Quantum computer

Abstract

The invention relates to a quantum computer (100) comprising: a quantum-mechanical system (110) having a single particle (120) with a non-zero rest mass, wherein the quantum-mechanical system (110) has a plurality of eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221), wherein the quantum-mechanical system (110) is designed and configured such that a subset of the eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) is used to realise at least two Q-N-its (241, 242, 243, 244, 245, 251, 252, 253), wherein a Q-N-it (241, 242, 243, 244, 245, 251, 252, 253) is a generalisation of a qubit to N states, N being an integer greater than or equal to two.

Description

[0001]U31281WO Vienna University of Technology Description Quantum Computer The invention relates to a quantum computer. Quantum computers are known in the prior art. There are various types of quantum computers based on different principles or technologies, e.g., ion traps, superconductors, neutral atom traps, in particular MOTs (magneto-optical traps), etc. These quantum computers typically use quantum bits. One object of the present invention is to improve upon the prior art. In particular, it is an object of the invention to realize a quantum computer with or in just a single particle. Another object of the invention is to provide a quantum computer whose quantum information is stored and processed in quantum bits. Yet another object of the invention is to provide a quantum computer whose computational complexity is lower compared to quantum computers of the prior art.Technology is reduced. A further object of the invention is to provide a quantum computer which has a low error rate and / or a long coherence time. It is a further object of the invention to provide a quantum computer which uses the same mechanism or force for addressing quantum units and for interaction between the quantum units. It is a further object of the invention to provide a quantum computer with increased security relevance. This object is achieved by a quantum computer with the features of independent claim 1. Advantageous embodiments of the invention are specified in the dependent claims. The following terms should be explained: A quantum mechanical system is understood to be a system which obeys the laws of quantum mechanics. A particle with a non-zero rest mass is a particle that possesses mass when it is at rest.Examples of particles with a non-zero rest mass are electrons, protons, neutrons, and atoms. In contrast, photons have a rest mass of zero. In other words, examples of a particle with a non-zero rest mass are: an electron, a proton, a neutron, and an atom. The atom can, for example, comprise at least one of the following or be one of the following: a hydrogen atom and an antihydrogen atom. It is known that quantum mechanical systems have eigenstates. The number of eigenstates can also be infinite. The term "multitude of eigenstates" can also be understood here to mean infinitely many eigenstates. A QN-it is understood here to be a generalization of a qubit to N states, where N is an integer greater than or equal to 2. A QN-it for the case N equals two is a qubit. A QN-it is thus a quantum information unit that is defined by a superposition of Nstates are described. These states are also called basis states. In this context, a subset M can also be understood as an improper subset. If the quantum mechanical system has infinitely many eigenstates, then a subset can also have the same infinite number of eigenstates. One advantage of the quantum computer described above is that it uses only a single particle. This advantageously means that decoherence, which in other types of quantum computers arises from the fact that, for example, information stored in a first qubit must be linked or coupled with quantum information stored in a second qubit, is not present in the present quantum computer. Another related advantage is that all quantum information is also stored in this single particle, so thatConnections between different QN-its can take place directly within this particle. It is therefore unnecessary to logically link QN-its located at different positions, which in the prior art is generally associated with significant time losses. Another advantage of the quantum computer described above is that the use of QN-its with N greater than or equal to two leads to a reduction in gate operations. The reduction of basic operations increases with the number of basis states N. A further advantage of the quantum computer described above is that, by using a single particle, it is advantageously achieved that, unlike in the prior art, the experimental setup of the quantum mechanical system does not reveal how a method for performing quantum computation is carried out. This advantageously leads toa heightened security relevance of the present quantum computer. According to a preferred embodiment, the quantum mechanical system comprises an electrically neutral particle arranged in a gravitational field above a particle reflector, wherein the quantum mechanical system of the electrically neutral particle in the gravitational field above the particle reflector exhibits infinitely many eigenstates. The particle reflector is preferably arranged horizontally. The gravitational field is preferably the gravitational field of the Earth, particularly at the Earth's surface, but it can also be another gravitational field. A particle reflector is a device that reflects the electrically neutral particle, which falls downwards in the gravitational field, upon contact with the particle reflector. The aforementioned preferred embodiment further comprises a unit for oscillating the particle reflector. Here, the unit for oscillating the particle reflector isThe device is designed and configured to couple two different eigenstates of the infinitely many possible eigenstates. Oscillating the particle reflector induces a rabioscillation between two eigenstates of the particle, which can be described here as acoustic or gravitational rabioscillation. An oscillation unit for the particle reflector is understood to be a device capable of setting the particle reflector into vibration. Such an oscillation unit could, for example, be a piezoelectric drive. Alternatively, a unit for generating an electromagnetic field can be used instead of the oscillation unit for the particle reflector. Alternating electromagnetic fields, particularly oscillating magnetic fields, are preferred. These electromagnetic fields also achieve coupling between two eigenstates of the particle. The unit for generating theThe electromagnetic field can be configured to provide an alternating electric field and / or an oscillating electric field. Such a unit for generating the electromagnetic field is particularly preferred in embodiments where the particle has an electric charge. In other words, in some embodiments, the single particle is arranged in a gravitational field above a unit for generating an electromagnetic field, wherein the quantum mechanical system of the single particle in the gravitational field above the unit for generating the electromagnetic field has infinitely many eigenstates; wherein the unit for generating the electromagnetic field is designed and configured to couple two different eigenstates of the infinitely many eigenstates; wherein the single particle and the unit for generating the electromagnetic field are such thatThe electrically neutral particle and the particle reflector oscillator are designed and configured such that a subset of the infinitely many eigenstates is used to realize the at least two QN-its. Optionally, the electromagnetic field generation unit is a unit for generating an alternating electromagnetic field, and further optionally, a unit for generating an oscillating magnetic field; for example, in embodiments where the only particle is an electrically neutral particle. Alternatively or additionally, the electromagnetic field generation unit can be configured to generate an alternating electric field and / or an oscillating electric field. The electrically neutral particle and the particle reflector oscillation unit are designed and configured such that a subset M of the infinitely many eigenstates is used to realize at least two QN-its. This can be achieved by appropriately controlling the particle reflector oscillation unit.particle reflector. The present embodiment advantageously achieves that all quantum information stored in the individual particle can be coupled or linked with only one unit for oscillating the particle reflector. This is a significant advantage over the prior art, for example, an ion trap, in which a qubit is stored in each ion, the quantum information of which must be logically linked with the quantum information of another ion in the ion trap using a common vibrational mode of an ion crystal. According to the present embodiment, all QN-its are located in the single particle. The quantum information of different QN-its in the particle is linked with the help of the gravitational field and the unit for oscillating the particle reflector. This feature further advantageously achieves that bothThe same mechanism or force is used for addressing quantum units as well as for interactions between quantum units. In this case, that mechanism is an oscillation of the single particle mediated by the particle reflector. Alternatively, in some embodiments, the single particle (e.g., the electrically neutral particle) and the electromagnetic field generation unit are designed and configured such that a subset M of the infinitely many eigenstates is used to realize at least two QN-its. Alternatively or additionally, in some embodiments, the electromagnetic field generation unit is designed and configured such that it couples states of the subset of the infinitely many eigenstates. According to preferred embodiments, the electrically neutral particle is one from the following group: a neutron and an atom (for example,a hydrogen atom or an antihydrogen atom). In particular, the electrically neutral particle can be one from the following group: an ultracold neutron and an ultracold atom. The particle reflector can be configured such that a surface of the particle reflector repels an ultracold particle (e.g., an ultracold neutron and / or an ultracold atom). In particular, the particle reflector can be configured such that the surface of the particle reflector repels the ultracold particle (e.g., the ultracold atom) using a van der Waals / Casimir polder (vdW / CP) potential. A suitable surface for a particle reflector for an ultracold neutron and / or an ultracold atom (in particular, an ultracold hydrogen atom) is described, for example, in(21-23] and [25-30]). The cited publications show that the attractive van der Waals / Casimir polder (vdW / CP) potential of a surface repels ultracold hydrogen atoms. The vdW / CP surface potential is expected to also reflect antiatoms (especially an ultracold antihydrogen atom) and thus be suitable for forming energy eigenstates of atoms (including hydrogen and antihydrogen atoms) in the gravitational potential. A suitable source of antihydrogen atoms is available, for example, at the European Organization for Nuclear Research (CERN). Conventional atoms (as opposed to antimatter atoms) can be provided by ion traps, such as those used in quantum computers. The surface of the particle reflector is preferably horizontal. In other words, the particle reflector is preferably a horizontal particle reflector (for example, having a particle reflector(the surface described above, wherein the surface is horizontal). Preferably, the particle is an ultracold particle. Particularly preferably, the particle is an ultracold neutral particle, for example, an ultracold neutron or an ultracold atom (such as an ultracold hydrogen atom or an ultracold antihydrogen atom). According to one possible definition, an ultracold particle / ultracold neutral particle is a particle / neutral particle whose kinetic energy is so small that it undergoes total internal reflection at the surface of the particle reflector even at perpendicular incidence, and / or a particle / neutral particle whose kinetic energy is less than a wall potential of the surface of the particle reflector. According to an alternative possible definition, the kinetic energy of the ultracold particle / ultracold neutral particle is less than 350 nanoelectronvolts, and / or the velocity of the ultracold particle / ultracold neutral particle is less than 350 nanoelectronvolts.neutral particle less than 17 m / s, particularly preferably less than 10 m / s. According to another possible definition, the wavelength of the ultracold particle / ultracold neutral particle is less than 100 nm. According to a further preferred embodiment, the electrically neutral particle is an ultracold neutron and the particle reflector is a neutron mirror. Ultracold neutrons are neutrons whose kinetic energy is so low that they undergo total internal reflection at a surface even at perpendicular incidence. The surface is preferably horizontal and more preferably the surface of a neutron mirror. The energy of an ultracold neutron (abbreviation UCN) is less than a wall potential. Preferably, the energy of the ultracold neutron is less than 350 nanoelectron volts. Preferably, the velocity of the ultracold neutron is less than 17 m / s, particularly preferably less than 10 m / s. Preferably, aThe wavelength of the ultracold neutron is less than 100 nm. According to a preferred embodiment, the quantum computer has at least one vertically oriented particle reflector in addition to the horizontal particle reflector. In corresponding embodiments, horizontal movement of the particle is locally restricted. It is further preferred that the quantum computer has at least two vertically oriented particle reflectors. This allows horizontal movement of the particle between the at least two vertically oriented particle reflectors to be restricted. According to another preferred embodiment, the quantum computer also has a ring-shaped, vertically oriented particle reflector. One axis of the ring-shaped, vertically oriented particle reflector can be vertical. In corresponding embodiments, a particle can be trapped inside the particle reflector in a horizontal direction.Preferably, the horizontal particle reflector is arranged at a lower end of the annular, vertically oriented particle reflector, so that the particle can be trapped above and within the annular, vertically oriented particle reflector. Preferably, the kinetic energy of an ultracold particle is so low that it is reflected by both the horizontal and the vertical particle reflectors. In this case, the ultracold particle can be trapped or stored in a vessel that has a horizontal particle reflector at its lower end and vertical particle reflectors as side walls. According to a preferred embodiment, at least one particle reflector (for example, the horizontal particle reflector and / or the vertical particle reflector) is arranged with vibration damping, for example, on a vibration-damped device, in particular aGlass block. According to a preferred embodiment, the quantum computer has, in addition to the horizontally oriented neutron mirror, at least one further vertically oriented neutron mirror, such that the horizontal movement of the neutron is locally restricted. It is further preferred that the quantum computer has at least two vertically oriented neutron mirrors, such that the horizontal movement of the neutron between the at least two vertically oriented neutron mirrors is restricted. According to another preferred embodiment, the quantum computer further comprises an annular, vertically oriented neutron mirror whose axis is vertical, such that a neutron is trapped inside this neutron mirror in a horizontal direction. More preferably, the horizontally oriented neutron mirror is arranged at a lower end of the annular neutron mirror, such that the neutron is trapped above the horizontally oriented neutron mirror.The neutrons can be trapped within the annular cylindrical neutron mirror. A neutron mirror, also known as a neutron supermirror, is a special type of mirror used in neutron transmission systems that increases the maximum reflection angle of the neutrons. Such a mirror has a glass or silicon substrate. Preferably, the mirror can have one or more layers of different metals applied to the substrate. The layer thickness decreases towards the substrate. Silicon, nickel, titanium, or alloys thereof are used, for example. The substrate is usually coated by sputtering. Neutron supermirrors can be designed to separate spin-up and spin-down neutrons, thus generating a polarized neutron beam. For this to work, one of the layer materials must be ferromagnetic, and the supermirror must be located in a magnetic field.The effect exploited is the splitting of the scattering length density of the magnetic material. This feature has the advantage, among others, that ultracold neutrons have long been known in technology and the corresponding methods are widely used. Furthermore, another advantage of the present quantum computer is that, due to its intrinsically very long coherence time, a very large number of gate operations can be performed. Preferably, the kinetic energy of an ultracold neutron is so low that it is reflected by both a horizontal and a vertical surface. Even more preferably, both the horizontal and the vertical surfaces are the surfaces of neutron mirrors. In this case, the ultracold neutron can be trapped in a vessel that has a horizontally oriented neutron mirror at one end and vertically oriented neutron mirrors as side walls.The data are stored. According to a preferred embodiment, the neutron mirror is arranged in a vibration-damped manner. Particularly preferably, the neutron mirror is arranged on a vibration-damped device, especially a glass block. This advantageously enables vibration excitation using the unit for oscillating the neutron mirror or the second unit for oscillating the second neutron mirror. If the quantum mechanical system is not sufficiently vibrationally damped, there is a risk that vibrations in the system will drive transitions between different eigenstates of the quantum mechanical system unintentionally. According to a preferred embodiment, the quantum computer further comprises a state selection unit, which is designed and / or configured to select a particle (in particular an ultracold particle and / or a neutral particle, preferably an ultracold neutral particle).to remove a particle that is not in its ground state from the quantum mechanical system. According to some embodiments, the state selection unit absorbs or scatters a particle that is not in its ground state. According to some embodiments, the state selection unit has a particle absorber, which is preferably arranged above the particle reflector (in particular above the horizontal particle reflector). This advantageously achieves that the particle (e.g., the ultracold particle and / or the neutral particle) can be brought into a predetermined, precisely defined state. This state is, in this case, the ground state. According to yet another preferred embodiment, the quantum computer further comprises a state selection unit which is designed and configured to remove an ultracold neutron that is not in its ground state from the quantum mechanical system. PreferablyThe state selection unit absorbs or scatters a neutron that is not in the ground state. It is further preferred that the state selection unit includes a neutron absorber, which is preferably arranged above the neutron mirror. Preferably, the state selection unit is operated such that ultracold neutrons are sent through the state selection unit, with neutrons that are not in the ground state, i.e., those with too high an energy, being absorbed by a neutron absorber. Preferably, the state selection unit has a rough surface at which an ultracold neutron is scattered in such a way that it is removed from the quantum mechanical system. This advantageously achieves the ability to bring the neutrons into a predetermined, precisely defined state. In this case, that state is the ground state. According to another preferred embodiment, the quantum computer further includes aA second particle reflector is arranged above the particle reflector (in particular, above the horizontal particle reflector). In some embodiments, the second particle reflector is horizontal (e.g., as described above) and / or is a second horizontal particle reflector. According to some embodiments, the second particle reflector (in particular, the second horizontal particle reflector) is arranged above the particle. According to some embodiments, the second particle reflector has a second unit for oscillating the second particle reflector. It is preferred that the second particle reflector is arranged parallel to the particle reflector. The second unit for oscillating the second particle reflector advantageously provides, in addition to the unit for oscillating the particle reflector, a second unit which couples quantum information stored in the individual particle.According to another preferred embodiment, the quantum computer further comprises a second neutron mirror, which is arranged above the neutron and which includes a second unit for oscillating the second neutron mirror. It is preferred that the second neutron mirror is arranged parallel to the neutron mirror. The second unit for oscillating the second neutron mirror advantageously provides, in addition to the unit for oscillating the neutron mirror, a second unit that can couple or link quantum information stored in the individual particle. Furthermore, the second neutron mirror can be used to energetically shift the energy level of an eigenstate, thereby preventing or enabling predetermined transitions. It is also preferred that the second neutron mirror be able to be used during an experiment.can be shifted. Thus, during an experiment, an energy level can be shifted accordingly, thereby enabling or preventing certain transitions. This allows for the use of specific quantum gates. According to a further preferred embodiment, the unit for oscillating the particle reflector and / or the second unit for oscillating the second particle reflector are configured to couple a first eigenstate of a first QN-it with a second eigenstate of the first or a second QN-it, such that a rabioscillation is driven between the