Method, quantum computer system, computer program and computer-readable storage medium for determining a physical information of a molecule with a quantum computer system

Abstract

A method for determining a physical information of a molecule with a quantum computer system is specified, the method comprising: - providing (S1) a fermionic Hamiltonian characteristic of an initial physical information of the molecule, - transforming (S2) the fermionic Hamiltonian to an initial qubit Hamiltonian comprising an initial qubit operator pool configured to act on at least two qubits, - determining (S3) at least one stable qubit from the at least two qubits when the initial qubit Hamiltonian is provided to the at least two qubits, - determining (S4) a reduced qubit operator pool dependent on the at least one stable qubit, and - determining (S5) the physical information dependent on the reduced qubit operator pool. Further, a quantum computer system, a computer program and a computer-readable storage medium are specified.

Description

[0001] P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0002] 1

[0003] Description

[0004] METHOD, QUANTUM COMPUTER SYSTEM, COMPUTER PROGRAM AND COMPUTER-READABLE STORAGE MEDIUM FOR DETERMINING A PHYSICAL INFORMATION OF A MOLECULE WITH A QUANTUM COMPUTER SYSTEM

[0005] The present disclosure relates to a method, a quantum computer system, a computer program, and a computer-readable storage medium for determining a physical information of a molecule with a quantum computer system.

[0006] An object to be achieved is to provide a method which improves an operator pool of a qubit Hamiltonian for determining information of molecules and molecular systems. Furthermore, a quantum computer system, a computer program, and a computer-readable storage medium for determining a physical information of a molecule are to be provided.

[0007] The object is achieved by the subject matter of the independent claims. Advantageous embodiments, implementations and further developments are the subject matter of the respective dependent claims.

[0008] The method for determining a physical information of a molecule with a quantum computer system is described.

[0009] Exemplarily, also a physical information of a molecular system can be determined according to the method as follows. In particular, the molecule and the molecular system can be interchanged accordingly.

[0010] The quantum computer system comprises, for example, a quantum processing unit. Exemplarily, the quantum processing unit is an ion trap. This means, for example, that the ion trap is P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0011] 2

[0012] part of the quantum computer system. The quantum computer system is in particular configured to operate the ion trap for determining the physical information. Exemplarily, the ion trap is configured to trap, confine and / or modify at least two ions in the ion trap, exemplarily to perform quantum computations with the at least two ions.

[0013] Exemplarily, the ion trap comprises a set of electrodes. For example, a radio frequency, RF, voltage is applied to at least some of the electrodes such that a time-varying electric field is provided that is configured to trap, confine and / or modify the at least two trapped ions. For example, a direct current, DC, voltage is applied to at least some of the other electrodes such that a static electric field is provided that is configured to trap, confine and / or modify at least two trapped ions.

[0014] For example, a magnetic gradient is provided to the at least two trapped ions. Exemplarily, the magnetic gradient is provided by a permanent magnet arrangement and / or an electromagnet arrangement. This means that the at least two trapped ions are advantageously individually addressable due to the magnetic gradient.

[0015] Exemplarily, the physical information of the molecule is characteristic of an electronic structure of the molecule and / or a quantum mechanical behaviour of the molecule. The physical information is in particular characteristic of a Hamiltonian, for example an Ising Hamiltonian, representative of the molecule. For example, the Ising Hamiltonian represents various aspects of the electronic structure and the quantum mechanical behaviour, such as a ground- state energy, spin interactions, spin correlations, a P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0016] 3

[0017] magnetization, electronic transitions, and / or electronic correlations.

[0018] According to at least one embodiment of the method, a fermionic Hamiltonian is provided which is characteristic of an initial physical information of the molecule. The fermionic Hamiltonian is, for example, characteristic of a system of fermions.

[0019] The fermionic Hamiltonian is determined, for example.

