Method for solving optimization problems on a quantum computer by utilizing local energy detunings

Abstract

This invention is based on the concept of solving an NP-complete optimization problem using a quantum computer by modelling the function to be optimized using the Hamilton function of a quantum system and then driving said quantum system into the basic state. Use of the basic state then solves the optimization problem. The problem on which the invention is based is solved by proposing a method for solving an optimization problem on a graph using Rydberg states, the method comprising the steps of: modelling the optimization problem by way of a graph having N nodes and K edges, encoding the N nodes of the graph by providing a system comprising N atoms consecutively numbered i ∈{1, …, N}, encoding the K edges of the graph, wherein an edge Ki,j between atoms (i,j) is encoded by way of interactions with interaction energy Vi,j between the atoms (i,j), adjusting energy detunings Δi0 of the individual atoms i so that the basic state of the system of N atoms solves the optimization problem on the graph, driving the system of N atoms into the basic state and reading said basic state, there being provision for the energy detunings Δi0 of the respective atoms to be adjusted individually.

Description

[0001] Description

[0002] Method for solving optimization problems on a quantum computer by using local energy detuning

[0003] 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.

[0004] Technological background

[0005] Such a method is known, for example, from US 2021 / 0279631 A1. This describes systems and methods relating to the selective arrangement of a plurality 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 plurality of qubits can be brought into a final state using various control techniques. The final state can be measured to identify an exact or approximate solution to the quantum computing problem.

[0006] Also known from EP 4 141 752 A1 is a method for optimizing a function with respect to a group of elements, the method comprising: obtaining a graph with vertices and edges, where the vertices represent the elements and the edges represent the properties between the elements; determining a subdivision of the vertices of the graph between two separate subsets to satisfy a partition criterion, where the partition criterion states that a cut number with respect to the intersection of the edges of the graph is maximal to obtain the partition, where the determination phase is performed by a quantum computer; optimizing a function with respect to the set of elements by dividing the elements of the set of elements into two separate subsets based on the determined partition. Methods and systems for performing non-classical calculations are known from WO 2021 / 178038.The methods and systems generally use a plurality of spatially separated optical trapping sites to trap a plurality of atoms, one or more electromagnetic delivery 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.

[0007] 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 allowed paths between traps of the trap array; loading atoms into the trap array to generate an initially loaded trap array; determining the positions of the atoms in the initially loaded trap array; calculating a sequence of moves using a reordering algorithm based on the initially loaded trap array and the allowed paths; and applying the sequence of moves to rearrange the atoms in the trap array and form a final loaded trap array.

[0008] Description of the invention: task, solution, advantages

[0009] The invention is based on the object of solving optimization problems, in particular NP-complete problems, preferably the maximum cut problem (MaxCut), with the aid of quantum computers. The maximum cut problem is the problem of partitioning a graph with N nodes and K, possibly differently weighted, edges into two subsets such that the total weight of the edges running between the two subsets is maximized. The maximum cut problem is NP-complete, which means that every problem in the NP class, in particular NP-hard problems, can be reduced to this problem in polynomial time, i.e. with a time expenditure 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, with classical computers to date, and probably in principle.

[0010] This invention is based on the idea of ​​solving an NP-complete optimization problem with the help of a quantum computer. Encoding the function to be optimized using the Hamiltonian function of a quantum system, which is then driven to the ground state. Assigning the ground state then solves the optimization problem.

[0011] To achieve the object 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, coding the N nodes of the graph by providing a system of N atoms, which are numbered with i G{1, ..., N}, coding the K edges of the graph, wherein an edge KJ between atoms (i,j) is encoded by interactions with interaction energy VJJ between the atoms (i,j), setting energy detunings A i0 of the individual atoms i, so 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 detunings A i0 of the respective atoms can be adjusted individually.

[0012] According to the method, 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. Preferably, the N atoms are neutral atoms, each in an atomic ground state |0 or a Rydberg state |l)j, where the interaction energy between two atoms is determined by the interaction between the respective Rydberg states. where d(i,j) is the distance between the i-th and the j-th atom and C6 is the van der Waals coefficient.

[0013] Preferably, each node i is represented by a single neutral atom in a ground state |0) f or a Rydberg state | l.

