comprises: obtaining a graph with vertices and edges, where the vertices represent the elements and the edges represent the properties between the elements; determining a partition of the vertices of the graph between two separate subsets to satisfy a partition criterion, wherein the partition criterion states that a cut number with respect to the cut of the edges of the graph is maximal to obtain the partition, the determination phase being carried out by a quantum computer; optimizing a function with respect to the set of elements by partitioning the elements of the set of elements into two separate subsets based on the determined partition.

[0004] Methods and systems for performing non-classical calculations are known from WO 2021 / 178038. These methods and systems generally employ a plurality of spatially separated optical trapping sites to trap a plurality of atoms, one or more electromagnetic feed units to apply electromagnetic energy to one or more atoms of the plurality to cause the atoms to assume one or more superposition states of a first atomic state and a second atomic state, one or more entanglement units to quantum mechanically entangle at least a subset of the one or more atoms in the one or more superposition states with at least one other atom of the plurality, and one or more optical readout units to perform measurements of the superposition states to obtain the non-classical calculation.

[0005] WO 2022 / 101145 A1 relates to a method for arranging atoms in a target array of optical traps with predefined positions, comprising: generating a given number of target traps at the predefined positions; generating reservoir traps, wherein the reservoir traps and the target traps form a trap array; defining admissible paths between traps of the trap array; loading atoms into the trap array to generate an initially charged trap array; determining the positions of the atoms in the initially charged trap array; computing a sequence of movements using a rearrangement algorithm based on the initially charged trap array and the admissible paths; and applying the sequence of movements to rearrange the atoms in the trap array and form a final charged trap array. Description of the invention: task, solution, advantages

[0006] The invention is based on the objective of solving optimization problems, in particular NP-complete problems, preferably the maximum-cut problem (MaxCut), using quantum computers.

[0007] The maximum-cut problem is the problem of partitioning a graph with N nodes and K edges (possibly with different weights) into two subsets such that the total weight of the edges between the two subsets is maximized. The maximum-cut problem is NP-complete, meaning that every problem in the class NP, especially NP-hard problems, can be reduced to this problem in polynomial time, i.e., with a time complexity that scales more slowly than exponentially with the length of the input. NP-hard problems have the property of not being solvable efficiently, i.e., not in polynomial time, by classical computers so far, and presumably in principle.

[0008] This invention is based on the idea of ​​solving an NP-complete optimization problem using a quantum computer by encoding the function to be optimized using the Hamiltonian of a quantum system and then driving the system into its ground state. The assignment of the ground state then solves the optimization problem.

[0009] To solve the problem underlying the invention, a method for solving an optimization problem on a graph using Rydberg states is proposed, the method comprising the steps: Modeling the optimization problem by a graph with N nodes and K edges, encoding the N nodes of the graph by providing a system of N atoms numbered with i ∈ {1, ..., N}, encoding the K edges of the graph, where one edge K i,j between atoms (i,j) through interactions with interaction energy V i,jbetween the atoms (i,j) is encoded, setting energy imbalances Δ i0 of the individual atoms i, such that the ground state of the system of N atoms solves the optimization problem on the graph, driving the system of N atoms into the ground state and reading it out, whereby it is provided that the energy imbalances Δ i0 The respective atoms can be individually adjusted.

[0010] According to the procedure, to solve an optimization problem on a graph, the N nodes of the graph are encoded by atoms in a trap, and the K edges between these nodes are encoded by the interaction between these atoms.

[0011] Preferably, the N atoms are neutral atoms, each in an atomic ground state |0〉 i or a Rydberg state |1〉 i present, whereby the interaction energy between two atoms is determined by the interaction between the respective Rydberg states. Vi,j=C6d(i,j)6 is given where d(i,j) is the distance between the i-th and the j-th atom and C6 is the van der Waals coefficient.

[0012] Preferably, each node i is represented by a single neutral atom in a ground state |0〉 i or a Rydberg state |1〉 i may be the case.