[0020] Exemplarily, the fermionic Hamiltonian is determined dependent on the initial physical information of the molecule. The initial physical information is, for example, predetermined, particularly being characteristic of at least one of a predetermined nuclear configuration of the molecule, a predetermined electronic configuration of the molecule, a predetermined interaction of electrons of the molecule, a predetermined interaction of electrons and nuclei of the molecule. This means that the initial physical information of the molecule is provided and, based on the initial physical information of the molecule, the corresponding fermionic Hamiltonian is determined.

[0021] In particular, the fermionic Hamiltonian comprises fermionic creation operators and fermionic annihilation operators. This means that the fermionic Hamiltonian is expressed in terms of the fermionic creation operators and the fermionic annihilation operators. Further, the fermionic Hamiltonian comprises, for example, a first coefficient characteristic of a one-body interaction and / or a second coefficient characteristic of a two-body interaction. P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0022] 4

[0023] According to at least one embodiment of the method, the fermionic Hamiltonian is transformed to an initial qubit Hamiltonian comprising an initial qubit operator pool configured to act on at least two qubits. In particular, the initial qubit Hamiltonian is determined by mapping the fermionic Hamiltonian to a qubit representation using a fermion-to-qubit transformation. For example, a Jordan-Wigner transformation, a Bravyi-Kitaev transformation or a Parity transformation is used for transforming the fermionic Hamiltonian to the initial qubit Hamiltonian.

[0024] Exemplarily, the initial qubit Hamiltonian comprises a plurality of qubit operators configured to act on the at least two qubits. In particular, the initial qubit Hamiltonian comprises a plurality of combinations of the qubit operators configured to act on the at least two qubits, forming the initial qubit operator pool. This means that the initial qubit Hamiltonian is expressed in terms of the qubit operators comprised in the initial qubit operator pool.

[0025] Further, the initial qubit Hamiltonian comprises, for example, a qubit coefficient.

[0026] Exemplarily, each qubit operator of the initial qubit operator pool is characteristic of an operation, when acting on a qubit, wherein the operation is characteristic of a flip of a state of the qubit, of a rotation of the qubit in space, or of a measure of a state of the qubit.

[0027] Each qubit on which the qubit operators act on is, for example, represented by an n-level quantum system, where n is a natural number bigger than or equal to 2, particularly a two-level quantum system. P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0028] 5

[0029] According to at least one embodiment of the method, at least one stable qubit is determined from the at least two qubits when the initial qubit Hamiltonian is provided to the at least two qubits. For example, for each stable qubit, the respective qubit operator or the respective combination of qubit operators is determined.

[0030] Exemplarily, a qubit is determined to be stable when the corresponding operation by a respective qubit operator or a respective combination of qubit operators does not flip a state of the respective qubit. Flipping a state is characteristic, for example, of when the state of the respective qubit is changed from one of the basic states to the other, i. e. from |0) to |1) or from |1) to |0).

[0031] According to at least one embodiment of the method, a reduced qubit operator pool is determined dependent on the at least one stable qubit. In particular, the qubit operator or the combination of qubit operators associated with the stable qubit is removed from the initial qubit operator pool for determining the qubit operator pool.

[0032] According to at least one embodiment of the method, the physical information is determined dependent on the reduced qubit operator pool. In particular, a reduced qubit Hamiltonian is determined based on the reduced qubit operator pool and, with the help of the qubit Hamiltonian, the physical information is determined. The qubit Hamiltonian serves in particular as a foundation for determining the physical information of the molecule by determining information regarding energy, dynamics, and statistical properties thereof. P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0033] 6

[0034] The method described herein above is, exemplarily, performed in the order indicated. The method described herein above is, exemplarily, a computer-implemented method.

[0035] An idea of the method described herein is, inter alia, to identify stable qubits, which are in particular qubits that do not flip to a different basic state to reduce an effective qubit Hamiltonian and the initial qubit operator pool.

[0036] Advantageously, using the reduced qubit operator pool leads to an adaptive ansatz that requires a smaller amount of ancilla qubits - particularly when determining the physical information.