[0014] The atoms are arranged at a distance from each other, preferably with the help of optical tweezers, so that in a first approximation only the interaction between two atoms in the Rydberg state Vi j = 6 is relevant because the Rydberg states have a much larger extension than the ground states. Here, C6 is the van der Waals coefficient of the corresponding Rydberg states, as explained, for example, in Vaillant et al., J. Phys. B: At. Mol. Opt. Phys. 45 135004 (2012). Here, the Rydberg states are preferably chosen such that C6 is positive, thus the interaction is repulsive.

[0015] Preferably, the atoms are positioned outside the Rydberg blockade radius. The method is thus not restricted to so-called "unit-disk encoding," as in PRX QUANTUM 4, 010316 (2023), for example. 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 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-l) / 2 possible edges between the N nodes. Preferably, the N atoms are individually fixed in optical tweezers. In this way, in particular, the distances d(i,j) can be adjusted.

[0016] With this encoding of the nodes and edges, the optimization problem can be represented by the following Hamiltonian: where n t = the occupation number of the i-th atom in the excited state, A i0 is the individual energy detuning of the i-th Rydberg state and VJJ is the weight of the edge between nodes i and j. By the d(i,j) 6 Decay of the interaction, in a first approximation only nearest-neighbor interactions are encoded.

[0017] By choosing the appropriate A i0 For the VJJ, various optimization problems and other graph problems can be represented for the graph (N,K).

[0018] In particular, the Hamiltonian (2) can be written in the space of excitations |0) f and | l^as Spin >2 - Ising-Hamiltonian with Oi £{-%, %}, Ji,j= -VJJ un ben, 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 A i0is caused by an energy detuning of the Rydberg state of the i-th atom to Alternatively, the optimization problem can also be a Maximum Independent Set (MiS) problem. In this case,

[0020] Further preferably, it can be provided that the energy detuning A f0 is an energy detuning of the Rydberg state of the i-th atom, which is produced by the AC Stark effect by a laser focused on the i-th atom.

[0021] As can be seen from Table 1 for 2 atoms with configuration sees, the system of equations (2) and (3) encodes the maximum-cut problem:

[0022] An edge between two nodes of the same state has a higher energy than an edge between two nodes of different states.

[0023] Preferably, driving the system to the ground state comprises the steps of: a) coupling all N atoms to an external laser field with the Rabi frequency Q; b) temporal variation of energy detunings Aj(t) of the respective atoms and of the external field Q(t), where in the final state (t=T) Q(T)=0 and Ai(T)=A i0 and c) reading the achieved state by fluorescence measurement of the N atoms.

[0024] To find the ground state of the interacting system, all atoms are preferentially coupled to another external laser field, which drives the transition between the states |0 and |1 with the Rabi frequency Q. The corresponding coupling Hamiltonian is given by where the Rabi frequency Q is proportional to the electric field strength of the external laser field.

[0025] It is preferably provided that in the initial state Q(0)=0, so that Q(t) is driven from 0 to a maximum and back to 0, wherein preferably Aj(0)=- Ajo applies and wherein particularly preferably the maximum of Q(t) coincides with the zero crossing of all A;(t).

[0026] Lasers are therefore preferred for adjusting the and the Q can be modulated over time, so that to drive the system to the ground state of the system a temporal progression of the values and Q(t) is set, where Q(t) is driven from 0 at t=0 via a maximum back to 0 at t=T and at the same time z3j(t) is driven from preferably -A i0 at t=0 to Aio at t=T.

[0027] After this procedure, the occupancy of the achieved state is determined, preferably by fluorescence measurement of the N atoms in the trap, by which the Rydberg states are de-excited by emitting light.

[0028] 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.

[0029] Using the statistics determined under d), an averaged energy expectation value E) is then determined.

[0030] Particularly preferably, the distribution determined in step d) is used to optimize the course of Q(t) and A(t) in a loop comprising steps a) to d) to minimize the energy of the measured states. For this purpose, Q(t) and A(t) are preferably varied in each iteration k of the loop, and an energy expectation value E) k The loop terminates when E) k from ( ') fc-1 by less than a threshold value e.

[0031] Particularly preferred for this purpose is the expectation value E) then used as a function to be minimized for a classical optimization of ZJj(t) and Q(t), as shown, for example, in Zohu et al, Phys. Rev. X, 10, 021067 (2020).

[0032] Also claimed is a device for solving optimization problems using quantum states.

[0033] 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, a second laser, configured to adjust energy detunings A i0of the atomic energy levels of the N atoms by the AC Stark effect, a third laser for the optical excitation of Rydberg states of the N atoms with the Rabi frequency O, a first local light modulator for modulating the first laser, an optical element for focusing the first and the second laser onto the vacuum chamber, and a measuring device for fluorescence measurement of the N atoms.

