Fast multi-photon quantum gates for optical qubits and qutrits

Abstract

The present disclosure relates to a system for performing a quantum manipulation protocol, e.g., a quantum computing algorithm, the system comprising: a trapping laser system for trapping neutral atoms in an optical trap array inside a vacuum chamber operated at a trapping wavelength λtr, wherein each neutral atom comprises a ground state |1S0>, a first metastable excited state |3P0> and a second metastable excited state |3P2>. The system further comprises a state manipulation laser system for generating laser radiation for coupling, via a phase-coherent multi-photon transition, the ground state |1S0> to the first metastable excited state |3P0> and / or to the second metastable excited state |3P2> as well as a magnetic field system for generating a magnetic field Bext at a location of the optical trap array inducing a Zeeman splitting for magnetic substates of the second metastable excited state |3P2>. The system further comprises a control system for controlling the laser radiation generated by the laser system to coherently modify a quantum state of the plurality of neutral atoms based on the quantum manipulation protocol and a quantum state readout system for determining the quantum state of at least a subset of the plurality of neural atoms based on the quantum manipulation protocol. According to some aspects, a direction of the magnetic field Bext with respect to a polarization direction of the optical trap array is selected such as to render the optical trap array operated at the trapping wavelength λtr a magic- wavelength optical trap for the second metastable excited state |3P2> and the first metastable excited state |3P0> and / or for the second metastable excited state |3P2> and the ground state |1S0> or both. A state-selective detection scheme as well as related devices and methods are also disclosed.

Description

November 6, 2025 Max-Planck-Gesellschaft zur Fbrderung der M177378WO ANE / BMNWissenschaften e.V. Ludwig-Maximilians-Universitat Miinchen, in Vertretung des Freistaates BayernFAST MULTI-PHOTON QUANTUM GATES FOR OPTICAL QUBITS AND QUTRITSFIELD OF INVENTION

[0001] Aspects of the present disclosure relate to quantum technologies using neutral atoms in optical traps as qubits and / or qutrits, and more particularly to techniques, systems, and devices for fast and high-fidelity qubit and / or qutrit state manipulation in engineered trapping potentials without state-dependent light-shifts.INTRODUCTION

[0002] Quantum technologies, including quantum computers, optical lattice clocks, and / or analog quantum simulators, can outperform classical devices in several applications. In neutral atom-based implementations of such quantum technologies, long-lived internal states of neutral atoms trapped in optical potentials, such as optical tweezer arrays or optical lattices maybe used. Neutral atom-based quantum computers, simulators and / or (optical) atom clocks typically trap neutral atoms (i.e. electrically neutral atoms) in optical potentials (e.g. in arrays of optical dipole traps or in optical lattices or combinations thereof), and use two or more long-lived (with respect to operation time) internal (electronic) states for performing quantum manipulation protocols such as a sequence of quantum gates of a quantum comptuting algorithm. The selected states of the atoms may thus form the states of a qubit and / or qutrit.

[0003] Such quantum manipulation systems typically require precise control over the internal states of the neutral atoms to perform high-fidelity operations such as single qubit gates, Ramsey sequences, etc. For example, quantum computers use physical qubits to store the basic unit of information and perform quantum gates on the qubits to process the stored information, e.g. according to processing instructions of a quantum computing algorithm. Running quantum algorithms requires single- and two- qubit gates, which are the basic computation operations acting on individual qubits andindividual pairs of qubits, respectively. However, achieving fast and coherent manipulations of such internal states in large quantum registers of neutral atoms still present significant challenges.SUMMARY

[0004] One of the main challenges in neutral atom-based quantum technology devices is the requirement for so-called magic trapping conditions (e.g. see: S. Zhang, F. Robicheaux, and M. Saffman: Magic-wavelength optical traps for Rydberg atoms; arXiv: 1106.246302 [physics. atom-ph] for general background in this field of technology), where a differential light shift caused by an optical trapping potential between two or more internal states of neutral atoms essentially vanishes (e.g., on time and precision scales relevant for the specific implementation). Such a constraint typically either limits the choice of trapping wavelengths or necessitates specifically engineered trapping potentials. In addition, driving optical clock transitions, e.g., in alkaline earth (like) atoms such as Yb and Sr typically requires significant optical power due to the weak optical coupling on the clock transition, which can lead to spurious light shifts, exacerbate lift-shift induced dephasing and thus may limit quantum operation fidelity. More specifically, ensembles of neutral atoms in optical tweezer arrays or optical lattices are a promising approach for realizing neutral-atom based quantum technologies. The dominant platforms use laser pulses to coherently manipulate the neutral atoms, either for quantum information processing or, for example, sensing, metrology, and / or analog quantum simulation. For example, in88Sr, established techniques exploit long-lived clock states coherently coupled to the electronic ground state. Driving the corresponding clock transitions typically requires suitable trapping conditions with vanishing differential light shifts (so-called “magicwavelength” conditions), which constrain the choice of the trapping wavelength of the optical trap array.

[0005] A known example of such a trapping configuration is the magic wavelength at 813 nm used in modern optical atomic clocks based on Strontium atoms. Alternatively, magic trapping conditions can be engineered with suitable combinations of trap polarization and magnetic fields, as demonstrated recently in several quantum physics experiments (see for example: S. Pucher, et all. Fine-Structure Qubit Encoded in Metastable Strontium Trapped in an Optical Lattice Phys. Rev. Lett. 132, 150605).Further, it is found that driving an optical clock transition even at magic-wavelength trapping conditions typically requires significant laser power, due to the weak (strictly speaking vanishing) optical coupling on the clock transition (e.g., the |1S0> to |3P0> transition shown in Fig. 3). The large, required laser power constitutes a significant bottleneck, as it also is accompanied by spurious light shifts due to nearby levels that limit the achievable operation quality in realistic experimental settings. Further, applying strong magnetic fields at arbitrary angles as required for magic angle tuning is experimentally challenging, which limits the degree to which angle-tuned magic wavelength traps can be utilized for applications.To address such and similar issues of neutral atom-based quantum technologies, in a first aspect, the present disclosure relates to a system for performing a quantum manipulation protocol, the system comprising a trapping laser system for trapping neutral atoms (e.g., alkaline earth atoms such as Sr or Yb) in an optical trap array inside a vacuum chamber operated at a trapping wavelength Xtr(e.g., 8i3nm, loonm, etc.), wherein each neutral atom comprises a ground state |1S0>, a first metastable excited state |3P0> and a second metastable excited state |3P2>. The system further comprises a state manipulation laser system for generating laser radiation for coupling, via a phase-coherent multi-photon transition, the ground state |1S0> to the first metastable excited state |3P0> and / or to the second metastable excited state |3P2> as well as a magnetic field system for generating a magnetic field Bextat a location of the optical trap array inducing a Zeeman splitting for magnetic substates of the second metastable excited state |3P2>, wherein a direction of the magnetic field Bextwith respect to a polarization direction of the optical trap array is selected such as to render the optical trap array operated at the trapping wavelength Xtra magic-wavelength optical trap for the second metastable excited state |3P2> and the first metastable excited state |3P0> and / or for the second metastable excited state |3P2> and the ground state |1S0>. The system further comprises a control system for controlling the laser radiation generated by the laser system to coherently modify a quantum state of the plurality of neutral atoms based on the quantum manipulation protocol and a quantum state readout system for determining the quantum state of at least a subset of the plurality of neural atoms based on the quantum manipulation protocol.