first eigenstate of the first QN-it and the second eigenstate of the first or the second QN-it. According to a further preferred embodiment, the unit for oscillating the neutron mirror and / or the second unit for oscillating the second neutron mirror are configured to couple a firstThe goal is to couple the eigenstate of a first QN-it with a second eigenstate of the first or a second QN-it, such that a Rabi oscillation is driven between the first eigenstate of the first QN-it and the second eigenstate of the first or the second QN-it. This feature advantageously allows Rabi transitions between different eigenstates of a QN-it, and even Rabi transitions between eigenstates of different QN-its, to be driven using the neutron mirror oscillation unit and / or the second neutron mirror oscillation unit. This is achieved simply by oscillating the neutron mirror and / or the second neutron mirror at the required frequency. This simple method thus advantageously allows the implementation of 1-QN-it gates as well as 2-QN-it gates, 3-QN-it gates, etc. A 1-QN-it gate is aA quantum operation that operates on a single QN-it, i.e., that changes the quantum state of a single QN-it. A 2-QN-it gate is a quantum operation that operates on two distinct QN-its. Here, for example, the state of the first QN-it can be changed depending on the state of the second QN-it. A 3-QN-it gate is a quantum operation that operates on three distinct QN-its. Here, for example, the state of the first QN-it can be changed depending on the states of the second and / or third QN-it. According to a further preferred embodiment, the unit for oscillating the particle reflector and / or the second unit for oscillating the second particle reflector are configured and arranged to couple eigenstates of the at least two QN-its such that a quantum gate for the at least two QN-its is realized. According to a further preferred embodiment, the unitThe unit is designed and configured to oscillate the neutron mirror and / or the second unit to oscillate the second neutron mirror, coupling the eigenstates of the at least two QN-its such that a quantum gate is implemented for the at least two QN-its. This advantageously allows different QN-its of the at least two QN-its to be coupled so that a quantum gate can be implemented for these different QN-its. The number of these different QN-its can be two or more. According to a further preferred embodiment, the quantum gate can be a Pauli X gate, a Pauli Y gate, a Pauli Z gate, a Hadamard gate, a phase gate, an S gate, a T gate, or a π / 8 gate. These gates are typically 1-QN-it gates. Furthermore, the quantum gate can be a CNOT gate, a controlled Z gate, or a swap gate. These gates are typically 2-QN-it gates. FurthermoreThe quantum gate can be a Toffoli gate, a Fredkin gate, or a Deutsch gate. These gates are typically 3-QN-it gates. However, some of the quantum gates mentioned here can also be implemented on more QN-its than specified above. For example, a CNOT gate can also be applied to three or more QN-its and is then called a generalized CNOT gate. In the case of three or more QN-its, the quantum gate can be a generalized CNOT gate, a generalized Toffoli gate, a generalized Fredkin gate, or a generalized Deutsch gate. According to a preferred embodiment, the quantum computer is designed and configured to implement a universal set of quantum gates. A universal set of quantum gates is a collection of quantum gates with which any computational operation can advantageously be implemented. For qubits, it has been shown that the CNOT gate, together with allOne-qubit gates form a universal set of quantum gates. According to a further preferred embodiment of the quantum computer, the unit for oscillating the particle reflector and / or the second unit for oscillating the second particle reflector are designed and configured to perform a Rabi pulse for each of the N states of the two QN-its, thus realizing a SWAP gate. A SWAP gate swaps the states of two QN-its. According to a further preferred embodiment of the quantum computer, the unit for oscillating the neutron mirror and / or the second unit for oscillating the second neutron mirror are designed and configured to perform a Rabi pulse for each of the N states of the two QN-its, thus realizing a SWAP gate. A SWAP gate swaps the states of two QN-its. It is known that using a Rabi-^ pulse, which couples two energy levels together,The populations of the respective energy levels are swapped. If, for each basis state or state of a first QN-it, a Rabi-^ pulse is performed with a corresponding basis state or state of a second QN-it, then all basis states of the first QN-it are swapped with all basis states of the second QN-it, thus realizing a SWAP gate. This advantageously allows a SWAP gate for a QN-it to be realized with simple operations, representing a significant simplification compared to the state of the art. The advantage of this feature will be illustrated using a SWAP gate for two qubits. In the present quantum computer, only two operations are required for the SWAP gate, regardless of which neutron states are used for the two qubits. In contrast, in a state-of-the-art quantum computer, it can happen that only adjacent qubits are swapped.can be linked together. In this case, to perform a swap gate for two non-adjacent qubits, it is necessary that there be a path of interconnected qubits between the two qubits to be linked. Then, starting from the first qubit to be linked, one can perform swap gates with each adjacent qubit until one reaches the second qubit to be linked. Since the original state of the second qubit to be linked is now in the qubit adjacent to the second qubit to be linked, further swap gates must be performed until one returns to the first qubit to be linked. This is an enormous effort compared to the two operations required by the present quantum computer. According to another embodiment, the quantum computer also has a readout unit for determining the occupancy probability of at least one of the eigenstates.This advantageously allows the occupation probability of one of the eigenstates to be determined. It is clear to those skilled in the art that the occupation probability of an energy level of a single particle can generally only be determined through multiple measurements. This can be achieved, for example, by repeated measurements on several identically prepared particles. In some embodiments, the readout unit (a spatially resolved detector for determining the density of particles of the same type as the single particle) is a spatially resolved detector for determining the density of neutrons (or atoms). The readout unit is preferably a spatially resolved detector for determining the neutron density. Such a spatially resolved detector can measure the square of the wave functions of the ultracold neutron.Determine. Through a mathematical fit, the respective population probabilities of the respective eigenstates can be determined. According to yet another embodiment, a population probability of a given eigenstate under investigation can be determined as follows. According to this embodiment, the unit for oscillating the particle reflector and / or the second unit for oscillating the second particle reflector is designed and configured to exchange a population of a state under investigation with a population of a ground state using a pulse. Furthermore, the state selection unit is designed and configured to determine a population probability of the resulting ground state. Since the population of the ground state was exchanged with the population of the state under investigation, the population of the state under investigation is ultimately determined. Through thisThe feature is thus advantageously achieved that a population probability of an arbitrary, given eigenstate can be determined. According to yet another embodiment, a population probability of a given eigenstate under investigation can be determined as follows. According to this embodiment, the unit for oscillating the neutron mirror and / or the second unit for oscillating the second neutron mirror is designed and configured to exchange a population of a state under investigation with a population of a ground state using a pulse. Furthermore, the state selection unit is designed and configured to determine a population probability of the resulting ground state. Since the population of the ground state has been exchanged with the population of the state under investigation, the population of the state under investigation is ultimately determined.This feature advantageously allows the probability of occupation of an arbitrary, predefined eigenstate to be determined. Preferably, the ground state is used as a control bit. This means that, for all quantum calculations used, the ground state is generally not a basis state of a QN-it. In this case, the ground state is used only for the preparation and readout described here. According to a preferred embodiment, the first excited state of the eigenstates of the quantum mechanical system is used as the first basis state of the first QN-it. The second excited state of the eigenstates of the quantum mechanical system is used as the second basis state of the first QN-it. This continues according to the discernible logic until the last basis state of the first QN-it. Subsequently, the next higher eigenstate of the quantum mechanical system is used as the firstThe basis state of the second QN-it is used. This is continued in the same manner. According to a further embodiment, the single particle is surrounded by a magnetic field such that the infinitely many eigenstates split into two eigenstates depending on a spin quantum number of the single particle. Preferably, the magnetic field is such that the size of the split is different for at least two, preferably at least three, and even more preferably for each of the infinitely many eigenstates. According to a further preferred embodiment, the magnetic field has a constant gradient along the height axis. The height axis is preferably a vertical axis. According to a further embodiment, the ultracold neutron is surrounded by a magnetic field such that the infinitely many eigenstates split into two eigenstates depending on a spin quantum number of the neutron. Preferably, the magnetic fieldsuch that the size of the splitting is different for at least two, preferably at least three, and even more preferably for each of the infinitely many eigenstates. According to a further preferred embodiment, the magnetic field has a constant gradient along the height axis. The height axis is preferably a vertical axis. Preferably, the magnetic field surrounding the single particle (or the ultracold neutron) is provided by the electromagnetic field generation unit described above. Alternatively or additionally, the electromagnetic field generation unit can be configured to provide the magnetic field surrounding the single particle (or the ultracold neutron). This advantageously achieves a doubling of the quantum states, so that more quantum information can be stored in the same particle. Furthermore, the feature whereby the size of the splitting is different forSince at least two of the eigenstates have different magnitudes, it is