[0034] The device further comprises a second local light modulator for modulating the second laser, which allows individual adjustment of the energy detunings A i0 of the N atoms. The device is configured to arrange the N atoms for encoding the N nodes of an optimization problem on a graph with N nodes and K edges.

[0035] The vacuum chamber is used to hold a large number of preferably ultracold atoms.

[0036] In this case, the first and second lasers are preferably split into several beams by a first and second local light modulator, respectively, and focused onto the vacuum chamber by means of an optical element, for example a lens.

[0037] The measuring device for performing fluorescence measurements on the N atoms held in the vacuum chamber can be a camera.

[0038] Preferably, the device is arranged to configure the N atoms in the vacuum chamber such that they are each in a ground state |0 or a Rydberg state |l\, wherein the coding of the graph comprises coding each edge KJJ of the graph by interaction between the atoms (i,j) in the respective Rydberg states with interaction energy Vij = 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.

[0039] Preferably, the distance d(i,j) is chosen so that it is larger than the Rydberg blockade radius of the Rydberg states used.-

[0040] Different weighting of the edges can be achieved, in particular, through different interaction strengths.

[0041] Preferably, the optimization problem is a max-cut problem or a maximum independent set problem.

[0042] Further preferably, the second laser is set to detune each Rydberg state to an energy detuning of A i0 where for the max-cut problem A zo = — - Vij and for the Maximum Independent Set Problem K fJ - = A i0 Aj0gilt.

[0043] Preferably, the claimed device further comprises a control unit, a first optical modulator for the time-dependent control of the second laser, a second optical modulator for the time-dependent control of the third laser, wherein the control unit is configured to a) control the first optical modulator, to modulate the energy detunings A;(t) such that Ai(T)=A i0 applies, wherein the control unit is further configured, b) to control the second optical modulator, to modulate the intensity of the third laser and thus the Rabi frequency Q of the transition such that Q(t) is driven from Q(0)=0 to a maximum and back to Q(T)=0, and wherein the control unit is further configured, c) to carry out a fluorescence measurement on the N atoms at time T using the measuring device.

[0044] Preferably, the device further comprises a fourth laser and a third optical modulator 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 — Aj O whereby the total energy detuning Aj(t) of the respective atom is thus generated by the second laser and the fourth laser, and the control unit is further configured to b') control the third optical modulator to modulate the energy detunings A;(t) such that Ai(T)=-A i0 . applies.

[0045] Preferably, the control unit is configured to run through steps a), b), c), and, optionally b'), several times and, in a step d), to generate statistics on the occupied states of the N atoms from the fluorescence measurements of steps c).

[0046] Preferably, the control unit is further configured to calculate an expected value ( ') for the energy of the system using the statistics thus obtained.

[0047] Further preferably, the control unit is configured to run through a loop comprising steps a) to d) several times in order to optimize the curves of Q(t) and A;(t) to minimize the energy of the measured states.

[0048] Preferably, the curves of Q(t) and A;(t) are optimized using a classical optimization method to minimize the energy of the measured states. Preferably, an expected value E) is determined during the k-th iteration of steps a) to d). k according to the curves Qk(t) and A i; k(t) is calculated, and the loop is aborted if !(£ < s for a corresponding pre-determined threshold value e.

[0049] In summary, one feature of the invention is the use of local energy detunings Ai to solve optimization problems such as the maximum cut or the maximum independent set problem (MIS) on a quantum computer in a hardware-efficient manner. Local energy detunings have not yet been used to directly encode and solve 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 small excitation energies of the Rydberg states. The resulting lower interaction energy between atoms can thus be fully compensated for by local light fields, thus enabling the realization of Hamiltonians, whose encoding on the Rydberg platform previously required a significant overhead in terms of the number of qubits.In particular, by choosing the appropriate local detunings Ai, the Ising Hamiltonian can be encoded without qubit overhead, which is relevant for a variety of optimization problems. This direct encoding of the Ising Hamiltonian without qubit overhead can be implemented on any quantum computer capable of implementing spin models and generating local energy detunings for individual qubits.