[0006] In some implementations, as illustrated in Fig. 7 and Fig. 8 discussed below, it is possible to select the direction of the magnetic field with respect to the polarization direction as well as the trapping wavelength Xtrof the optical trap array such that a triple-magic- wavelength trap ca be realized for the second metastable excited state 13P2>, the first metastable excited state |3Pi> and the ground state |1S0>.

[0007] Thus, aspects of the present disclosure overcome typical limitations as discussed above an enable fast optical coupling compatible with engineered trapping potentials with essentially vanishing differential light shifts.

[0008] Advantages include substantially improved coherence times suitable for quantum technology applications under these conditions. Exploiting the flexibility the present disclosure, allows to realize a triple-magic trap for alkaline earth atoms such as Sr. In the context of quantum computing, this offers the exceptional possibility of dynamically mapping qubit information onto different states to exploit either the faster and recoil-free coupling of the fine-structure states (e.g., of the second metastable excited state |3P2> and the first metastable excited state |3P0>) or the exceptionally long coherence times of the first metastable excited state |3P0> with respect to the ground state |1S0>.

[0009] Furthermore, in the context of quantum metrology, the present disclosure enables direct access to both clock transitions (i.e. the |1S0> to |3P0> transition and the |1S0> to |3P2> transition) using the same hardware system. Additionally, in the context of quantum sensing, the use of dynamical decoupling sequences enables the tailoring of the sensor's sensitivity for specific frequency ranges.

[0010] Such and similar applications are enabled by the combination of angle- tuned trapping potentials with coherent and fast all-to-all optical couplings (see Fig 6A to Fig. 6C), which offers new flexibility in engineering trapping potentials without sacrificing optical coupling strength.

[0011] As a further advantage, exploiting this flexibility, an addressable 90° magic lattice setup providing a particularly power-efficient, scalable platform for neutral atom processors can be realize (see Fig. 10). For example, using a suitable range of trapping wavelengths, a magic-wavelength trap can be realized simultaneously for a horizontally installed optical lattice and for orthogonally propagating opticaladdressing beams, e.g., enabling the coherent transport of atoms within the quantum register. The present disclosure also relates to a corresponding method for quantum computing as specified in the appended claims as well as to further implementation details as well specified in the dependent claims.

[0012] A further aspect of the present disclosure relates to a quantum computing system comprising a trapping laser system for trapping neutral atoms in an optical trap array inside a vacuum chamber for forming a quantum register of qubits, wherein qubits states |o> and |i> of the qubits are encoded as a first metastable excited state (e.g., 13P0>) and a second metastable excited state (e.g. |3P2>; see Fig. 15 for an example) of the neutral atoms as well as a state manipulation laser system for generating laser radiation for coupling the first metastable excited state to the second metastable excited state, preferably via a Raman transition involving an intermediate state (e.g.,|3Si>) of the neutral atoms. The system may further comprise a qubit entangling laser system for generating laser radiation for coupling selected pairs of neutral atoms in the first metastable excited state (e.g., |3P0>) to a Rydberg state |rx> or selected pairs of neutral atoms in the second metastable excited state (e.g.,|3P2>) to a Rydberg state |r2> which maybe the same as the Rydberg state |rx> or a different state. The system may further include a quantum state readout system for determining a quantum state of at least a subset of the plurality of neural atoms adapted for generating laser radiation for (i) selectively transferring neutral atoms in the second metastable excited state |3P2> to a ground state |1S0> of the neutral atoms, (ii) transferring neutral atoms in the first metastable excited state |3P0> to the ground state |1S0> of the neutral atoms, and (iii) generating a fluorescence signal from neutral atoms in the ground state |1S0> (e.g., as discussed with reference to an examplary implementation shown in Fig. 15), as well as a control system for controlling operation of the state manipulation laser system, the qubit entangling laser system and the quantum state readout system to perform a plurality of quantum gates of a quantum algorithm and to determine a result of the quantum algorithm by selectively detecting neutral atoms in the second metastable excited state, and, subsequently, selectively detecting neutral atoms in the first metastable excited state of the neutral atoms.

[0013] While some conventional readout schemes for atomic systems of qubits may involve converting atoms occupying one of two qubit states into atom loss and imaging the remaining atoms in a state-insensitive way, such a scheme cannotdistinguish population lost already prior to imaging from the loss intentionally induced during the state-sensitive imaging. For example in Rydberg-state based neutral-atom quantum information processors, this deficiency may particularly be problematic as atom losses might occur regularly due to the Rydberg state-based entangling operations. To overcome such issues with conventional systems the systems and methods discussed herein are capable of reconstructing the population of both qubit states (e.g.,3P2> and3P0>) within one computational sequence. As a result, atom loss can be readily identified and compromised data excised. As will be discussed in more detail below with reference to some illustrating examples, some key aspects may involve cycling on a highly state-selective repumping transition that selectively transfers population from one of the qubits states to a detection state, such as a ground state |1S0> of the neutral atoms form which the population can be reliably, fast, and efficiently detected via fluorescence imaging, which ideally is essentially destructive, such that after fluorescence imaging only population in the other qubit state remains which can subsequently be detected (for details see the non-limiting example of Fig. 16).

[0014] Thus, in some aspects the laser radiation generated for selectively transferring neutral atoms in the second metastable excited state to the ground state of the neutral atoms may be adapted to transfer neutral atoms in the second metastable excited state to a third metastable excited state (e.g., 13Pi>) which subsequently decays into the detection state (e.g., the ground state | iSo>) of the neutral atoms. Further, the laser radiation generated for transferring neutral atoms in the first metastable excited state to the detection state (e.g., the ground state | iSo>) of the neutral atoms may be adapted to transfer neutral atoms in the first metastable excited state and the second metastable excited state to the third metastable excited state which subsequently decays into the ground state of the neutral atoms for detection e.g., via fluorescence imaging.

[0015] In some aspects, the quantum state readout system may thus comprise a fluorescence generation laser system adapted to illuminate neutral atoms in the detection state (e.g., the ground state | iSo>) of the neutral atoms with a pair of essentially counterpropagating laser beams e.g., adapted for coupling the ground state | iSo> to a 11P1> excited state of the neutral atoms on a dipole-allowed transition. Such a detection transition may result in a photon induced recoil for the atoms being imagedthat is large enough to remove these atoms from the optical trap array thereby rendering the detection essentially fully destructive, e.g., because the detected atoms are then no longer trapped and will thus not be detected in a subsequent imaging procedure, e.g., for detecting the population that remains in the first excited state. In this manner it can be ensured that after the atoms in the second exited state are detected, only atoms in the other qubit state remain trapped which can then be detected using a state-insensitive imaging scheme (for further details see example of Fig. 16). In this manner, state-resolved detection can be realized efficiently and reliably with minimal hardware requirements.