[0013] The atoms are arranged at a distance from each other, preferably with the aid of optical tweezers, so that, to a first approximation, only the interaction between two atoms in the Rydberg state is observed. Vi,j=C6d(i,j)6 This is relevant because the Rydberg states have a much larger extent than the ground states. Here, C6 is the van der Waals coefficient of the corresponding Rydberg states, as explained by zbin Vaillant et al., J. Phys. B: At. Mol. Opt. Phys. 45 135004 (2012). The Rydberg states are preferentially chosen such that C6 is positive, meaning the interaction is repulsive.

[0014] Preferably, the atoms are positioned outside the Rydberg blockade radius. The method is therefore not restricted to so-called "unit-disk encoding," as, for example, in PRX QUANTUM 4, 010316 (2023). This means that, within the framework of the method, the graph of the optimization problem can be represented directly by the atoms and does not first need to be converted into a unit-disk graph. This reduces the simulation effort, since each atom can directly correspond to one of the N nodes of the graph and not, as in unit-disk encoding, to one of the N(N-1) / 2 possible edges between the N nodes.

[0015] Preferably, the N atoms are individually fixed in optical tweezers. In this way, the distances d(i,j) can be adjusted in particular.

[0016] With this encoding of nodes and edges, the optimization problem can be represented by the following Hamiltonian: H0=∑iΔi0ni+12∑i,jVi,jninj where ni = |1〉〈1| i the occupation number of the i-th atom in the excited state, Δ i0 the individual energy imbalance of the i-th Rydberg state and V i,j The weight of the edge between nodes i and j is represented by the d(i,j) 6 As a first approximation, only nearest-neighbor interactions are encoded.

[0017] By appropriately choosing the Δ i0 to the V i,j Various optimization problems and other graph problems can be represented for the graph (N,K).

[0018] In particular, the Hamiltonian (2) can be expressed in the space of excitations |0) i and |1〉 i as spin ½ - Ising-Hamiltonian HI=−12∑i,jJi,jσiσj−∑ihjσj with σ i ∈ {-½, ½}, J i,j = -V i,j and hi=−Δi−12∑jVi,j describe, so that the present invention can also be used to solve general Ising problems.

[0019] Preferably, the optimization problem is a max-cut problem, and the energy detuning Δ i0 is caused by an energy detuning of the Rydberg state of the i-th atom Δi0=12∑jVi,j set.

[0020] Alternatively, the optimization problem can also be a Maximum Independent Set (MiS) problem. In this case, Vi,j=Δi0Δj0.

[0021] It may be further preferred that the energy imbalance Δ i0 an energy detuning of the Rydberg state of the i-th atom, which is generated by means of the AC Stark effect by a laser focused on the i-th atom.

[0022] As can be seen from Table 1, using the example of 2 atoms with configuration |n1n2〉, the system of equations (2) and (3) encodes the maximum-cut problem: Atomic configuration Energy of the configuration |00〉 0 |01〉 Δ2=−12V1.2 |10〉 Δ1=−12V1,2 |11〉 Δ1+Δ2+V1,2=−12V1,2−12V1,2+V1,2=0

[0023] An edge between two nodes of the same state has a higher energy than an edge between two nodes of different states.

[0024] Preferably, driving the system to its ground state includes the steps: a) coupling all N atoms to an external laser field with the Rabi frequency Ω; b) temporal variation of energy imbalances Δ i (t) of the respective atoms and the external field Ω(t), where in the final state (t=T) Ω(T)=0 and Δ i (T)=Δ i0 applies; and c) reading out the achieved state by fluorescence measurement of the N atoms.

[0025] To find the ground state of the interacting system, all atoms are preferentially coupled to another external laser field, which defines the transition between the states |0〉 i and |1〉 i with the Rabi frequency Ω. The corresponding coupling Hamiltonian is by HΩ=ℏΩ2∑i(|0〉〈1|i+|1〉〈0|i) given, where the rabbi frequency Ω is proportional to the electric field strength of the external laser field.

[0026] Preferably, it is provided that in the initial state Ω(0)=0, so that Ω(t) is taken from 0 to a maximum and back to 0, preferably Δ i (0)=-Δ i0 holds and where the maximum of Ω(t) with the zero crossing of all Δ is particularly preferred i (t) coincides.