advantageously achieved that transitions from a first eigenstate of the quantum mechanical system to a second eigenstate of the quantum mechanical system can be driven, which depend on a spin quantum number of the first eigenstate and / or the second eigenstate. If the splitting of the first and second eigenstates were equal, the energy difference between a lower, i.e., energetically lower, spin state of the first eigenstate and a lower spin state of the second eigenstate would be exactly the same as the energy difference between an upper, i.e., energetically higher, spin state of the first eigenstate and an upper spin state of the second eigenstate. Spectroscopy of these transitions would thus be unable to distinguish between these two different transitions. In the present case, where the splitting is different for at least two of the eigenstates,Since the energy levels of the transitions differ, a desired transition can be selectively driven based on the different energies of the respective transitions. Conversely, this means that a transition, for example, from the upper spin state of the first eigenstate to the upper spin state of the second eigenstate, can be driven with a predetermined oscillation frequency, while no other transition between the first and second eigenstates can be driven using the same oscillation frequency. A CNOT gate can advantageously be implemented using this mechanism. According to a further preferred embodiment, the switching time of a quantum gate is smaller than the coherence time of the quantum mechanical system. Preferably, the switching time of the quantum gate is smaller than one-thousandth of the coherence time of the quantum mechanical system. Particularly preferably, the switching time of the quantum gate is smaller than one ten-thousandth of the coherence time of thequantum mechanical system. The switching time of a quantum gate is understood as the duration required to perform a specific quantum operation necessary for the quantum gate. Such a quantum operation could, for example, be a rabioscillation between two quantum states. The time magnitude of the switching time for such a rabioscillation is approximately the inverse of the resonant frequency of the rabioscillation used. In quantum computing, a quantum gate is a time-controlled interaction of quantum states with each other or with the environment. The switching time can depend on various factors, including the type of quantum gate, the specific properties of the quantum states, and the technology used to implement the quantum computer. Preferably, the switching time of a quantum gate lies between one millisecond and 1000 seconds. The coherence time of the quantum mechanical system is the time interval...understood is the coherence time in which a QN-it can maintain its superposition state before decoherence occurs. The coherence time is a critical parameter for the performance of quantum computers, as it determines the maximum time in which quantum information can be reliably stored and processed. The longer the coherence time, the better a quantum computer can perform complex calculations. According to the present invention, essentially N switching times are required to execute a SWAP gate for a QN-it. For a SWAP gate that swaps the quantum state of one QN-it with the quantum state of another QN-it, N ^-pulses are required, with each ^-pulse requiring one switching time. Using this feature, it can advantageously be achieved that enough gate operations of a quantum gate can be performed before the superposition, essential for quantum computing, is destroyed by decoherence. According to a furtherIn a further preferred embodiment, the quantum mechanical system is designed and configured to have a coherence time greater than 1 millisecond. It is further preferred that the coherence time be greater than 10 milliseconds. According to a further preferred embodiment, the coherence time is greater than 100 milliseconds. With such a coherence time, at least one quantum gate can be performed. It is even more preferred that the coherence time be greater than 1 second. A still more preferred embodiment has a coherence time greater than 800 seconds. It is known that the coherence time of the present quantum mechanical system depends on several factors, including the vibration damping of the entire system, the physical and mechanical properties of the neutron mirror, and the temperature of the ultracold neutrons. However, it is advantageous to claim the coherence time itself, since this, for one thing, allows for greater precision and control.This feature is advantageous because the coherence time is a crucial parameter of the quantum mechanical system, and because the aforementioned factors, such as vibration damping and the physical properties of the neutron mirror, cannot be specified as precisely as the coherence time. With a switching time in the range of approximately 10 milliseconds, this feature advantageously enables approximately 10,000 gate operations to be performed within a coherence time of 100 seconds. Exemplary embodiments of the invention are illustrated in the drawings and are explained in more detail in the following description. Figure 1 shows a schematic representation of a quantum computer according to one embodiment of the invention; Figure 2 shows energy eigenstates and the gravitational potential of a neutron in a quantum mechanical system that implements a quantum computer according to one embodiment of the invention; Figures 3 and 4 each show how different QN-its are implemented.Energy eigenstates of a neutron of a quantum mechanical system of a quantum computer according to one embodiment of the invention can be split; Figures 5 to 8 each show experimental setups for realizing a quantum computer according to one embodiment of the invention; Figure 9 shows a splitting of gravitational energy eigenstates in an external magnetic field into two spin eigenstates each, as well as the corresponding gravitational potentials, which is used in the implementation of a CNOT gate in a quantum computer according to one embodiment of the invention; Figure 10 shows an influence of a second neutron mirror on gravitational energy eigenstates of the quantum mechanical system of the quantum computer according to one embodiment of the invention; and Figure 11 shows measured neutron density distributions of a spatially resolved detector for the detection of QN-its, which are used in a quantum computer according to one embodiment of the invention.Figure 1 shows a schematic representation of a quantum computer 100, which is realized by a quantum mechanical system 110 with a single ultracold neutron 120. The neutron 120 is positioned in the Earth's gravitational field 160 above a horizontally oriented neutron mirror 140. The direction of acceleration of the Earth's gravitational field 160 is indicated by an arrow in Figure 1. The quantum mechanical system 110 of the neutron 120 in the gravitational field 160 above the neutron mirror 140 has infinitely many eigenstates. The eleven lowest eigenstates 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221 are shown in Figure 2. Figure 2 shows the wavefunction ^ as a function of the height z above the neutron mirror 140 for each of the eleven eigenstates 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221. The respective wavefunctions ^ are plotted along the vertical axis, which corresponds to the energy of theThe eigenstates are represented at their respective positions, corresponding to the eigenenergy of the respective wavefunction ^. The eigenenergies of the eigenstates are denoted E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, where E1 is the eigenenergy of the first eigenstate 211 and E11 is the eigenenergy of the eleventh eigenstate 221. The energies are in the picoelectronvolt range (abbreviation: peV), with E1 being approximately 1.41 peV and E11 approximately 8.24 peV. It is important to note that the distance between adjacent eigenstates decreases towards higher eigenstates. Furthermore, Figure 2 shows the gravitational potential 240 of a neutron 120 as a function of height z. It should also be noted that the wavefunctions ^ vanish at z equal to zero, since the neutron mirror 140 is located at this point. Furthermore, the wave function vanishes exponentially beyond the gravitational potential 240. The gravitational potential 240 canThis can be expressed as a formula as follows: ^^ = ^^ ∙^^ ∙ ^^, where V in physics usually denotes a potential, here the gravitational potential 240, m the mass of the neutron, g the acceleration due to gravity, and z the height above the neutron mirror 140. A subset of the eigenstates is used to realize at least two QN-its. There are numerous ways to distribute the QN-its among the eigenstates 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, and 221. Two exemplary possibilities are shown in Figures 3 and 4. The numbers 211 to 221 represent the respective eigenstates 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221 from Figure 2. Typically, the lowest eigenstate 211 is used as a so-called control bit to select a population of an eigenstate under investigation (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221). This means that the lowest eigenstate 211 is usuallyis not used as a basis state of a QN-it. Figures 3 and 4 show that state 211 is not assigned to any QN-it. In Figure 3, the second eigenstate 212 and the third eigenstate 213 are used as the two basis states of a first qubit 241. The fourth eigenstate 214 and the fifth eigenstate 215 are used as the two basis states of a second qubit 242. The sixth eigenstate 216 and the seventh eigenstate 217 are used as the two basis states of a third qubit 243. The eighth eigenstate 218 and the ninth eigenstate 219 are used as the two basis states of a fourth qubit 244. The tenth eigenstate 220 and the eleventh eigenstate 221 are used as the two basis states of a fifth qubit 245. Higher eigenstates can be used as further qubits according to this rule. Figure 4 shows a different partitioning. The lowest eigenstate 211 is also used here as a control bit.The second eigenstate 212, the third eigenstate 213, and the fourth eigenstate 214 are used as the three basis states of a first Q-3-it 251. The fifth eigenstate 215, the sixth eigenstate 216, and the seventh eigenstate 217 are used as the three basis states of a second Q-3-it 252. The eighth eigenstate 218, the ninth eigenstate 219, and the tenth eigenstate 220 are used as the three basis states of a third Q-3-it 253. Higher eigenstates can be used as further Q-3-its according to this rule. For example, the eleventh eigenstate 221 can be used as a basis state of a fourth Q-3-it (not shown). Furthermore, it is possible to use qubits and Q-3-its in a mixed manner. Those skilled in the art understand that many other possibilities exist. Furthermore, the quantum computer 100 has a unit 142 for oscillating the neutron mirror 140, with which two differentEigenstates 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221 can be coupled to each other, see e.g. Figure 1. The unit 142 for oscillating the neutron mirror 140 is, in this case, a piezoelectric drive coupled to the neutron mirror 140. If the piezoelectric drive of the unit 