[0016] Further details, aspects and advantages of the present disclosure are discussed below with reference to the drawings and are the subject of the claims which define the scope of the present disclosure.BRIEF DESCRIPTION OF THE DRAWINGS

[0017] So that the above-recited features of the present disclosure can be understood in detail, a more particular description, briefly summarized above, may be had by reference to aspects, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only some typical aspects of this disclosure and are therefore not to be considered limiting of its scope, for the description may admit to other equally effective aspects. The same reference numbers in different drawings may identify the same or similar elements.

[0018] FIG. 1 illustrates aspects of a system for trapping and manipulating neutral atoms for quantum computing, metrology, simulation and / or sensing applications according to a possible implementation of the present disclosure.

[0019] Fig. 2 illustrates a block diagram of a system for performing a quantum manipulation protocol, such as a quantum computing algorithm according to aspects of the present disclosure.

[0020] FIG. 3 shows an atomic level scheme with multi-photon laser couplings for the bosonic strontium isotope88Sr that can be used as qubit and / or qutrit in some implementations of the present disclosure.

[0021] FIG. 4 illustrates aspects of a system for generating a magnetic field at the location of the optical trap array inside a vacuum chamber according to aspects of the present disclosure.

[0022] FIG. 5 illustrates aspects of magic-angle tuning / trap engineering according to aspects of the present disclosure for a single optical tweezer trap.

[0023] FIG. 6A to Fig 6C illustrate three exemplary multi-photon coupling schemes that can be used for fast quantum gates / state manipulations according to aspects of the present disclosure.

[0024] FIG. 7 illustrates the magic angle for different pairs of states as function of the trapping wavelength. The top trace corresponds to the first line in the box inset and the lower trace to the second line.

[0025] FIG. 8 illustrates measurements of light shifts as function of the magic angle for the scalar magic wavelength 813 nm to identify conditions for a triple-magic- wavelength trap.

[0026] FIG. 9 illustrates measurements of light shift as function of trapping wavelengths for an angle of 90°.

[0027] Fig. 10 illustrates further aspects of a system for trapping and manipulating neutral atoms for quantum computing, metrology and / or sensing applications according to a possible implementation of the present disclosure using a folded optical lattice and optical tweezer traps.

[0028] FIG. 11 shows a process diagram of a quantum computing method according to a possible implementation of the present disclosure.

[0029] FIG. 12 shows coherence measurements of the fine- structure qubit according to a possible implementation of the present disclosure.

[0030] Fig. 13 illustrates a block diagram of quantum computing system according to aspects of the present disclosure.

[0031] FIG. 14 shows a process diagram of a quantum computing method according to a possible implementation of the present disclosure.

[0032] FIG. 15 shows a state-resolved detection scheme for a fine-structure qubit according to a possible implementation of the present disclosure.

[0033] FIG. 16 shows an optimized detection scheme for a fine-structure qubit according to a possible implementation of the present disclosure.

[0034] FIG. 17 shows Rabi Oscillations for a fine-structure qubit according to a possible implementation of the present disclosure.

[0035] Fig. 18 shows exemplary typical branching rations for the optical pumping transition used for selectively transferring atoms / population in the second qubit state (e.g., |3Po>) to the detection state (e.g. |iSo>) via a short-lived intermediate state (e.g., 13P1> ) in an example implementation of the present invention.DESCRIPTION OF ILLUSTRATIVE EXAMPES

[0036] Various aspects of the present disclosure are described in more detail hereinafter with reference to the accompanying drawings. The present disclosure may, however, be implemented in many different forms and should not be construed as limited to any specific structure or function presented herein. Rather, these aspects are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present disclosure to those skilled in the art. Based on the teachings herein one skilled in the art should appreciate that the scope of the present disclosure isintended to cover any aspect of the present disclosure disclosed herein, whether implemented independently of or combined with any other aspect of the present disclosure. For example, a device or system maybe implemented, or a method maybe practiced using any number of the aspects set forth herein. In addition, the scope of the present disclosure is intended to cover such a device, system or method which is practiced using other structure, functionality, or structure and functionality in addition to or other than the various aspects of the present disclosure set forth herein. Any aspect of the present disclosure disclosed herein may be implemented by one or more elements of a claim. While specific feature combinations are described in the following with respect to certain aspects of the present disclosure, it is to be understood that not all features of the discussed examples must be present for realizing the technical advantages of the devices, systems, methods and computer programs disclosed herein. Disclosed aspects may be modified by combining certain features of one aspect with one or more features of other aspects. A skilled person will understand that features, steps, components and / or functional elements of one aspect can be combined with compatible features, steps, components and / or functional elements of any other aspect of the present disclosure.

[0037] Several aspects of quantum computation, metrology and / or simulation with neutral atoms will now be presented with reference to various devices, systems and methods that are described in the following detailed description and illustrated in the accompanying drawings by various blocks, modules, components, circuits, steps, processes, algorithms, and / or the like (collectively referred to as “elements”). These elements may be implemented using hardware, software, or combinations thereof. Whether such elements are implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system.

[0038] While aspects of the present disclosure are presented in the following using the bosonic Strontium isotope88Sr, it is to be understood, that any other species of neutral atom with a suitable internal level structure may also be used in other implementations of the present disclosure.

[0039] FIG. 1 shows aspects of a system for performing a quantum manipulation protocol, e.g., a neutral atom-based quantum computing device. Fig. 2 shows anexamplary functional block diagram of such a system 200 according to aspects disclosed herein. The system 200 comprises a trapping laser system 210 for trapping neutral atoms (e.g.,88Sr atoms) in an optical trap array 110 inside a vacuum chamber 115 operated at a trapping wavelength, e.g., Xtr= 8i3nm, losonrn, looonm etc.

[0040] As exemplarily shown in Fig. 3 each neutral atom comprises a ground state 11S0>, a first metastable excited state |3P0> and a second metastable excited state |3P2>. The system 200 further comprises an atomic state manipulation laser system 220 generating laser radiation 130 for coupling, via a phase-coherent multi-photon transition, the ground state |1S0> to the first metastable excited state |3P0> or to the second metastable excited state |3P2>. As exemplarily shown in Fig. 3 for88Sr atoms the ground state |1S0> can be coupled to the first metastable excited state |3P0> via a three-photon transition with wavelengths 689nm, 688nm, and 679nm, and to the second metastable excited state |3P2> via a corresponding three-photon transition with wavelengths 689nm, 688nm, and yoynm. Similarly, the states |3P0> and |3P2> of the so-called fine structure qubit can be coupled via a two-photon Raman transition with wavelengths 6y9nm and yoynm. In this manner, the three states can be used to form a qutrit and / or pairs of qubits with different properties.