[0027] Therefore, lasers are preferred for adjusting the Δ i and of Ω time-modulatable, so that to drive the system into the ground state of the system a time course of the values ​​Δ i (t) and Ω(t) is set, where Ω(t) is driven from 0 at t=0 through a maximum back to 0 at t=T and simultaneously Δ i (t) of preferred -Δ i0 at t=0 to Δ i0 is driven at t=T.

[0028] After this procedure has been carried out, the occupancy of the achieved state is preferably determined by fluorescence measurement of the N atoms in the trap, by which the Rydberg states are de-excited by emission of light.

[0029] Preferably, steps a) to c) are repeated several times and in a further step d) a statistical distribution of the states measured in the respective steps c) is determined.

[0030] Using the statistics determined under d), an average energy expectation value 〈E〉 is then determined.

[0031] The distribution determined in step d) is particularly preferred for use in a loop encompassing steps a) to d) to determine the course of Ω(t) and Δ i (t) to optimize to minimize the energy of the measured states.

[0032] For this purpose, Ω(t) and Δ are preferably determined in each iteration k of the loop. i(t) varies, and an energy expectation value 〈E〉 k determined. The loop breaks when 〈E〉 k of 〈E〉 k-1 differs by less than a threshold value ε.

[0033] The expected value 〈E〉 is particularly preferred for this purpose, as shown, for example, in Zohu et al., Phys. Rev. X, 10, 021067 (2020), as the function to be minimized for a classical optimization of Δ i (t) and Ω(t) are used.

[0034] Also claimed is a device for solving optimization problems using quantum states.

[0035] This device comprises a vacuum chamber, a first laser for generating optical tweezers to hold N individual atoms at defined distances from each other in the vacuum chamber, and a second laser configured to adjust energy imbalances Δ i0the atomic energy levels of the N atoms by the AC Stark effect, a third laser for optical excitation of Rydberg states of the N atoms with the Rabi frequency Ω, a first local light modulator for modulating the first laser, an optical element to focus the first and second lasers onto the vacuum chamber, and a measuring device for fluorescence measurement of the N atoms.

[0036] The device further includes a second local light modulator for modulating the second laser, which allows for individual adjustment of the energy detuning Δ i0 The device enables the N atoms to be arranged on a graph with N nodes and K edges to encode the N nodes of an optimization problem.

[0037] The vacuum chamber is used to hold a large number of preferably ultracold atoms.

[0038] In this process, the first and second lasers are preferably each split into several beams by a first and second local light modulator respectively, and focused onto the vacuum chamber using an optical element, for example a lens.

[0039] The measuring device for performing fluorescence measurements on the N atoms held in the vacuum chamber can be a camera.

[0040] Preferably, the device is configured to configure the N atoms in the vacuum chamber such that they are each in a ground state |0〉 i or a Rydberg state |1〉 i are present, where the encoding of the graph is the encoding of each edge K i,j of the graphene through interaction between the atoms (i,j) in the respective Rydberg states with interaction energy Vi,j=C6d(i,j)6 includes, where d(i,j) is the distance between the i-th and the j-th atom and C6 is the van der Waals coefficient.

[0041] Preferably, the distance d(i,j) is chosen such that it is larger than the Rydberg blockage radius of the Rydberg states used.

[0042] In particular, different interaction strengths can be used to achieve different weightings of the edges.

[0043] Preferably, the optimization problem is a max-cut problem, or a maximum independent set problem.

[0044] Furthermore, the second laser is preferably set to each Rydberg state with an energy detuning of Δ i0 to adjust, whereby for the Max-cut problem Δi0=−12∑jVi,j and for the Maximum Independent Set Problem V i,j = Δ i0 Δ j0 applies.

[0045] Preferably, the claimed device further comprises a control unit, a first optical modulator for time-dependent control of the second laser, a second optical modulator for time-dependent control of the third laser, wherein the control unit is configured to a) control the first optical modulator, the energy deviations Δ i (t) to modulate such that Δ i (T)=Δ i0 a) the control unit is set up to control the second optical modulator, to modulate the intensity of the third laser and thus the Rabi frequency Ω of the transition so that Ω(t) is driven from Ω(0)=0 to a maximum and back to Ω(T)=0, and where the control unit is set up to perform a fluorescence measurement on the N atoms at time T using the measuring device.