[0037] According to at least one embodiment of the method, the reduced qubit operator pool is determined by a classical computing device.

[0038] According to at least one embodiment of the method, the physical information is determined by a quantum computing device. For example, the quantum processing unit is part of the quantum computing device.

[0039] For example, the classical computing device and the quantum computing device are part of the quantum computer system. Advantageously, the method is a hybrid quantum computer method. In particular, a classical computing approach is performed by the classical computing device and a quantum computational approach is performed by the quantum computing device, thus combining the benefits of both approaches.

[0040] According to at least one embodiment of the method, qubits of the quantum computing device are initialized based on the reduced qubit operator pool. Advantageously, by using the P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0041] 7

[0042] reduced qubit operator pool, resources of the quantum computing device can be saved compared to the initialization of the qubits based on the initial qubit operator pool.

[0043] According to at least one embodiment of the method, the reduced qubit Hamiltonian is determined dependent on the reduced qubit operator pool, and the qubits of the quantum computing device are initialized based on the reduced qubit Hamiltonian. Thus, the reduced qubit Hamiltonian is more compact than the initial qubit Hamiltonian, saving resources in both the classical computing device and the quantum computing device.

[0044] According to at least one embodiment of the method, the reduced qubit Hamiltonian is characteristic of molecular dynamics of the molecule.

[0045] According to at least one embodiment of the method, the reduced qubit Hamiltonian has a complexity which is smaller than a complexity of the fermionic Hamiltonian. Thus, a corresponding quantum calculation can be performed in a more resource - saving manner.

[0046] According to at least one embodiment of the method, a number of qubit operators comprised by the reduced qubit operator pool is smaller than a number of qubit operators comprised by the initial qubit operator pool. Additionally or alternatively, a number of combinations of qubit operators comprised by the reduced qubit operator pool is smaller than a number of combinations of qubit operators comprised by the initial qubit operator pool. P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0047] 8

[0048] According to at least one embodiment of the method, the at least one stable qubit is characteristic of a state of a respective qubit which does not introduce a change to a different basic state when the initial qubit operator pool acts on the at least two qubits. Thus, the stable qubit in particular does not flip its state, as described above.

[0049] According to at least one embodiment of the method, the initial qubit operator pool comprises a set of single-qubit terms and double-qubit terms. The single-qubit terms are, in particular, each characteristic of one qubit operator. The double-qubit terms are, in particular, each characteristic of one combination of two qubit operators.

[0050] According to at least one embodiment of the method, the single-qubit terms and the double-qubit terms are formed of a Pauli-X operator, Xi, a Pauli-Y operator, Yi, a Pauli-Z operator, Zi, and an Identity-I operator, Ii.

[0051] According to at least one embodiment of the method, the Pauli-X operator is characteristic of flipping a state of a respective qubit and the Pauli-Y operator is characteristic of applying a complex rotation to a state of a respective qubit. Exemplarily, the Pauli-X operator and / or the Pauli-Y are characteristic of a change to a different basic state.

[0052] According to at least one embodiment of the method, the Pauli-Z operator is characteristic of changing a phase of a state of a respective qubit and the Identity-I operator is characteristic of leaving a state of a respective qubit unchanged. Exemplarily, the Pauli-Z operator and / or the Identity-I operator are characteristic of no change to a different basic state. P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0053] 9

[0054] According to at least one embodiment of the method, the physical information is determined by a Variational Quantum Eigensolver, VQE, method, in particular an Adaptive Variational Quantum Eigensolver, ADAPT-VQE, method. In this embodiment, the quantum computer system comprises the classical computing device and the quantum computing device, wherein the classical computing device is used for determining the reduced qubit operator pool and the classical computing device and the quantum computing device are used for the VQE method.

[0055] In particular, in the VQE method, the qubits are initialized in the quantum computing device by using the reduced qubit operator pool. In particular, due to the reduced qubit operator pool and / or the reduced qubit Hamiltonian, the VQE is more effective and resource saving than using the initial qubit operator pool and / or the initial qubit Hamiltonian.