[0041] For example, implementing the |1S0> to |3P0> and / or the |1S0> to |3P2> coupling required for many quantum technologies is commonly done using a single light field with narrow linewidth. Driving the clock transitions under these conditions requires a strong magnetic quantization axis to boost the achievable Rabi frequency. Aspects of the present disclosure allows to overcome this constraint by realizing the coherent couplings with three phase-coherent light fields on a three-photon transition. In this case, the slow dipole-forbidden coupling on the clock transitions can be avoided and instead a coupling using dipole-allowed transitions via two intermediate excited states,3Pi and3Si can be implemented. To avoid unwanted scattering from these intermediate states, a detuning can be used, which gives rise to an effective two-level description approximately equivalent to a direct drive.

[0042] The relevant laser coupling schemes are also shown in Fig. 6A to Fig. 6C, e.g., the coupling fromJS0to3P0and the coupling from ^oto the3P2mj =0 magnetic substate. Additionally, under triple-magic conditions, the two clock states(3P0,3P2nij =o) can be directly coupled with a coherent two-photon scheme, thereby forming a so-called fine structure qubit, which allows for high-speed and nearly recoil- free qubit rotations. Combined, this constitutes a qutrit with fast all-to-all coupling enabled by a combination of multi-photon transitions and tailored angle-tuned trapping potentials. Despite the non-scalar trapping potentials (illustrated by reference number 515 in Fig. 5), where local polarization imperfections may directly affect the differential light shift it is possible to obtain long coherence times for the fine structure qubit (see Fig. 12), demonstrating the applicability of the present disclosure for quantum technology applications. Fig. 12 shows coherence measurements of the fine- structure qubit. An atom-atom coherence time of up to 1.4s can be realized using magic angle tuning in an optical tweezer array demonstrating the applicability of angle-tuned trapping potentials disclosed herein for coherent quantum technologies.

[0043] Fig. 5 also illustrates that the two clock states in88Sr typically experience different energy shifts 515 when placed inside an optical trapping potential 510. Using a magnetic field B applied under a suitable angle 0 with respect to the linearly polarized (Et) trapping potentials, allows tuning of the differential energy shift to an essentially vanishing degree (see Fig. 7 and Fig. 8).

[0044] As further shown in Fig. 1, the multi-wavelength laser radiation 130 (Raman beams) can be applied to the plurality of neutral atoms in the trap array 110 via a single single-mode, polarization maintaining optical fiber 135, that, preferably, is length and temperature stabilized. The system 200 may optionally further comprise multi-wavelength waveplates (not shown) which rotate the polarization of a first wavelength of the laser radiation 130 but leave a second wavelength essentially unaffected.

[0045] In this manner, using88SR atoms greatly simplifies hardware requirements and improves quantum protocol speed and fidelity. For example, in order to suppress differential phase noise all light fields can be applied via the same polarization maintaining optical fiber 135. Thereby, the optical path for the different light fields is shared which minimizes phase noise due to path-length fluctuations, relevant in particular inside the optical fiber 135. Driving three-photon transitions from the ground state to either of the clock states typically requires light fields with mt ando± polarization components. Under the constraint of common linear polarization, which is particularly simple to realize, it is possible to choose an angle of approximately 35° between the linear light polarization and the magnetic quantization axis provided by the magnetic field Bext, thereby maximizing the three-photon Rabi frequency. However, such parameter settings also may lower the two-photon coupling strength between the clock states in comparison to ideal settings for this transition. This limitation can be overcome by using tailored waveplates which rotate the polarization of the 688nm and 68qnm light fields while leaving the polarization of the 679nm and 7O7nm light fields unaffected, for example. This provides a light field with linear polarization where the 679nm / 7O7nm polarization is orthogonal to the 688nm / 689nm polarization. This choice further boosts the three-photon Rabi frequency and simultaneously provides the optimal coupling strength between the fine-structure states. Such a design combines passive stability to achieve a low phase-noise light delivery with optimal polarization settings to maximize the optical coupling strength.

[0046] The system 200 further comprises a magnetic field system 230 for generating a magnetic field Bextat a location of the array of optical traps 110 inside the vacuum chamber 115 inducing a Zeeman splitting (shown in Fig. 3) for the magnetic substates of the second metastable excited state |3P2>.

[0047] As mentioned above, for example, the long-lived clock states in88Sr are promising qubit candidates and require magic trapping conditions where the differential light shift between the qubit states vanishes. This either constrains the choice of the trapping wavelength or requires a specifically engineered trapping potential. Tuning of the differential polarizability can be achieved by applying the magnetic field Bextat a specific angle 0 with respect to the linearly polarized trapping potentials (see Fig. 5). Tuning this angle arbitrarily in space requires a suitable arrangement of magnetic field coils (see coils 410a to 420b in Fig. 4). The achievable magnetic field strength is thus typically limited by the requirement to tune the field angle in space arbitrarily. This is problematic for applications that require a fast coupling of the qubit states, like quantum computing, where fast single photon coupling conventionally requires a strong magnetic field. The incompatibility of strong magnetic fields with arbitrary orientation limits the applicability of angle-tuned trapping potentials in neutral atoms quantum computers and similar systems.

[0048] Thus, in the system 200 described herein, a direction of the magnetic field Bextwith respect to a polarization direction of the optical trap array is selected such as to render the array of optical traps operated at the trapping wavelength Xtra magicwavelength optical trap for the second metastable excited state |3P2> and the first metastable excited state |3P0> and / or for the second metastable excited state |3P2> and the ground state |1S0>. For example, as shown in Fig. 5, the optical trapping laser beams 510 may be propagating essentially vertically, e.g., through high-resolution objective 125 shown in Fig. 1, and maybe linearly polarized. In such a configuration, as shown in Fig. 5, the magnetic field Bextand the polarization vector Etof the optical trap array may have an angle 0 that can be easily adjusted, e.g., by rotating the linear polarization of the trapping beam and / or by changing the direction of the magnetic field B, e.g., by changing the electric currents of one or more of the pairs of coils 410, 415, 420 shown in Fig. 4 to be arranged around the vacuum chamber 115.

[0049] As mentioned above, using multi-photon transitions such as the example transitions shown for88Sr atoms in Fig. 3 allows to overcome the limitations discussed above and to achieve fast optical coupling compatible with engineered e.g., angle-tune optical trapping potentials. Aspects of the present disclosure thus make use of fast multi-photon coupling schemes to implement the optical coupling between different atomic states, e.g., for the coupling schemes shown in Fig. 6A to Fig. 6C. Using such multi-photon transitions driven by phase-coherent laser beams instead of singlephoton transitions allows for fast coupling at low magnetic field strength ~ 10 G and moderate laser intensities. This combination constitutes a key advantage of the present disclosure, making fast optical coupling compatible with engineered e.g., angle-tuned optical trapping potentials. As shown in Such a technique has applications across a broad wavelength range (see Fig. 7).

[0050] Fig. 7 shows magic angle condition for different wavelength. Trapping conditions with vanishing differential light shift can be realized for different states across a broad range of wavelength. At 8i3nm and an angle of ~ 8° triple-magic conditions can be realized to implement a qutrit as discussed above. In addition, the wavelengths with 90° magic angle are of interest to realize magic conditions simultaneously for different potentials which allows coherent qubit transport (see Fig. 10).