[0046] Preferably, the device further includes a fourth laser and a third optical modulator for time-dependent control of the fourth laser, wherein the fourth laser is adjusted, with the aid of the second local light modulator, to each Rydberg state to an individual energy detuning of - Δ i0 to adjust, whereby the total energy imbalance Δ i (t) of the respective atom is thus generated by the second laser and the fourth laser, and the control unit is further set up to b') control the third optical modulator, the energy imbalances Δ i (t) to modulate such that Δ i (T)=-Δ i0 . applies.

[0047] Preferably, the control unit is set up to repeat steps a), b), c), and, if applicable, b'), multiple times and in step d) to generate statistics on the occupied states of the N atoms from the fluorescence measurements of steps c).

[0048] Preferably, the control unit is further configured to calculate an expected value 〈E〉 for the energy of the system using the statistics thus obtained.

[0049] Preferably, the control unit is configured to repeatedly execute steps a) to d) in a loop to determine the behaviors of Ω(t) and Δ. i (t) to optimize to minimize the energy of the measured states.

[0050] Preferably, the curves of Ω(t) and Δ are i (t) optimized using a classical optimization procedure to minimize the energy of the measured states.

[0051] Preferably, an expected value 〈E〉 is obtained during the k-th iteration of steps a) to d). k according to the Ω curves k (t) and Δ i,k (t) is calculated, and the loop is terminated when |〈E〉 k - 〈E〉 k-1 | < ε for a corresponding, previously determined threshold value ε.

[0052] In summary, a feature of the invention is the use of local energy imbalances Δ iTo solve optimization problems such as the maximum cut or the maximum independent set (MIS) problem in a hardware-efficient manner on a quantum computer, local energy detuning has not yet been used for the direct encoding and solution of optimization problems. In particular, the atoms can be positioned outside the so-called Rydberg blockade radius, which can be achieved either by larger distances between the atoms or by using low excitation energies for the Rydberg states. The resulting lower interaction energy between atoms can then be completely compensated by local light fields, thus enabling the realization of Hamiltonians, the encoding of which on the Rydberg platform previously required a significant overhead in the number of qubits. In particular, by choosing a suitable local detuning Δ iThe Ising-Hamiltonian can be encoded without qubit overhead, which is relevant for a wide variety of optimization problems. This direct encoding of the Ising-Hamiltonian without qubit overhead can be implemented on any quantum computer capable of realizing spin models and generating local energy detuning for individual qubits.

[0053] The described hardware-efficient coding allows problems like the MaxCut or MIS problems to be encoded without additional overhead in the number of qubits. This significantly reduces the requirements for the number and quality of available qubits, thereby considerably increasing the number and size of solvable optimization problems. Furthermore, the use of local light fields in a variational algorithm offers the possibility of correcting local inhomogeneities, e.g., in the depth of the optical tweezers, and thus dynamically addressing a significant source of hardware errors. Short description of the characters

[0054] They show Fig. 1 a flow chart of a process according to embodiments of the present invention, Fig. 2a an example of a graph with weighted edges, Fig. 2b an example of an atomic arrangement that forms the graph from Fig. 2a implemented, Fig. 2c an example of the optimized curves of Ω(t) and Δ i (t) to solve the maximum-cut problem on the graph from Fig. to solve 2a, and Fig. 3 an arrangement according to an embodiment of the present invention. Detailed description of the characters

[0055] Fig. Figure 1 shows the flow chart of a process in accordance with the present invention.

[0056] In the first step (101), an optimization problem is formulated. This problem is then mapped in the next step (102) to a graph problem, for example, a maximum-cut problem. In the following step (103), this graph problem is then transformed into a two- or three-dimensional system of atoms, where the nodes are represented by atoms whose edge weights w ij on Rydberg interactions V i,j and the cost function E to be optimized by the system Hamiltonian H including local detuning Δ i , i.e., energy imbalances of the individual atoms i are represented.