142 causes the neutron mirror 140 to oscillate at a frequency corresponding to the energy difference between the second eigenstate 212 and the fourth eigenstate 214, a reciprocal oscillation is driven between the second eigenstate 212 and the fourth eigenstate 214. In this way, by appropriately choosing the oscillation frequency and oscillation period of unit 142 to oscillate the neutron mirror 140, a rabioscillation between arbitrary eigenstates 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221 of the quantum mechanical system 110 can be driven. The experimental setup of the quantum computer is described below.100 and methods for realizing quantum gates with the quantum computer 100 are described. Figure 5 shows the experimental setup 200 of the quantum computer 100. Ultracold neutrons 120 are introduced into the experimental setup 200 from the left in the representation of Figure 5. Experiments dealing with neutrons are usually located in close proximity to a neutron source. Neutrons originating from a fission reactor generally have a Maxwell-Boltzmann distribution with a maximum velocity distribution at about 2200 m / s. Ultracold neutrons, however, have velocities in the range of a few meters per second. These thermal neutrons can be converted into ultracold neutrons 120 primarily by two principles: thermalization in a cold source with liquid deuterium or Doppler shifting by scattering with a neutron turbine. A velocity of an ultracold neutron 120 inThe velocity in the horizontal direction, i.e., perpendicular to the surface of the first neutron mirror 140, is less than 17 m / s. Thus, an ultracold neutron has an energy of less than 1500 nanoelectron volts. However, the velocity of the ultracold neutron 120 also has a velocity component perpendicular to the first neutron mirror 140, which is significantly less than the aforementioned velocity of 17 m / s. The energy corresponding to this velocity component is therefore significantly less than 1500 nanoelectron volts. Preferably, this energy is less than 335 nanoelectron volts. This energy is less than the wall potential of the first neutron mirror 140. The material-dependent wall potential is approximately 335 nanoelectron volts for a 58Ni coating on the wall. Since a high and continuous flux of ultracold neutrons is required, it is preferred that the experiment take place at PF2 (Physique Fondamentale 2), one of the UCN sources of theThe research reactor of the Institut Laue-Langevin in Grenoble, France. The experimental setup 200 of the quantum computer 100 is divided into three segments 202, 204, and 206. In the first segment 202, a state of the quantum mechanical system 110 is prepared; in the second segment 204, the system is manipulated, for example, quantum gates are performed; in the third segment 206, the state achieved in the second segment 204 is analyzed and read out. After entering the experimental setup 200, the ultracold neutron 120 is located in the first region 202 above a first neutron mirror 140 and below a neutron absorber 144. The first neutron mirror 140 and the neutron absorber 144 are configured such that neutrons not in the ground state, i.e., in state 211, are scattered out of the system. Since one underside 145 of the neutron absorber 144 has a rough surface, neutrons 120 that are not in theThe neutrons 120 in the ground state are scattered from the rough surface 145 out of the quantum mechanical system 110. Since the wave function of the neutron 120 in the ground state 211 almost vanishes at the underside 145 of the neutron absorber 144, but the wave function of the neutron 120 not in the ground state 211 does not vanish there, there is a high probability that neutrons 120 not in the ground state 211 are scattered from the underside 145 of the neutron absorber 144, after which they can no longer reach the second region 204. The entire experimental setup 200, and thus also each of the neutron mirrors 140, is arranged on a vibrationally damped glass block (not shown). Thus, only one neutron 120 in the ground state 211 reaches the second region 204. In the second region 204, the neutron 120 is located above another neutron mirror 140, which is connected to a unit 142 for oscillating theThe unit 142 is connected to the neutron mirror 140. Using the unit 142 to oscillate the neutron mirror 140, targeted quantum operations can now be performed starting from the ground state 211. If the unit 142 excites the neutron mirror 140 with a resonance frequency of the quantum mechanical system 110, transitions from the ground state 211 to a higher state can be driven. This is the case if and only if the following equation is satisfied: ^^^^ ∙ ^^ = ^^, where ^^^^ is the Rabi frequency, which depends on the oscillation strength and the overlap integral between the initial and final states, and ^^ is the interaction time, i.e., the duration for which the unit 142 causes the neutron mirror 140 to oscillate. This is called a ^-pulse or ^-flip. If one considers the two-level system of the ground state 211 and the higher state in the image of the Bloch sphere, this corresponds to a transition of the vector in the Bloch sphere from the south pole to the north pole. This is aBasic manipulation. Generally, significantly more complex operations are performed, e.g., quantum gates such as a SWAP gate, a phase gate, a CNOT gate, or a Hadamard gate. These gates can be implemented not only for qubits but also for the more general QN-its. Thus, the gates mentioned above are more accurately described as generalized SWAP gates, generalized phase gates, generalized CNOT gates, or generalized Hadamard gates. A number of gates are described in detail below. After the second region 204, there are two ways to read out the state prepared in the second region 204. According to the first method, a ^-pulse is used to exchange a population of a state under investigation with a population of the ground state 211. This ^-pulse is performed in the second region 204 after the state preparation. This ^-pulse is formally already part of the selection, however, it mustThis step is carried out in the second region 204, as this requires an oscillation of the neutron mirror 140. The population to be determined is now in the ground state 211. In the third region 206, the probability with which neutron 120 is in the ground state can now be determined using the same setup as in the first region 202. If neutron 120 is in the ground state, it passes through the third region 206 and is detected in a detector 180, e.g., a neutron counter. If neutron 120 is not in the ground state, it is scattered by a bottom surface 145 of another neutron absorber 144, which is located in the third region 206, and removed from the quantum mechanical system 110. By repeatedly preparing the identical state, a probability with which neutron 120 is in the ground state can thus be determined. In this case, theThe ground state is called the control bit. Those skilled in the art understand that 1 bit, or 1 qubit, has two electronic states, but the ground state is only a single electronic state. Alternatively, a spatially resolved detector 182 can be used as the readout unit to determine the neutron density. This embodiment is shown in Figure 6. Instead of the neutron mirror 140 and the neutron absorber 144 in the third region 206 of the embodiment of Figure 5, only the spatially resolved detector 182 is used in the embodiment of Figure 6. A measured neutron density distribution for a 5-qubit system is shown in Figure 11 as a function of the height z. Here, a first graph 281 shows a count rate CR in arbitrary units, which is proportional to a neutron density distribution, for the case where all 5 qubits are in the lower state, which can be called the 0 state or down state. A second graph 282 showsThe measured neutron density distribution is shown for the case where the fourth qubit has been flipped, i.e., for the case where all qubits except the fourth are in the 0 state. This difference is clearly discernible, and the exact population probabilities of the respective states can be determined using a fit. In addition to the embodiment shown in Figure 5, the experimental setup 200 of the quantum computer 100 can further include a second neutron mirror 141 with a second unit 143 for oscillating the second neutron mirror 141. Figure 7 shows this embodiment with a detector 180, and Figure 8 shows an embodiment with a spatially resolved detector 182. The second neutron mirror 141 is arranged above the neutron 120 and, like the first neutron mirror 140, can be used to drive Rabi transitions in an ultracold neutron 120. This can be done simultaneously with or after excitation with the first neutron mirror 140This can happen. Furthermore, the second neutron mirror 141 can be used to shift eigenstates of the quantum mechanical system 110. The second neutron mirror 141 can also be shifted during an experiment. Shifting an eigenstate can advantageously be used to enable or prevent certain transitions. This can be used to implement selective quantum gates, such as a CNOT gate. A series of quantum gates are described below. To implement a SWAP gate, an ultracold neutron 120 is prepared in the ground state as described above. In the subsequent operations in the second segment 204, the ground state 211 is used as a control bit, and from the second eigenstate 212 onward, the eigenstates for two QN-its are used, where N can be an integer greater than or equal to two. A SWAP gate exchanges the state of the first QN-it with the stateof the second QN-it. Before the SWAP gate operation is performed, the two QN-its can be prepared in any desired state. This can be done using either the first neutron mirror 140 or the first neutron mirror 140 and the second neutron mirror 141. Once any desired state has been prepared, the SWAP gate operation can be performed as follows: a ^-pulse is applied to each of the N basis states of the first and second QN-its. Specifically, this means that a ^-pulse is applied to both the first basis state of the first QN-it and the first basis state of the second QN-it, so that the population of the first basis state of the first QN-it is swapped with the population of the first basis state of the second QN-it. Then, a ^-pulse is performed for the second basis state of the first QN-it and the second basis state of the second QN-it, such that the population of the second basis state of the first QN-it is matched with theThe population of the second basis state of the second QN-it is swapped. This procedure is continued until the Nth basis state of the first QN-it and the second QN-it is reached. At the end of this procedure, the quantum state of the first QN-it is swapped with the quantum state of the second QN-it, thus realizing the SWAP gate. It should be emphasized that such a SWAP gate is significantly easier to implement for the present quantum computer than for any known prior art quantum computer. The readout of the result of the SWAP gate is performed as described above using a detector 180 or a position-resolving detector 182. A phase gate for a qubit is described below. The phase gate is also alternatively referred to as an S-gate. In the Bloch sphere diagram, such a phase gate rotates the phase by 90° around the