[0056] According to at least one embodiment of the method, a pharmaceutical substance is produced dependent on the physical information. In particular, the pharmaceutical substance comprises the molecule with the physical information. For example, the physical information is used for designing and optimizing molecular structures of the pharmaceutical substance to be produced.

[0057] In particular, for designing the pharmaceutical substance, the physical information of the molecule, e.g. being characteristic of the electronic structure, can be used to determine at least one of a chemical reactivity of the molecule, stability of the molecule, and interaction of the molecule with other elements. With this information, the P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0058] 10

[0059] pharmaceutical substance can be produced advantageously precisely to have particularly predetermined characteristics.

[0060] Furthermore, a quantum computer system for determining a physical information of a molecule is described. The quantum computer system is configured to perform the method described herein. Therefore, all features and embodiments disclosed in connection with the method are also disclosed in connection with the quantum computer system and vice versa.

[0061] In addition, a computer program is specified which comprises instructions which, when the computer program is executed by a computer, cause the computer program to execute the method described herein.

[0062] Further, a computer-readable storage medium is specified on which the computer program described herein is stored.

[0063] In the following, the method and the quantum computer system are explained in more detail with reference to exemplary embodiments and the associated Figures.

[0064] Figure 1 shows a flowchart of the method according to an exemplary embodiment.

[0065] Figure 2 shows a quantum computer system according to an exemplary embodiment.

[0066] Elements that are identical, similar or have the same effect are given the same reference signs in the figures. The figures and the proportions of the elements shown in the figures are not to be regarded as true to scale. Rather, P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0067] 11

[0068] individual elements may be shown exaggeratedly large for better representability and / or for better comprehensibility.

[0069] In method stage SI according to the exemplary embodiment of Figure 1 a fermionic Hamiltonian is provided which is characteristic of an initial physical information of a molecule. Exemplarily, the fermionic Hamiltonian is defined with a predetermined equation that describes a dynamic of the molecule.

[0070] In method stage S2, the fermionic Hamiltonian is transformed to an initial qubit Hamiltonian comprising an initial qubit operator pool configured to act on at least two qubits.

[0071] Exemplarily, the initial qubit operator pool is defined as a set of single and double excitations in the form of a set of Pauli operators.

[0072] Subsequently, at least one stable qubit is determined in method stage S3 from the at least two qubits when the initial qubit Hamiltonian is provided to the at least two qubits.

[0073] Further, a reduced qubit operator pool is determined in method stage S4 dependent on the at least one stable qubit.

[0074] Finally, the physical information is determined dependent on the reduced qubit operator pool.

[0075] The quantum computer system 1 according to Figure 2 exemplarily comprises an ion trap 2 as a processing unit of the quantum computer system, wherein the ion trap is located within a chamber 3. The ion trap 2 is connected to external components of the quantum computer system through the chamber 3 by a plurality of connections 4. For example, the P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0076] 12

[0077] connections 4 connect the ion trap 2 with electronic devices 5 and a classical computing device 6.

[0078] The electronic devices 5 comprise, exemplarily, a laser, a wavemeter, an acousto-optic modulator, an electro-optic modulator, a detector, a signal generator, an amplifier, a power supply, a piezo controller, a motor, analog-to-digital converters, signal generators such as radio frequency generators, microwave signal generators, low-frequency signal generators, and / or direct current signal generators. The electronic devices 5 can also be partially arranged within the chamber 3. The chamber 3 can be an ultra-high vacuum chamber, an extreme-high vacuum chamber and / or a cryostat.

[0079] The classical computing device 6 is configured, for example, to receive input data, e.g. the process information.

[0080] Exemplarily, the ion trap 2 is provided with a magnet arrangement which is configured to establish a magnetic gradient to the trapped ions of the ion trap 2.