[0057] In the subsequent step 104, the ground state of the system encoded in step 103 is prepared. This is done by coupling the ground |0〉 i and Rydberg states |1〉 i of the atoms via a Rabi frequency Ω, where both the Δ iBoth (t) and Ω(t) are varied over time. In particular, Ω(t) runs from zero through a maximum and back to zero, while Δ i (t) in advantageous ways like f(t) Δ i The process is carried out where f(t) progresses from a starting value, preferably -1, to 1. In the following step 105, the populations in the state reached after traversing according to step 104 are measured, and in step 106 the cost function, i.e., the energy of the reached state, is calculated.

[0058] In decision step 107, it is now checked whether the achieved energy is minimal, for example iteratively by identifying a minimum when varying the parameters. If the energy is not identified as minimal, i.e., if, for example, the energy E achieved in the k-th step is not k , or the energy expectation value 〈E〉 calculated from several measurements of this step k by more than one, preferably predetermined, threshold value ε of the energy of the previous pass Ek-1 , respectively the expected value of the previous trial 〈E〉 k-1 , distinguishes, in step 108 the form of f(t) and Ω(t), and preferably the positions of the atoms are varied, and the procedure is continued in preparation step 103.

[0059] If the energy E achieved k or the achieved expected value 〈E〉 k If the minimum value is recognized in step 108, the achieved minimum is output in step 109 and the procedure is terminated.

[0060] Fig. Figure 2a shows an example of a graph with weighted edges modeled in step 102 of the procedure. It depicts a prototypical connected graph with 4 nodes (black spheres) and 3 edges, for which the MaxCut problem is to be solved.

[0061] Fig. Figure 2b shows the atom configuration generated in step 103 for the graph in Fig.2a, where the atoms correspond to the nodes of the graph. The weights at the edges in (a) are encoded as Rydberg interactions between the atoms, the strength of which can be adjusted by choosing suitable distances between the atoms. The spatial configuration of the atoms is chosen such that unwanted interactions between atoms without edges are minimized.

[0062] Fig. Figure 2c shows an optimal protocol applied in step 104, i.e., the product of classical optimization by varying the parameters. Initially, all atoms are in their ground state, in which no interactions occur. The global laser intensity, proportional to Ω(t), which is experienced uniformly by all atoms, and the local light displacement Δ i (t) that the i-th atom experiences are varied in an optimal way over time so that the ground state of the interacting system is reached.

[0063] The weights of the graph here are w 14 =6, w 24 =3 and w 34 =1, the final values ​​of the local detunings are Δ1 =-1 / 2V(r 14 )=-w 14 , Δ2=-1 / 2V(r 24 )=-w 24 , Δ3=-1 / 2V(r 34 )=-w 34 and Δ4=-1 / 2(V(r 14 )+V(r 24 )+V(r 34 ))=-(w 14 +w 24 +w 34 These values ​​ensure that the model's ground state solution also represents the solution to the MaxCut problem for the problem graph (see inset in the top left of the bottom panel). The calculated fidelity F, which quantifies the overlap of the instantaneous ground state with the solution ground state, shows that the claimed method can approximate the ground state of the target system very well and thus solves the MaxCut problem.

[0064] Fig.Figure 3 shows a device (300) according to an embodiment of the present invention. Atoms (302) in a vacuum chamber (301) are trapped in an optical tweezer potential (310) generated by illuminating a first local light modulator (311). The position of the individual atoms can be controlled with this first local light modulator to map the respective graph problem. Further light fields (320, 320') are used to control the local energy imbalances Δ i to generate at the position of each atom.

[0065] With a second local light modulator (321), the relative light intensity at each atomic position can be precisely controlled to adjust the detuning Δ i to adjust for each individual atom. By using frequency components that are detuned by the resonance (blue (+δ) and red (-δ) both positive and negative values ​​of detuning can be achieved to adjust the ramps in Fig.2c or step 104 to be implemented.