[0051] The system 200 further comprises a control system 240 for controlling the laser radiation 130 generated by the laser system 220 to coherently modify a quantum state of the plurality of neutral atoms based on the quantum manipulation protocol. For example, the following application scenarios may benefit from exploiting angle-tuned trapping potentials combined with fast multi-photon transitions.

[0052] First, as shown in Fig. 3 an optical qutrit can be realized. For instance, in88Sr theJS0ground state and the well-known3P0clock state can be magically trapped at 813 nm. Using a magnetic field with moderate strength (on the order of 10 G) applied under an angle of approximately 78° simultaneous magic- wavelength conditions can be realized for the internal states discussed above (see Fig. 8). This offers new possibilities in quantum computing which can exploit the fast coupling of the fine- structure states and the exceptionally long coherence times of the clock qubit states, e.g., by dynamically mapping quantum information onto different qubits for different parts of a quantum algorithm. To overcome the technically challenging generation of a strong magnetic field under magic conditions, the fast multi-photon coupling schemes disclosed herein are employed.

[0053] Fig. 8 also shows a triple-magic angle measurement at a wavelength of 8i3nm. For a magnetic field angle of approximately 78° with respect to the linearly polarized trapping potential the differential light shifts between the states discussed above vanish.

[0054] Second, a magic lattice setup can be implemented. For specific wavelengths between 1000 and i020nm (see Fig. 9) magic trapping conditions can be realized for an angle of 90° between the magnetic field and the trap polarization. Such an arrangement offers additional flexibility. Considering a vertically polarized optical lattice in a power-efficient “folded” configuration (shown in Fig. 10) it is possible to realize simultaneous magic-wavelengths conditions for the optical lattice 1010 and the addressing beams 1020. In particular, these wavelengths maybe within the range of high-power laser amplifiers, which ease the scalability of this approach to large quantum registers.

[0055] Fig- 9 shows measurements indicating IR wavelengths suitable for high- fidelity low-loss imaging at the 90° magic wavelength for the fine-structure qubit in88Sr. In addition this allows for long trapping lifetimes.

[0056] Fig. 10 illustrates a combination of the trapping and addressing optics. A magic lattice 1010 at the 90° magic wavelength can be applied in the horizontal plane with vertical polarization realizing a power-efficient and scalable trapping potential inside the vacuum chamber 115. Using the top or bottom objective addressing tweezers optical lattice (at 90° magic wavelength) resorting / addressing tweezers 1020 array for trapping can be applied which simultaneously satisfy magic trapping conditions and are therefore suitable for coherent qubit transport. Coupling the qubit states under magic trapping conditions (which constrains the magnetic field) is implemented with fast multi-photon transitions.

[0057] Thirdly, a coherent depumping scheme can be implemented, e.g., for multi-photon laser cooling. To this end a two-photon coherent depumping via the 3P1 state can be employed using the same lasers involved in the coupling 3P1-3S1-3P2 (or 3P1-3S1-3P0). This can allow for controlled qubit reset in the fine-structure qubit or in the clock qubit with minimal additional heating of the motional degrees of freedom. This has applications in designing special quantum error correction schemes as well as fast laser cooling of large-scale atomic arrays in variety of trap settings, including those where 1S0 and 3P1 are non-magic.

[0058] Going beyond the cases discussed above aspects of the present disclosure provide further advantages for engineered trapping potentials if the magic angle is > 45°. In these cases it is possible to realize simultaneous magic trapping conditions for two orthogonally polarized traps by applying the magnetic field under a suitable angle out of the plane spanned by the polarization of the traps. This opens the possibility to power-efficiently combine trapping light on polarizing beam splitters, e.g., to combine the light from a spatial light modulator with an acousto-optic deflector before focusing them with a high-resolution objective. The fast multi-photon coupling scheme requires phase-coherent light fields which have to be delivered to the atomic ensemble without inducing additional phase noise. Low relative phase noise is crucial for the high-fidelity operation of single-qubit gates driven by multi-color light fields. The present disclosurethus allows to design a simple optical setup to phase-coherently deliver multi-photon light fields using a combination of passively stable elements and identify the optimal laser polarization for this setup.

[0059] As further shown in Fig. 2, the system 200 may comprise a quantum state readout system 250 for determining the quantum state of at least a subset of the plurality of alkaline earth atoms based on the quantum manipulation protocol, e.g., via state-resolved fluorescence imaging using the lower high-resolution objective 145 shown in Fig. 1

[0060] In some cases, the neutral atoms may be alkaline earth atoms such as88Sr atoms. Further, as discussed above, the angle 0 is selected between 78° and 790, and the wavelength Xtrof the array of optical tweezer traps is selected to be 813 nm. Further, the polarization direction of the optical trap array may be essentially vertical, the angle 0 may be selected between 89° and 910, preferably 90°, and the wavelength Xtrof the optical trap array may be selected to be between 1000 nm and 1020 nm.

[0061] Further, the optical trap array my be formed by an optical lattice, preferably by a folded optical lattice, and / or the system 200 may further comprise one or more auxiliary optical traps having an auxiliary trap wavelength Xauxand a polarization direction that is essentially horizontal, wherein the auxiliary trap wavelength Xauxand the polarization direction of the one or more auxiliary optical traps with respect to the direction of the magnetic field Bextare selected such that a differential light shift induced by the one or more auxiliary optical traps on the second metastable excited state with respect to the first metastable excited state or with respect to the ground state or with respect to both does not affect a fidelity of the quantum manipulation protocol.

[0062] As mentioned above, the laser radiation generated by the state manipulation laser system 220 may be applied to the plurality of neutral atoms via a single single-mode, polarization maintaining optical fiber, that, preferably, is length and temperature stabilized; the system optionally further comprising multi-wavelength waveplates which rotate the polarization a first wavelength of the laser radiation but leave a second wavelength essentially unaffected.

[0063] The present disclosure also relates to a neutral atom quantum computer comprising the system as discussed above and an interface, for receiving, via a network 270 from a remote user device 260, instructions of a quantum algorithm, and for sending, via the network, a result of the quantum algorithm to the remote user device.

[0064] Fig. 11 shows a method for quantum computing comprising obtaining 1110 a set of instructions of a quantum algorithm, forming 1120 a quantum register by trapping a plurality of neutral atoms in an optical trap array inside a vacuum chamber, wherein a ground state, a first metastable excited state and a second metastable excited state of the neutral atoms form a qutrit and / or qubits used for quantum computing, and performing 1130, based on the obtained set of instructions of the quantum algorithm, a sequence of quantum gates on a subset of the plurality of neutral atoms. As discussed above for the operation of the system 200 of Fig. 2, performing the sequence of quantum gates comprises generating a magnetic field Bextat a location of the optical trap array for inducing a Zeeman splitting for magnetic sub-states of the second metastable excited state, and illuminating the subset of the plurality of neutral atoms with laser radiation coupling, via a multi-photon transition, the ground state to the first meta-stable excited state, and / or the ground state to the second metastable excited state.