Z-axis, which is one of the two horizontal axes in the Bloch sphere diagram. The phase gate is alternativelyalso known as a √^^ gate. For this purpose, an ultracold neutron 120 is first prepared in its ground state. As described above, the ground state 211 is used as a control bit. The second eigenstate 212 is used as the ground state of the qubit, i.e., the 0 state, and the third eigenstate 213 as the excited state, i.e., the 1 state, of the quantum mechanical system. To bring the population into the ground state of the qubit, a ^ pulse is used from the ground state 211 of the quantum mechanical system 110 to the second eigenstate 212, i.e., the ground state of the qubit. A phase gate does not change the state of the qubit if the qubit is in the 0 state or the 1 state. Thus, a change in the qubit can only be measured if the qubit is in a superposition of its ground state and its excited state. Thus, in the next step, the qubit is transformed into a desired superposition of the ground state of the qubit and the excited state of the qubit.A point on the equator of the Bloch sphere is selected. A half-pulse is used for this purpose, which is achieved by means of an oscillation of the lower neutron mirror 140. In the next step, the vector on the Bloch sphere is rotated by a predetermined phase, i.e., the vector is rotated by a predetermined angular amount as seen from the center of the Bloch sphere. For this purpose, both the first, lower neutron mirror 140 and the second, upper neutron mirror 141 are set into oscillation by means of the first unit 142 for the oscillation of the first neutron mirror 140 and the second unit 143 for the oscillation of the second neutron mirror 141. The oscillation frequency of the neutron mirrors 140, 141 corresponds to the transition from eigenstate 212 to eigenstate 213. However, the oscillations of the first unit 142 and the second unit 143 exhibit a phase difference, which corresponds to the phase gate. The oscillation is carried out as long asuntil the vector on the Bloch sphere has been rotated by the predetermined phase. The phase gate is thus completed, and in the final step, the prepared state is read out in a known manner. A CNOT gate for two qubits is described below. For this purpose, a magnetic gradient field is used, which increases in the direction of the negative vertical axis. This magnetic field leads to a change in the effective acceleration of neutron 120 towards the lower neutron mirror 140. While without a magnetic field the acceleration of neutron 120 is the acceleration due to gravity g, the acceleration with this magnetic field is ± ∙ |∇|, where ∇ is the magnetic moment of neutron 120 and ∇ is the magnetic field gradient. This leads to a splitting of the gravitational energy eigenstates into two eigenstates each, which depend on the spin orientation of neutron 120 in the magnetic field. It is important to mention that the splitting is different for eachThe gravitational eigenstate differs and increases from the ground state to higher states. These resulting eigenstates are shown in Figure 9 for gravitational eigenstates 212 and 213. The second eigenstate 212 is alternatively denoted by |2^ in ket notation, and the third eigenstate 213 by |3^. The two spin settings of the neutron 120 are denoted by |^^^^^ and |^^^^^^^^^. The gravitational ground state 211 is used as a control bit and is not shown in Figure 9. Figure 9 shows the energy of the second gravitational eigenstate 212 and the third gravitational eigenstate 213 as a function of the height z. The second gravitational eigenstate 212 splits into the two states |^^^^^|2^ and |^^^^^^^^^|2^. The third gravitational eigenstate 213 splits into the two states |^^^^^|3^ and |^^^^^^^^^|3^. Furthermore, Figure 9 shows two with the different spin settings of the neutron 120.The connected gravitational potentials 262, 264 are shown. A transition 271 from state |^^^^^|2^ to state |^^^^^|3^ can be achieved by mechanical oscillation excitation of the first neutron mirror 140 and / or the second neutron mirror 141 at a frequency ^^^^^^. A transition 272 from state |^^^^^^^^^|2^ to state |^^^^^^^^^|3^ can be achieved by mechanical oscillation excitation of the first neutron mirror 140 and / or the second neutron mirror 141 at a frequency ^^^^^^^^^^. Since the splitting of the third eigenstate 213 or |3^ is larger than the splitting of the second eigenstate 212 or |2^, the frequency ^^^^^^ is greater than the frequency ^^^^^^^^^^. This can be used to drive a state-dependent transition, as described below. The CNOT gate is described below. The CNOT gate operates on a quantum register of two qubits. Here, the qubit, which is defined by themagnetic states |^^^^^ and |^^^^^^^^^ is characterized as the control bit and the quantum bit, which is characterized by the gravitational states |3^ and | 2 ^The target bit is designated as the target bit. The CNOT gate is implemented as follows. First, as described above, an ultracold neutron 120 is prepared in ground state 211, which serves as the control bit. To bring the population into the ground state of the gravitational qubit, a ^-pulse is used from the ground state 211 of the quantum mechanical system 110 to the second eigenstate 212. The spin of the neutron 120 is then brought into either the state |^^^^^, |^^^^^^^^^, or a superposition of |^^^^^ and |^^^^^^^^^ states. The spin state is prepared with radio frequency (RF) pulses. In the next step, unit 142 excites the first neutron mirror 140 to oscillate at frequency ^^^^^^.Since the frequency ^^^^^^ can only drive transition 271 between states |^^^^^|2^ and |^^^^^|3^, but not the non-resonant transition 272 between states |^^^^^^^^^^|2^ and |^^^^^^^^^|3^, a transition only occurs if neutron 120 is in the spin |^^^^^ state. Transition 271 is driven until the populations of states |^^^^^|2^ and |^^^^^|3^ have exchanged. This corresponds to a ^-pulse. Ultimately, one can see that the states with spin |^^^^^-state, i.e., states |^^^^^|2^ and |^^^^^|3^, are swapped, while the states with spin |^^^^^^^^^^^-state, i.e., states |^^^^^^^^^|2^ and |^^^^^^^^^|3^, remain unchanged. This corresponds exactly to the logic of a CNOT gate. If neutron 120 is in a superposition of the |^^^^^- and |^^^^^^^^^^^ states before the CNOT gate is executed, e.g.If neutron 120 is in the state (^^∙ |^^^^^+ ^^∙ |^^^^^^^^^)|2^, where ^^ and ^^ are complex numbers, then after the CNOT gate operation, neutron 120 will be entangled in the following configuration: ^^∙ |^^^^^|3^+^^∙ |^^^^^^^^^|2^. If the lower mirror oscillates with ^up, there is a transition between states 2 and 3 if the neutron is in state |^^^^^. If the neutron is in state |^^^^^^^^^, no transition is possible. The frequency ^up is outside the resonance frequency. To excite transitions, the frequency ^down would have to be chosen. The readout of the CNOT gate result is carried out as described above with a detector 180 or a spatially resolved detector 182. This can preferably be done spin-selectively. The following briefly explains, with reference to Figure 10, how a second mirror 141, which is arranged above the neutron 120, can be used to change an energy level of given eigenstates.Figure 10 shows, firstly, the energy of the eigenstates 211, 212, 213 as a function of height z. Secondly, the square of the magnitude of the wave functions of the respective eigenstates 211, 212, 213 is shown. Furthermore, the gravitational potential 240 is shown as a function of height z. Solid lines represent the energy of the eigenstates 211, 212, 213 for the case where only a single neutron mirror 140 is present in the quantum mechanical system 110. The neutron mirror 140 is located at z = zero, with the neutron 120 situated above the neutron mirror 140. Dashed lines represent the energy of the eigenstates 211, 212, 213 for the case where two neutron mirrors 140, 141 are present in the quantum mechanical system 110.Neutron 120 is located here between neutron mirror 140, positioned at z = 0, and the first neutron mirror 141, which is located at a height of 25 µm. It can be seen that the ground state 211, which has a very low probability of being found at the first neutron mirror 141, is hardly changed by the presence of the upper first neutron mirror 141. However, the energy level of the first excited eigenstate 212 shifts slightly due to the first neutron mirror 141 being located at a height of 25 µm. The probability of finding the first excited eigenstate 212 also changes noticeably, since the probability of finding neutron 120 in the first excited eigenstate 212 at a height of 25 µm is non-zero in the case with only one neutron mirror 140.It is clear that if a second neutron mirror 141 is arranged there, the probability of finding neutron 120 must then vanish at the second neutron mirror 141. Thus, it is clear that the wavefunction changes. For higher energy levels, i.e., from the second excited eigenstate 213 onwards, the energy levels and the wavefunctions change even more than for the first excited eigenstate 212. The second excited eigenstate 213 experiences an energy shift of almost 1 peV. This allows transitions into or out of resonance, i.e., a transition is enabled or no longer possible. In general, energy levels can be changed with the help of the upper neutron mirror 141 as a function of the height of the upper neutron mirror 141 above the lower neutron mirror 140. This allows transitions to be enabled or prevented. A Hadamard gate for a QN-it is described below.For this purpose, an ultracold neutron 120 is first prepared in the ground state 211, as described above. The ground state 211 is again used as a control bit. Here, a Q-4-it is considered. The four basis states of the Q-4-it are therefore the first excited eigenstate 212, the second excited eigenstate 213, the third excited eigenstate 214, and the fourth excited eigenstate 215. In the next step, four quarter-pulses are performed starting from the ground state 211 of the control bit. The first 1 / 4 pulse couples the ground state 211 with the first excited eigenstate 212, the second 1 / 4 pulse couples the ground state 211 with the second excited eigenstate 213, the third 1 / 4 pulse couples the ground state 211 with the third excited eigenstate 214, the fourth 1 / 4 pulse couples the ground state 211 with the fourth excited eigenstate 215.Ultimately, the population of the ground state 211 is uniformly distributed among the four excited eigenstates 212, 213, 214, and 215. The Q-4-it is now in a uniform superposition of the four basis states of the QN-it. For the general case of a QN-it, N^N pulses are performed starting from the ground state 211. In each pulse, one Nth of the population from the ground state 211 is distributed to each of the N excited states. A typical switching time for one of the quantum gates described above is on the order of 10 milliseconds. The coherence time of the quantum mechanical system is limited by the neutron lifetime of 878 seconds. Nearly 100,000 switching times fit within this time. In contrast, a swap gate with two qubits requires only two switching times. A swap gate for two Q-5-its requires only five switching times.This shows that extensive quantum calculations can be performed with the available quantum computer.