[0066] The temporal form f(t) of the local energy imbalances Δ(t) = f(t)(Δ1,Δ2,...,Δ) can be determined by optical modulators (here exemplarily 322 and 323) controlled by a control unit (340). N ) are controlled. Simultaneously, the atoms are globally illuminated with light (330) that is resonant with the Grund-Rydberg transition. Finally, the distribution of the Rydberg excitations is measured with a camera (305), e.g., using fluorescence imaging (304).

[0067] For each set of variation parameters, the values ​​n are obtained (105) for the occupation of the Rydberg states for each atom in order to calculate the corresponding energy of the system according to equation (2) (106). The control unit (340) is set up to repeat the entire experimental procedure multiple times in order to obtain the expectation value 〈E〉, which is then minimized by updating the variation parameters in a classical optimization loop (108) in order to obtain the ground state and thus solve the optimization problem. List of reference symbols 101 Optimization Problem 102 Graph problem 103 Coding the graph problem using atoms 104 Preparation of the ground state 105 Measurement of Occupations 106 Calculation of energy 107 Check if the energy is minimal 108 Variation of the parameters 109 Solution 301 Vacuum chamber 302 atoms 303 lens 304 Fluorescence 305 camera 310 Light field of the optical tweezers 311 local light modulator 320 light field for positive energetic mood changes 320' light field for negative energetic imbalances 321 local light modulator 322 optical modulator 323 optical modulator 330 light field for the Rydberg excitations 331 optical modulator 340 Control unit QUOTES INCLUDED IN THE DESCRIPTION

[0000] This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited patent literature

[0000] US 2021 / 0279631 A1

[0002] EP 4 141 752 A1

[0003] WO 2021 / 178038

[0004] WO 2022 / 101145 A1

[0005] Cited Non-Patent Literature

[0000] Vaillant et al., J. Phys. B: At. Mol. Opt. Phys. 45 135004 (2012

[0013] Zohu et al, Phys. Freeze. X, 10, 021067 (2020

[0033]