[0081] The invention is not limited to the exemplary embodiments by the description of the latter. Rather, the invention encompasses any new feature as well as any combination of features, which in particular includes any combination of features in the claims, even if this feature or combination itself is not explicitly indicated in the claims or exemplary embodiments. P2024, 0778 WO N / E2024, 0117 October 28, 2025

[0082] - 13 -

[0083] Reference signs

[0084] 1 quantum computer system

[0085] 2 ion trap

[0086] 3 chamber

[0087] 4 connections

[0088] 5 electronic devices

[0089] 6 classical computing device

[0090] S1…S5 method stages

Claims

P2024, 0778 WO N / E2024, 0117 October 28, 202514Claims1. Method for determining a physical information of a molecule with a quantum computer system, the method comprising:- providing (S1) a fermionic Hamiltonian characteristic of an initial physical information of the molecule,- transforming (S2) the fermionic Hamiltonian to an initial qubit Hamiltonian comprising an initial qubit operator pool configured to act on at least two qubits,- determining (S3) at least one stable qubit from the at least two qubits when the initial qubit Hamiltonian is provided to the at least two qubits,- determining (S4) a reduced qubit operator pool dependent on the at least one stable qubit, and- determining (S5) the physical information dependent on the reduced qubit operator pool.

2. Method according to claim 1, wherein- the reduced qubit operator pool is determined by a classical computing device, and / or- the physical information is determined by a quantum computing device.

3. Method according to claim 2, wherein- qubits of the quantum computing device are initialized based on the reduced qubit operator pool.

4. Method according to any one of claims 2 or 3, wherein - a reduced qubit Hamiltonian is determined dependent on the reduced qubit operator pool, and- the qubits of the quantum computing device are initialized based on the reduced qubit Hamiltonian.P2024, 0778 WO N / E2024, 0117 October 28, 2025- 15 -5. Method according to claim 4, wherein- the reduced qubit Hamiltonian is characteristic of molecular dynamics of the molecule.

6. Method according to any one of claims 3 or 4, wherein - the reduced qubit Hamiltonian has a complexity which is smaller than a complexity of the fermionic Hamiltonian.

7. Method according to any one of claims 1 to 6, wherein - a number of qubit operators comprised by the reduced qubit operator pool is smaller than a number of qubit operators comprised by the initial operator pool.

8. Method according to any one of claims 1 to 7, wherein - the at least one stable qubit is characteristic of a state of a respective qubit which does not introduce a change to a different basis when the initial qubit operator pool acts on the at least two qubits.

9. Method according to any one of claims 1 to 8, wherein - the initial qubit operator pool comprises a set of single-qubit terms and double-qubit terms, and- the single-qubit terms and the double-qubit terms are formed of a Pauli-X operator, Xi, a Pauli-Y operator, Yi, a Pauli-Z operator, Zi, and an Identity-I operator, Ii.

10. Method according to claim 9, wherein- the Pauli -X operator is characteristic of flipping a state of a respective qubit and the Pauli -Y operator is characteristic of applying a complex rotation to a state of a respective qubit, andP2024, 0778 WO N / E2024, 0117 October 28, 202516- the Pauli-Z operator is characteristic of changing a phase of a state of a respective qubit and the Identity-I operator is characteristic of leaving a state of a respective qubit unchanged.

11. Method according to any one of claims 1 to 10, wherein - the physical information is determined by a Variational Quantum Eigensolver, VQE, method, in particular an Adaptive Variational Quantum Eigensolver, ADAPT-VQE, method.

12. Method according to any one of claims 1 to 11, wherein - a pharmaceutical substance is produced dependent on the physical information.

13. Quantum computer system (1) for determining a physical information of a molecule, wherein the system is configured to perform the method according to one of the preceding claims.

14. Computer program comprising instructions which, when the computer program is executed by a computer, cause the computer program to execute the method according to one of claims 1 to 12.

15. Computer - readable storage medium on which the computer program according to claim 14 is stored.

Images