[0065] In some implementations, the method may further comprise applying two-photon coherent depumping for controlled qubit state reset and, optionally, laser cooling the plurality of neutral atoms in an optical trap array based at least in part on applying the two-photon coherent depumping for the controlled qubit state reset. For example, multi-photon coherent side-band cooling maybe implemented by the coherent depumping.

[0066] In some implementations, the method may further comprise obtaining, via a network form a remote user device, the set of instructions of the quantum algorithm, and sending a result of the quantum algorithm via the network to the remote user device, e.g., to perform quantum computing as a service via the internet.

[0067] FIG. 12 shows coherence measurements of the fine- structure qubit according to a possible implementation of the present disclosure. Further details aredescribed in arXiv :2411.02869V! [physics.atom-ph] submitted on 5 Nov 2024 and published on 6 Nov 2024.

[0068] Fig. 13 illustrates a block diagram of quantum computing system according to aspects of the present disclosure. As the system of Fig. 2, the system 1300 may comprise a trapping laser system 210 for trapping neutral atoms in an optical trap array 110 inside a vacuum chamber 115 for forming a quantum register of qubits. The qubits states |o> and |i> of the qubits maybe encoded as a first metastable excited state (e.g., |3Po>) and a second metastable excited state (e.g., |3P2>) of the neutral atoms. The system may comprise a state manipulation laser system 220 for generating laser radiation 130 for coupling the first metastable excited state to the second metastable excited state, preferably via a Raman transition involving an intermediate state (e.g., |3Si> in some cases) of the neutral atoms, e.g., to perform arbitrary single qubit gates. Further, a qubit entangling laser system 222 may be operated for generating laser radiation for coupling selected pairs of neutral atoms in the first metastable excited state (e.g., |3Po>) to a Rydberg state |r> or selected pairs of neutral atoms in the second metastable excited state (e.g., |3P2>) to a Rydberg state |r>. Further, a quantum state readout system 250 may be used for determining a quantum state of at least a subset of the plurality of neural atoms and may be adapted for generating laser radiation for selectively transferring neutral atoms in the second metastable excited state to a detection state, e.g., a ground state (e.g., | iSo>) of the neutral atoms, for transferring neutral atoms in the first metastable excited state to the detection state, e.g., the ground state |iSo> of the neutral atoms, and for generating a fluorescence signal from neutral atoms in the detection state, e.g., the ground state |iSo>, e.g., via fluorescence imaging.

[0069] In addition, a control system 240 may be used for controlling operation of the state manipulation laser system, the qubit entangling laser system and the quantum state readout system to perform a plurality of quantum gates of a quantum algorithm and to determine a result of the quantum algorithm for example by selectively detecting neutral atoms in the second metastable excited state, and, subsequently, selectively detecting neutral atoms in the first metastable excited state of the neutral atoms. In this manner, a novel imaging protocol capable of reconstructing the population of bothqubit states may be implemented within one computational sequence. As a result, atom loss can be readily identified and affected data excised.

[0070] In some aspects, the laser radiation for selectively transferring neutral atoms in the second metastable excited state to the detection state, e.g., the ground state | iSo> of the neutral atoms may be adapted to transfer neutral atoms in the second metastable excited state to a third metastable excited state (e.g., 13Pi>) which subsequently decays into the detection state, e.g., the ground state | iSo> of the neutral atoms. For example, as discussed below, a highly state-selective repumping transition (e.g., from |3P2> to |3D2> at a wavelength of 496 nm for Strontium 88 atoms) has been shown to transfer a great majority of population in the |3P2> qubit state into the |3P1> state, transferring less than 0.1% e.g., only -0.035% of population into the other qubit state |3Po>.

[0071] In some implementations, the laser radiation for transferring neutral atoms in the first metastable excited state to the detection state, e.g., the ground state | iSo> of the neutral atoms may be adapted to transfer neutral atoms in the first metastable excited state and the second metastable excited state to the third metastable excited state which subsequently decays into the detection state, e.g., the ground state |iSo> of the neutral atoms.

[0072] Further, the system may comprise a fluorescence generation laser system 1310 adapted to illuminate neutral atoms in the detection state, e.g., the ground state | iSo> of the neutral atoms with a pair of essentially counterpropagating laser beams coupling the ground state | iSo> to an excited state (e.g., 11P1>) of the neutral atoms (see Fig. 16). Moreover, the fluorescence generation laser system may comprises an optical switching device (e.g., an AOM or AOD or similar device) for each laser beam of the pair of beams adapted to illuminate the neutral atoms in the detection state e.g., the ground state | iSo> of the neutral atoms with the pair of essentially counterpropagating laser beams. The control system 250 may be adapted to control the switching devices such that the neutral atoms in the ground state | iSo> of the neutral atoms are illuminated in an alternating manner.

[0073] In some implementations, the fluorescence generation laser system may be further adapted to illuminate the neutral atoms in the ground state | iSo> of the neutral atoms with the pair of essentially counterpropagating laser beams such that a polarization of the laser beams is oriented with respect to a quantization axis defined by an external magnetic field such that a n-transition between the ground state | iSo> and the 11P1> excited state is driven (for details see Fig. 17). In addition, the quantum state readout system 250 may comprise an imaging objective 150 for collecting the fluorescence photons, wherein the imaging objective maybe a high-resolution objective that may comprise a numerical aperture >= 0.5, preferably >=0.65. Further, in order to maximize detection efficiency the imaging objective maybe oriented perpendicular to a quantization axis defined by an external magnetic field (for details see Fig. 17).

[0074] The systems discussed herein may be part of or used in or implement a neutral atom quantum computer, where optionally an interface may be provided, for receiving, via a network (e.g., via the Internet, a cloud system, etc.) from a remote user device (e.g., a user operating a cloud computing system), instructions of a quantum algorithm, and, for sending, via the network, a result of the quantum algorithm to the remote user device. In other words, such an interface may enable the neutral atom quantum computer to provide quantum computing as a service (QCaaS) to remote users.

[0075] FIG. 14 shows a process diagram of a quantum computing method according to a possible implementation of the present disclosure. The method starts with obtaining 1410 a set of instructions of a quantum algorithm, e.g., from a remote user device via a network Step 1420 may comprise forming a quantum register of qubits by trapping a plurality of neutral atoms in an optical trap array inside a vacuum chamber, wherein qubits states |o> and |i> of the qubits are encoded as a first metastable excited state (e.g., |3P0>) and a second metastable excited state (e.g., |3P2>) of the neutral atoms. Step 1430 may comprise performing, e.g., based on the obtained set of instructions of the quantum algorithm, a sequence of quantum gates on a subset of the plurality of neutral atoms, wherein performing the sequence of quantum gates may comprise coupling the first metastable excited state to the second metastable excited state, preferably via a Raman transition involving an intermediate state (e.g., 13Si>) of the neutral atoms, and coupling selected pairs of neutral atoms in the firstmetastable excited state to a Rydberg state | r> or selected pairs of neutral atoms in the second metastable excited state to the same or a different Rydberg state. Step 1440 may comprise determining a result of the quantum algorithm comprising selectively detecting neutral atoms in the second metastable excited state, and, subsequently, selectively detecting neutral atoms in the first metastable excited state of the neutral atoms. In this manner, state-selective imaging of the qubit states can be implemented. This may be used, for example to implement an imaging protocol capable of reconstructing the population of both fine-structure qubit states within one computational sequence. As a result, atom loss can be readily identified and data excised.