Claims

1 U31281WO Vienna University of Technology Patent Claims 1. Quantum computer (100) comprising: a quantum mechanical system (110) with a single particle (120) having a non-zero rest mass, wherein the quantum mechanical system (110) has a plurality of eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221), wherein the quantum mechanical system (110) is designed and configured such that a subset of the eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) is used to generate at least two QN-its (241, 242, 243, 244, 245, 251, 252, 253) to realize, wherein a QN-it (241, 242, 243, 244, 245, 251, 252, 253) is a generalization of a qubit to N states, where N is an integer greater than or equal to two.

2. Quantum computer (100) according to claim 1, wherein the quantum mechanical system (110) comprises: an electrically neutral particle (120),which is arranged in a gravitational field (160) above a particle reflector (140), wherein the quantum mechanical system (110) of the electrically neutral particle in the gravitational field above the particle reflector (140) has infinitely many eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221); and a unit (142) for oscillating the particle reflector (140), wherein the unit (142) for oscillating the particle reflector (140) is designed and configured to couple two different eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) of the infinitely many eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) together; characterized in that the electrically neutral particle (120) and the unit (142) for oscillating the particle reflector (140) are designed and configured such that, 2. the subset of the infinitely many eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) is used to realize the at least two QN-its (241, 242, 243, 244, 245, 251, 252, 253).

3. Quantum computer (100) according to claim 2, wherein the electrically neutral particle (120) is one of the following group: a neutron and an atom.

4. Quantum computer (100) according to claim 2 or 3, wherein the electrically neutral particle (120) is one of the following group: a neutron, a hydrogen atom, and an antihydrogen atom.

5. Quantum computer (100) according to one of claims 2 to 4, characterized in that the electrically neutral particle (120) is an ultracold neutron (120) and the particle reflector (140) is a neutron mirror (140).6.

7. Quantum computer (100) according to any one of claims 1 to 5, further comprising: a state selection unit (144) which is designed and configured to remove a particle (120) that is not in the ground state (211) from the quantum mechanical system (110).

8. Quantum computer (100) according to claim 6, wherein the particle is a neutral particle.

9. Quantum computer (100) according to claim 6, wherein the particle is an ultracold neutral particle.

10. Quantum computer (100) according to claim 5, further comprising: a state selection unit (144) which is designed and configured to remove an ultracold neutron (120) that is not in the ground state (211) from the quantum mechanical system (110).

11. Quantum computer (100) according to any one of claims 2 to 9. 3 further comprising: a second particle reflector (141) arranged above the particle reflector (140) and comprising a second unit (143) for oscillating the second particle reflector (141).

11. Quantum computer (100) according to claim 10, wherein the second particle reflector (141) is arranged above the particle (120).