[0050] The hardware-efficient coding described above allows problems such as the MaxCut or MIS problem to be encoded in the number of qubits without additional overhead. This significantly reduces the requirements for the number and quality of available qubits and thus significantly increases the number and size of solvable optimization problems. In addition, the use of local light fields in a variational algorithm offers the possibility of correcting local inhomogeneities, for example, in the depth of the optical tweezers, thus dynamically eliminating a major source of hardware error. Brief description of the figures

[0051] It shows

[0052] Fig. 1 is a flow chart of a method according to embodiments of the present invention,

[0053] Fig. 2a an example of a graph with weighted edges,

[0054] Fig. 2b shows an example of an atom arrangement that implements the graph from Fig. 2a,

[0055] Fig. 2c shows an example of the optimized curves of Q(t) and Aj(t) to solve the maximum-cut problem on the graph of Fig. 2a, and

[0056] Fig. 3 shows an arrangement according to an embodiment of the present invention.

[0057] Detailed description of the characters

[0058] Fig. 1 shows the flow chart of a method in accordance with the present invention.

[0059] In the first step 101, an optimization problem is posed. This problem is then mapped to a graph problem, for example, a maximum-cut problem, in the next step 102. In the next step 103, this graph problem is transferred to a two- or three-dimensional system of atoms, where the nodes are represented by atoms, the edge weights w by Rydberg interactions Vjj, and the cost function E to be optimized by the system Hamiltonian H including local detunings Ai, i.e., energy detunings of the individual atoms i.

[0060] In the following step 104, the ground state of the system coded in step 103 is prepared. This is done by coupling the ground |0) f and Rydberg states | l) fof the atoms via a Rabi frequency Q, where both A;(t) and Q(t) are varied over time. In particular, Q(t) runs from zero via a maximum back to zero, while A;(t) runs advantageously like f(t) Ai, where f(t) runs 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, ie the energy of the reached state, is calculated.

[0061] In decision step 107, it is now checked whether the achieved energy is minimal, for example, iteratively by detecting a minimum when varying the parameters. If the energy is not detected as minimal, for example, if the energy Ek achieved in the k-th step, or the energy expectation value E calculated from several measurements of this step, kby more than one, preferably predetermined, threshold value e from the energy of the previous pass Ek-i, or the expected value of the previous pass E) k-1 , the form of f(t) and Q(t), as well as preferably the positions of the atoms, are varied in step 108, and the process is continued in the preparation step 103.

[0062] If the achieved energy Ek or the achieved expected value E) k was recognized as minimal in step 108, the minimum reached is output in step 109 and the method is terminated.

[0063] Fig. 2a shows an example of a graph with weighted edges modeled in step 102 of the method. It shows a prototypical connected graph with 4 nodes (black balls) and 3 edges, for which the MaxCut problem is to be solved.

[0064] Fig. 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 appropriate distances between the atoms. The spatial configuration of the atoms is chosen to minimize unwanted interactions between atoms without edges.

[0065] Fig. 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 the ground state, where no interactions occur. The global laser intensity, proportional to Q(t), experienced equally by all atoms, and the local light shift Aj(t) experienced by the i-th atom are varied over time in an optimal manner so that the ground state of the interacting system is reached.

[0066] The weights of the graph here are w i4 =6, w 24 =3 and w 34 =l, the final values ​​of the local detunings are Ai =-l / 2V(ri4)=-Wi4, A2=-l / 2V(r 24 )=-W24, A3=-l / 2V(r 34 )=-w 34 and A4=-l / 2(V(ri4)+V(r 24 )+V(r 34 ))=-(wi4+w 24 +w 34These values ​​ensure that the ground-state solution of the model also represents the solution to the MaxCut problem for the problem graph (see inset top left in 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 excellently approximate the ground state of the target system and thus solves the MaxCut problem.

[0067] Fig. 3 shows an apparatus (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 image the respective graph problem. Additional light fields (320, 320') are used to generate the local energy detunings Ai at the position of each atom.

[0068] With a second local light modulator (321), the relative light intensity at each atom position can be precisely controlled to adjust the detuning Ai for each individual atom. By using frequency components detuned from the resonance blue (+δ) and red (-δ), both positive and negative values ​​of detuning can be realized to achieve the ramps in Fig. 2c and step 104, respectively.

[0069] By means of optical modulators (here exemplified 322 and 323), which are controlled by a control unit (340), the temporal form f(t) of the local energy detunings A(t) = f(t)(Ai,A2,...,A N ) are controlled. At the same time, the atoms are globally illuminated with light (330) that is resonant to the fundamental Rydberg transition. Finally, the distribution of Rydberg excitations is measured with a camera (305), e.g., by fluorescence imaging (304).