Claims

[1] A method for solving an optimization problem on a graph using Rydberg states, comprising: Modeling (102) the optimization problem by a graph with N nodes and K edges; encoding (103) the N nodes of the graph by providing a system of N atoms (302) numbered by i ∈{1, ..., N}; Encode the K edges of the graph, where an edge K i,j between atoms (i,j) by interactions with interaction energy V i,j is encoded between the atoms (i,j); Setting energy imbalances Δ i0 of the individual atoms i, so that the ground state of the system of N atoms (302) solves the optimization problem on the graph; Driving (104) the system of N atoms (302) into the ground state and Reading (105, 106) of the same, characterized by that the energy imbalances Δ i0of the respective atoms can be adjusted individually. [2] The method of claim 1, wherein N atoms (302) are neutral atoms each in an atomic ground state |0〉 i or a Rydberg state |1〉 i and where the interaction energy between two atoms is determined by the interaction between the respective Rydberg states Vi,j=C6d(i,j)6 where d(i,j) is the distance between the i-th and the j-th atom and C6 is the van der Waals coefficient, with the atoms preferentially positioned outside the Rydberg blockade radius of the corresponding Rydberg states. [3] The method of claim 2, wherein the optimization problem is a max-cut problem, and wherein the energy detuning Δ i0 by an energy detuning of the Rydberg state of the i-th atom to Δi0=−12∑jVi,j is set, or where the optimization problem is a Maximum Independent Set Problem, and where the energy detuning Δ i0 by detuning the energy of the Rydberg state of the i-th atom so that V i,j = Δ i0 Δ j0 . [4] Method according to one of claims 1 to 3, wherein the N atoms (302) are individually fixed in optical tweezers (310) and / or wherein the energy detuning Δ i0 is an energy detuning of the Rydberg state of the i-th atom, which is produced by the AC Stark effect by a laser (320) focused on the i-th atom. [5] The method of any one of claims 1 to 4, wherein driving (104) the system to the ground state includes: a) coupling all N atoms to an external laser field (330) with the Rabi frequency Ω; b) Temporal variation of energy imbalances Δ i(t) of the respective atoms and the external field Ω(t), where in the final state (t=T) Ω(T)=0 and Δ i (T)=Δ i0 applies; and c) Reading (105) of the achieved state by fluorescence measurement (304) of the N atoms (302). [6] Method according to claim 5, wherein in the initial state Ω(0)=0, so that Ω(t) is driven from 0 to a maximum and back to 0, wherein preferably Δ i (0)=-Δ i0 and particularly preferably the maximum of Ω(t) with the zero crossing of all Δ i (t), whereby preferably steps a) to c) are repeated several times and in a further step d) a statistical distribution of the states measured in the respective steps c) is determined, wherein particularly preferably the distribution determined in step d) is used to determine the course of Ω(t) and Δ i (t) to minimize the energy of the measured states (108). [7] Device (300), preferably designed to carry out a method according to one of the preceding claims, comprising: a vacuum chamber (301), a first laser (310) for generating optical tweezers to hold N individual atoms (302) at defined distances from each other in the vacuum chamber, a second laser (320) arranged to adjust energy detunings Δ i0 the atomic energy levels of the N atoms by the AC Stark effect, a third (330) laser for optical excitation of Rydberg states of the N atoms with the Rabi frequency Ω, a first local light modulator (311) for modulating the first laser (310); an optical element (303) for focusing the first and second lasers (310, 320) onto the vacuum chamber (301), and a measuring device (305) for fluorescence measurement (304) of the N atoms, characterized by , that the device comprises a second local light modulator (321) for modulating the second laser (320), which allows individual adjustment of the energy detunings Δ i0 which allows N atoms, and that the device is arranged to arrange the N atoms (302) for encoding (103) the N nodes of an optimization problem on a graph with N nodes and K edges. [8] Device (300) according to claim 7, wherein the device is arranged to configure the N atoms (302) in the vacuum chamber (301) such that they are each in a ground state |0〉 i or a Rydberg state |1〉 i where the coding (103) of the graph involves coding each edge K i,j of the graphene by interaction between the atoms (i,j) in the respective Rydberg states with interaction energy Vi,j=C6d(i,j)6 wherein d(i,j) is the distance between the i-th and the j-th atom and C6 is the Van der Waals coefficient, wherein the atoms are preferably positioned outside the Rydberg blockade radius, wherein further preferably the optimization problem is a max-cut problem, and wherein even more preferably the second laser is set to detune each Rydberg state to an energy detuning of Δi0=−12∑jVi,j to set. [9] The device (300) of claim 8, further comprising a control unit (340); a first optical modulator (322) for time-dependent control of the second laser (320); and a second optical modulator (331) for time-dependent control of the third laser (330), wherein the control unit (340) is arranged to a) control the first optical modulator, the energy detunings Δ i (t) so that Δ i (T)=Δ i0applies, wherein the control unit (340) is further configured, b) to control the second optical modulator (331), to modulate the intensity of the third laser (330) and thus the Rabi frequency Ω of the transition such that Ω(t) is driven from Ω(0)=0 to a maximum and back to Ω(T)=0, and wherein the control unit (340) is further configured, c) to carry out a fluorescence measurement (304) on the N atoms (105) at time T using the measuring device. [10] The apparatus of claim 9, further comprising a fourth laser (320'); and a third optical modulator (323) for time-dependent control of the fourth laser, wherein the fourth laser is set to adjust each Rydberg state to an individual energy detuning of - Δ i0 to set, where the total energy detuning Δ i(t) of the respective atom is thus generated by the second laser (320) and the fourth laser (320'), and the control unit is further configured to b') control the third optical modulator (323), the energy detunings Δ i (t) so that Δ i (T)=-Δ i0 . applies. [11] Device according to claim 9 or 10, wherein the control unit (340) is arranged to run through steps a), b), c), and, if referred back via claim 10, b'), several times and in a step d) to generate statistics about the occupied states of the N atoms from the fluorescence measurements (304) of steps c), wherein preferably the control unit (340) is further arranged to run through a loop comprising steps a) to d) several times in order to determine the courses of Ω(t) and Δ i (t) to minimize the energy of the measured states.

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