12. Quantum computer (100) according to claim 5 or 9, further comprising: a second neutron mirror (141) arranged above the neutron (120) and comprising a second unit (143) for oscillating the second neutron mirror (141). 13.Quantum computer (100) according to claim 2, optionally with the features of any one of claims 2 to 12, characterized in that the unit (142) for oscillating the particle reflector (140) is designed and configured to couple a first eigenstate of a first QN-it (241, 242, 243, 244, 245, 251, 252, 253) with a second eigenstate of the first or a second QN-it (241, 242, 243, 244, 245, 251, 252, 253) such that a connection is established between the first eigenstate of the first QN-it (241, 242, 243, 244, 245, 251, 252, 253) and the second eigenstate of the first or the second QN-it (241, 242, 243, 244, 245, 251, 252, 253) a rabioscillation is driven. 14.Quantum computer (100) according to claim 10, 11 or 13, characterized in that the second unit (143) is designed and configured to oscillate the second particle reflector (141) and to couple a first eigenstate of a first QN-it (241, 242, 243, 244, 245, 251, 252, 253) with a second eigenstate of the first or a second QN-it (241, 242, 243, 244, 245, 251, 252, 253) such that a connection exists between the first eigenstate of the first QN-it (241, 242, 243, 244, 245, 251, 252, 253) and the second eigenstate of the first or the second QN-it (241, 242, 243, 244, 245, 251, 252, 253) a rabioscillation is driven. 4 15. Quantum computer (100) according to claim 5, 9 or 12, characterized in that the unit (142) for oscillating the neutron mirror (140) is designed and configured to couple a first eigenstate of a first QN-it (241, 242, 243, 244, 245, 251, 252, 253) with a second eigenstate of the first or a second QN-it (241, 242, 243, 244, 245, 251, 252, 253) such that a connection exists between the first eigenstate of the first QN-it (241, 242, 243, 244, 245, 251, 252, 253) and the second eigenstate of the first or the second QN-it (241, 242, 243, 244, 245, 251, 252, 253) a rabioscillation is driven. 16.Quantum computer (100) according to claim 12 or 15, characterized in that the second unit (143) is designed and configured to oscillate the second neutron mirror (141) and to couple a first eigenstate of a first QN-it (241, 242, 243, 244, 245, 251, 252, 253) with a second eigenstate of the first or a second QN-it (241, 242, 243, 244, 245, 251, 252, 253) such that a connection exists between the first eigenstate of the first QN-it (241, 242, 243, 244, 245, 251, 252, 253) and the second eigenstate of the first or the second QN-it (241, 242, 243, 244, 245, 251, 252, 253) a rabioscillation is driven. 17.Quantum computer (100) according to claim 2, optionally with the features of any one of claims 2 to 16, wherein the unit (142) for oscillating the particle reflector (140) is designed and configured to couple eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) of the at least two QN-its (241, 242, 243, 244, 245, 251, 252, 253) such that a quantum gate for the at least two QN-its (241, 242, 243, 244, 245, 251, 252, 253) is realized.

18. Quantum computer (100) according to one of claims 10, 11, 13, 14 and 17, characterized in that the second unit (143) is designed and configured to oscillate the second particle reflector (141), eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) of the at least two QN-its (241, 242, 243, 244, 245, 251, 252, 253) so. 5 to couple that a quantum gate is realized for the at least two QN-its (241, 242, 243, 244, 245, 251, 252, 253).

19. Quantum computer (100) according to one of claims 5, 9, 12, 15 and 16, characterized in that the unit (142) for oscillating the neutron mirror (140) is designed and configured to couple eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) of the at least two QN-its (241, 242, 243, 244, 245, 251, 252, 253) such that a quantum gate for the at least two QN-its (241, 242, 243, 244, 245, 251, 252, 253) is realized. 20.Quantum computer (100) according to one of claims 12, 15, 16 and 19, characterized in that the second unit (143) is designed and configured to oscillate the second neutron mirror (141) and to couple eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) of the at least two QN-its (241, 242, 243, 244, 245, 251, 252, 253) such that a quantum gate for the at least two QN-its (241, 242, 243, 244, 245, 251, 252, 253) is realized.

21. Quantum computer (100) according to any one of claims 17 to 20, characterized in that the quantum gate is a Pauli X gate, a Pauli Y gate, a Pauli Z gate, a Hadamard gate, a phase gate or S gate, a T gate or π / 8 gate, a CNOT gate, a controlled Z gate, a swap gate, a Toffoli gate, a Fredkin gate, a Deutsch gate, a generalized Toffoli gate, a generalized Fredkin gate or a generalized Deutsch gate. 22.Quantum computer (100) according to claim 2, optionally with the features of one of claims 2 to 20, characterized in that the unit (142) for oscillating the particle reflector (140) is designed and configured to perform a Rabi-^-pulse for each state of N states of two QN-its (241, 242, 243, 244, 245, 251, 252, 253), such that for these. 6 two QN-its (241, 242, 243, 244, 245, 251, 252, 253) a SWAP gate is implemented.

23. Quantum computer (100) according to one of claims 10, 11, 13, 14, 17, 18 and 22, characterized in that the second unit (143) for oscillating the second particle reflector (142) is designed and configured to perform a Rabi-^ pulse for each of N states of two QN-its (241, 242, 243, 244, 245, 251, 252, 253), such that a SWAP gate is realized for these two QN-its (241, 242, 243, 244, 245, 251, 252, 253).

24. Quantum computer (100) according to one of claims 5, 9, 12, 15, 16, 19 and 20, characterized in that the unit (142) for oscillating the neutron mirror (140) is designed and configured to perform a Rabi-^ pulse for each of the N states of two QN-its (241, 242, 243, 244, 245, 251, 252, 253), such that a SWAP gate is implemented for these two QN-its (241, 242, 243, 244, 245, 251, 252, 253). 25.Quantum computer (100) according to any one of claims 12, 15, 16, 19, 20 and 24, characterized in that the second unit (144) for oscillating the second neutron mirror (142) is designed and configured to perform a Rabi-^ pulse for each of the N states of two QN-its (241, 242, 243, 244, 245, 251, 252, 253), such that a SWAP gate is implemented for these two QN-its (241, 242, 243, 244, 245, 251, 252, 253).

26. Quantum computer (100) according to any one of the preceding claims, further comprising: a readout unit (180) for determining a. 7 Occupation probability of at least one of the eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221).

27. Quantum computer (100) according to claim 26, characterized in that the readout unit (180) is a spatially resolved detector (182) for determining a density of particles of the same type as the single particle; or the readout unit (180) is a spatially resolved detector (182) for determining the neutron density.

28. Quantum computer (100) according to claim 2, optionally with the features of any one of claims 2 to 27, characterized in that the unit for oscillating the particle reflector (140) is designed and configured to exchange a population of a state to be investigated with a population of a ground state by means of a ^-pulse, and the state selection unit is designed and configured to determine an occupancy probability of the resulting ground state. 29.Quantum computer (100) according to any one of claims 10, 11, 13, 14, 17, 18, 22, 23 and 28, characterized in that the second unit (144) for oscillating the second neutron mirror (142) is designed and configured to exchange a population of a state to be investigated with a population of a ground state using a ^-pulse, and the state selection unit is designed and configured to determine an occupation probability of the resulting ground state.

30. Quantum computer (100) according to any one of claims 5, 9, 12, 15, 16, 19, 20, 24 and 25, characterized in that the unit for oscillating the neutron mirror (140) is designed and configured.

8. quantum computer (100) according to any one of claims 12, 15, 16, 19, 20, 24, 25 and 30, characterized in that the second unit (144) for oscillating the second neutron mirror (142) is designed and configured to exchange a population of a state under investigation with a population of a ground state using a pulse, and the state selection unit is designed and configured to determine an occupation probability of the resulting ground state.

32. quantum computer (100) according to any one of the preceding claims, characterized in that the energy of the single particle is less than 350 nanoelectron volts. 33.Quantum computer (100) according to claim 5, optionally with the features of any one of claims 6 to 32, characterized in that the energy of the ultracold neutron (120) is less than 350 nanoelectron volts.

34. Quantum computer (100) according to any one of the preceding claims, characterized in that the single particle (120) is surrounded by a magnetic field such that the infinitely many eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) split into two eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) depending on a spin quantum number of the single particle (120). 9 35. Quantum computer (100) according to claim 5, optionally with the features of one of claims 6 to 34, characterized in that the ultracold neutron (120) is surrounded by a magnetic field, such that the infinitely many eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) split into two eigenstates (211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221) depending on a spin quantum number of the neutron (120).

36. Quantum computer (100) according to claim 2, optionally with the features of any one of claims 6 to 35, characterized in that the particle reflector (140) is arranged in a vibration-damped manner.

37. Quantum computer (100) according to claim 5, optionally with the features of any one of claims 6 to 36, characterized in that the neutron mirror (140) is arranged in a vibration-damped manner. 38.Quantum computer (100) according to one of the preceding claims, characterized in that the switching time of a quantum gate is smaller than the coherence time of the quantum mechanical system.

39. Quantum computer (100) according to claim 38, characterized in that the quantum mechanical system (110) is designed and configured such that the coherence time is greater than 1 millisecond, preferably greater than 800 seconds.

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