[0070] For each set of variational parameters, the values ​​ni for the population of the Rydberg states for each atom are obtained from (105) to calculate the corresponding energy of the system according to equation (2) (106). The control unit (340) is configured to repeat the entire experimental procedure several times to obtain the expected value (E), which is then minimized by updating the variational parameters in a classical optimization loop (108) to obtain the ground state and thus solve the optimization problem.

[0071] List of reference symbols

[0072] 101 Optimization Problem

[0073] 102 Graph Problem

[0074] 103 Coding the graph problem by atoms

[0075] 104 Preparation of the ground state

[0076] 105 Measurement of occupations

[0077] 106 Calculation of energy

[0078] 107 Check if the energy is minimal

[0079] 108 Variation of parameters

[0080] 109 Solution

[0081] 301 Vacuum Chamber

[0082] 302 atoms

[0083] 303 lens

[0084] 304 Fluorescence

[0085] 305 Camera

[0086] 310 Light field of the optical tweezers

[0087] 311 local light modulator

[0088] 320 light field for positive energetic moods

[0089] 320' light field for negative energetic imbalances

[0090] 321 local light modulator

[0091] 322 optical modulator

[0092] 323 optical modulator

[0093] 330 Light field for the Rydberg excitations

[0094] 331 optical modulator

[0095] 340 Control Unit

Claims

Patent 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 i G{1, N}; Encoding the K edges of the graph, where an edge KJ between atoms (i,j) is encoded by interactions with interaction energy VJJ between the atoms (i,j); Setting energy imbalances A 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) thereof, characterized in that the energy detunings A i0 of the respective atoms can be adjusted individually.

2. The method according to claim 1, wherein N atoms (302) are neutral atoms each in an atomic ground state a Rydberg state | l)i, and where the interaction energy between two atoms is determined by the interaction between the respective Rydberg states K fJ - = 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 according to claim 2, wherein the optimization problem is a max-cut problem, and wherein the energy detuning A i0 by a Energy detuning of the Rydberg state of the i-th atom to A i0 = will, or where the optimization problem is a Maximum Independent Set Problem, and where the energy detuning A i0by detuning the energy of the Rydberg state of the i-th atom so that 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 A f0 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 according to any one of claims 1 to 4, wherein driving (104) the system to the ground state comprises: a) coupling all N atoms to an external laser field (330) with the Rabi frequency Q; b) temporal variation of energy detunings Ai(t) of the respective atoms and of the external field Q(t), wherein in the final state (t=T) Q(T)=0 and Ai(T)=A i0 and c) reading (105) the achieved state by fluorescence measurement (304) of the N atoms (302).

6. Method according to claim 5, wherein in the initial state Q(0)=0, so that Q(t) is driven from 0 to a maximum and back to 0, wherein preferably Ai(0)=-A io applies and particularly preferably the maximum of Q(t) coincides with the zero crossing of all A;(t), wherein preferably the steps a) to c) are run through 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 in a loop comprising the steps a) to d) the course of Q(t) and Ai(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 one another in the vacuum chamber, a second laser (320) designed to adjust energy detunings A i0of the atomic energy levels of the N atoms by the AC Stark effect, a third (330) laser for optically exciting Rydberg states of the N atoms with the Rabi frequency Q, 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 in that the device comprises a second local light modulator (321) for modulating the second laser (320), which allows individual adjustment of the energy detunings A i0 of the 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 N atoms (302) in the vacuum chamber (301) in such a way that they are each in a ground state a Rydberg state | l)i, where the coding (103) of the graph is the coding of each edge KJ of the graph by interaction between the atoms (i,j) in the respective Rydberg states with interaction energy Vij = 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, 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 A zo = to set.

9. Device (300) according to 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 configured to a) control the first optical modulator, to modulate the energy detunings Ai(t) such that Ai(T)=A i0 applies, 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 Q of the transition such that Q(t) is driven from Q(0)=0 to a maximum and back to Q(T)=0, and wherein the control unit (340) is further configured, c) to carry out a fluorescence measurement (304) on the N atoms at time T with the aid of the measuring device (105).

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 adjusted to adjust each Rydberg state to an individual energy detuning of — Aj O whereby the total energy detuning Aj(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) to modulate the energy detunings Aj(t) such that Ai(T)=-A i0 . applies.

11. Device according to claim 9 or 10, wherein the control unit (340) is set up 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 set up to run through a loop comprising steps a) to d) several times in order to optimize the courses of Q(t) and A;(t) to minimize the energy of the measured states.

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