[0076] In some examples, determining the result of the quantum algorithm ay comprise selectively transferring neutral atoms in the second metastable excited state to a ground state (e.g., |1S0>) of the neutral atoms, and generating a fluorescence signal from the neutral atoms transferred from the second metastable excited state to the ground state, and, optionally, transferring neutral atoms in the first metastable excited state to the ground state of the neutral atoms and generating a fluorescence signal from the neutral atoms transferred from the first metastable excited state to the ground state.

[0077] In further cases, generating the fluorescence signal from the neutral atoms may comprise illuminating the neutral atoms in the ground state of the neutral atoms with a pair of essentially counterpropagating laser beams e.g., coupling the ground state to an excited state (e.g., | ‘P,>) of the neutral atoms, optionally, in an alternating manner, and, optionally, such that a polarization of the laser beams is oriented with respect to a quantization axis defined by an external magnetic field such that a .n-transition between the ground state and the excited state is driven. In this manner efficient and, if needed, destructive detection of the atoms transferred to the detection state (e.g., the ground state) may be implemented with high fidelity.

[0078] Further, determining the result of the quantum algorithm may further comprise collecting the generated fluorescence with an imaging objective that comprises a numerical aperture >= 0.5, preferably >=0.65; and / or that is orientedperpendicular to a quantization axis defined by an external magnetic field. In this manner a photon count of >0.15 can be achieved.

[0079] The method may further comprise obtaining, via a network form a remote user device, a set of instructions of the quantum algorithm, and sending a result of the quantum algorithm via the network to the remote user device.

[0080] FIG. 15 shows an exemplary state-resolved detection scheme for a fine- structure qubit implemented with Strontium 88 atoms according to a possible implementation of the present disclosure. In panel a) of Fig. 15 the relevant atomic levels and transitions used for state-resolved detection are shown. For state- selective imaging of the second qubit state (here implemented as |3P2>), laser radiation is applied as discussed above, adapted to pump, essentially, all atoms in the second qubit state to a detection state (here implemented as the ground state | iSo>). In the shown example, the optical pumping to the detection state is implemented via laser radiation that couples the second qubit state |3?2> to a further excited state |3D2> which then decays mainly into a further short-lived intermediate state |3P1> (the lifetime in this state in this example is <= 30ps) which then decays, exclusively, to the detection state, e.g., |iSo>. Using the |3D2> state or a similar state with suitable properties has the advantage that it is simple (i.e., only a single photon is used per atom), fast (e.g., optical pumping to the | iSo> state can be achieved with >99% effectiveness in less than 40 ps) and highly state selective because the other qubits state |3Po> is not affected by the repumping laser pulse.

[0081] The duration and / or laser intensity of the optical pumping may be selected such that any atom / population that initially returns from |3D2> to the second qubit state, e.g.,|3P2> is excited again until, eventually, all population (e.g., more than 99% or more than 99.9%) statistically will be pumped to the detection state - in the shown example to the | iSo> ground state via the short-lived |3P1> intermediate state. For the illustrated example, the effectiveness of the optical pumping, e.g., quantified by how much population / atoms statistically are not pumped to the detection state but, e.g., to the first qubit state, e.g., |3Po> was determined to be below 0.035% for the example system of Fig. 15 using Strontium 88 as atomic qubits.Panel a) further shows an example of a non-state selective imaging scheme for the remaining population in qubit state |3Po> which were not affected by the state- selective imaging of the other qubit state |3P2>. Here, optical pumping laser radiation is applied coupling the |3P2> and the |3Po> state to a 13Si> state which will decay via the short-lived state |3Pi> to the detection state |iSo>. Similar as described above, eventually, all atoms / population initially in the first qubit state |3Po> will thus be transferred to the detection state and can be detected via fluorescence imaging as described above.

[0082] Panel b) of Fig. 15 shows an exemplary timing sequence for the state- selective imaging scheme for the second qubit state (e.g. |3P2>) and for the subsequent imaging of the other qubit state (e.g., |3Po>). In the illustrated example a first fluorescence laser pulse is applied to clear all atoms that may be in the detection state (e.g., | iSo>) next, an optical pumping pulse for the |3P2> state is applied followed by an imaging pulse for detecting the atoms / population transferred to the detection state (e.g., | iSo>) in a deep optical trap array (see trace “Tweezers” in panel b)), to enhance spatial accuracy of the imaging. Due to the photon recoil of the fluorescence imaging transition (e.g., | iSo> to 11P1>), the detection of the atoms / population in the detection state (e.g. |3D2>) is essentially destructive, in the sense that a large majority of the detected atoms are lost from the trap due to the photon recoil. In some cases, for example as shown in Fig. 15, a small fraction of imaged atoms is not lost from the trap and would thus affect the subsequent detection of the atoms in the first qubit state (e.g. |3Po>). To avoid this effect, the optical pumping pulse for the second qubit state and the subsequent imaging pulse may be repeated one or more times to ensure that after detection of the population / atoms initially in the second qubit state (e.g., |3P2>) only atoms / population in the first qubit state remain in the optical trap array. For example, in the system used for the results of Fig. 15, a 30 ps long imaging stage reveals population in |iSo>) originating from |3P2>) with minimum influence on population in |3Po>). The pumping and fast imaging are repeated once more to reduce the leakage error from the non-cyclicity of the imaging transition at 461 nm. After two rounds of pumping and fast imaging, the population previously in |3P2>) can thus be determined. Since, as discussed above, the fast imaging is essentially destructive, the remaining population can only be in the |3Po> state, which can be read out using a state-insensitive imaging scheme with corresponding repump lasers as discussedabove. Traps are blinked off (dashed) during the |3P2> repumping pulse to avoid photo-induced losses

[0083] Panel c) of Fig. 15 shows a probability mass function (PMF) of photons emitted by atoms in |iSo> transferred from |3P2> and recorded during fast imaging. The resulting histogram, binarized using a high-fidelity pre-image, shows a classification fidelity> 0.993 averaged over all tweezers at the optimal threshold.

[0084] FIG. 16 shows an optimized detection scheme for a fine-structure qubit as discussed above or similar qubit implementations according to a possible implementation of the present disclosure. To optimize efficient fluorescence photon collection the dipole emission pattern of the individual atoms is leveraged. In particular, the imaging beams may both be linearly polarized (double-arrowed) relative to the quantization axis defined by a 19 G magnetic field (single-arrowed) in this example. The photon collection efficiency is about 0.16 when both imaging beams drive n-transition. The intensities are pulsed in an alternating fashion to balance momentum kicks. In a specific implementation, about 10 mW laser light is applied in each of the counter-propagating arms of the imaging system. The polarizations of both imaging beams are largely parallel to the quantization axis defined by 19 G magnetic field to drive n-transition on the |iSo> to |1P1> line. With a high-resolution objective (NA = 0.65) intentionally placed at 90° relative to the quantization axis, an optimal photon collection efficiency of 0.16 can be achieved considering the dipole emission pattern alone. The imaging beams are resonant with the target transition in a trap with a depth of 55 pK, to produce maximal scattering. The RF diving signals for two optical modulators are pulsed so that the intensities I;, i = 1, 2 of both imaging beams are on in an alternating fashion to avoid uncontrolled spreading of momentum at saturation (see inset). In this manner the | iSo> population in can be detected within approximately 30 ps, a prerequisite for mid-circuit erasure conversion.

[0085] Fig. 17 shows that the qubit states |o> (e.g., |3Po> and |i> (e.g., |3P2>) can be efficiently coupled via a Raman transition e.g., via a |3Si> intermediate state and state-selectively detected as discussed above. This demonstrates highly coherent Rabi oscillations between the two qubit states and thus control over the fine-structure qubit. The erasure detection scheme is also effective against leakage errors e.g., due tooff-resonant scattering e.g., of |3S1> into |3P1>, which quickly decays to the |iSo> state owing to its 21 us lifetime. In this example, branching of |3D2> into the |3PJ> manifold is such that 99.965% of the population decays to | iSo> via |3Pi>, leaving -0.035% in |3Po>, which amounts to a small detection error. The population in can then be detected and / or pushed out of the trap with an intense 461 nm laser pulse. Next, the remaining population in |3Po> can be imaged as discussed above.

[0086] Fig. 18 shows typical branching rations for the optical pumping transition used for selectively transferring atoms / population in the second qubit state (e.g., |3Po>) to the detection state (e.g. | iSo>) via a short-lived intermediate state (e.g., 13Pi>). The ratios are calculated for the example embodiment of using Strontium 88 atoms as qubits discussed above.

[0087] The scientific publication Maximilian Ammenwerth et al. Realization of a fast triple-magic all-optical qutrit in88Sr, arXiv: 2411.0286901 [physics.atom-ph] submitted on 5 Nov 2024 and published on 6 Nov 2024 contains further implementations details of the present disclosure. To avoid redundancies it is incorporated by reference in its entirety and forms an integral part of the present disclosure.

[0088] The foregoing disclosure provides illustration and description but is not intended to be exhaustive or to limit the aspects to the precise form disclosed.Modifications and variations may be made in light of the above disclosure or may be acquired from practice of the aspects. As used herein, the term component is intended to be broadly construed as hardware, firmware, or a combination of hardware and software. As used herein, a processor is implemented in hardware, firmware, or a combination of hardware and software.

[0089] It will be apparent that systems and / or methods described herein may be implemented in different forms of hardware, firmware, or a combination of hardware and software. The actual specialized control hardware or software code used to implement these systems and / or methods is not limiting of the aspects. Thus, the operation and behavior of the systems and / or methods were described herein without reference to specific software code— it being understood that software and hardwarecan be designed to implement the systems and / or methods based on the description herein.

[0090] Even though particular combinations of features are recited in the claims and / or disclosed in the specification, these combinations are not intended to limit the disclosure of various aspects. In fact, many of these features may be combined in ways not specifically recited in the claims and / or dis-closed in the specification. Although each dependent claim listed below may directly depend on only one claim, the disclosure of various aspects includes each dependent claim in combination with every other claim in the claim set. A phrase referring to “at least one of’ a list of items refers to any combination of those items, including single members. As an example, “at least one of: a, b, or c” is intended to cover a, b, c, a-b, a-c, b-c, and a-b-c, as well as any combination with multiples of the same element (e.g., a-a, a-a-a, a-a-b, a-a-c, a-b-b, a- c-c, b-b, b-b-b, b-b-c, c-c, and c-c-c or any other ordering of a, b, and c).

[0091] No element, act, or instruction used herein should be construed as critical or essential unless explicitly described as such. Also, as used herein, the articles “a” and “an” are intended to include one or more items, and maybe used interchangeably with “one or more.” Furthermore, as used herein, the terms “set” and “group” are intended to include one or more items (e.g., related items, unrelated items, a combination of related and unrelated items, and / or the like), and may be used interchange-ably with “one or more.” Where only one item is intended, the phrase “only one” or similar language is used. Also, as used herein, the terms “has,” “have,” “having,” and / or the like are intended to be open-ended terms.

[0092] As used herein, the phrase “based on” shall not be construed as a reference to a closed set of information, one or more conditions, one or more factors, or the like. In other words, the phrase “based on A” (where “A” may be information, a condition, a factor, or the like) shall be construed as “based at least on A” unless specifically recited differently.

[0093] As used herein, the term “or” is an inclusive “or” unless limiting language is used relative to the alternatives listed. For example, reference to “X being based on A or B” shall be construed as including within its scope X being based on A, X being basedon B, and X being based on A and B. In this regard, reference to “X being based on A or B” refers to “at least one of A or B” or “one or more of A or B” due to “or” being inclusive. Similarly, reference to “X being based on A, B, or C” shall be construed as including within its scope X being based on A, X being based on B, X being based on C, X being based on A and B, X being based on A and C, X being based on B and C, and X being based on A, B, and C. In this regard, reference to “X being based on A, B, or C” refers to “at least one of A, B, or C” or “one or more of A, B, or C” due to “or” being inclusive. As an example of limiting language, reference to “X being based on only one of A or B” shall be construed as including within its scope X being based on A as well as X being based on B, but not X being based on A and B.

[0094] Further, process diagrams such as Fig. 11 and Fig. 14 do not necessarily indicate a particular order or sequence of steps. For example, steps may also be performed in a different order or, if hardware capabilities allow it, simultaneously, without deviating from the scope of the present disclosure.

Claims

November 6, 2025 Max-Planck-Gesellschaft zur Fbrderung der M177378WO ANE / BMNWissenschaften e.V.Ludwig-Maximilians-Universitat Miinchen, in Vertretung des Freistaates BayernCLAIMS1. System (200) for performing a quantum manipulation protocol, comprising: a trapping laser system (210) for trapping neutral atoms in an optical trap array (110) inside a vacuum chamber (115) operated at a trapping wavelength Xtr; wherein each neutral atom comprises a ground state |1S0>, a first metastable excited state |3P0> and a second metastable excited state |3P2>; a state manipulation laser system (220) for generating laser radiation (130) for coupling, via a phase-coherent multi-photon transition, the ground state |1S0> to the first metastable excited state |3P0> and / or to the second metastable excited state l3P2>; a magnetic field system (230) for generating a magnetic field Bextat a location of the optical trap array inducing a Zeeman splitting for magnetic substates of the second metastable excited state |3P2>; a control system (240) for controlling the laser radiation generated by the laser system to coherently modify a quantum state of the plurality of neutral atoms based on the quantum manipulation protocol; a quantum state readout system (250) for determining the quantum state of at least a subset of the plurality of neural atoms based on the quantum manipulation protocol; wherein a direction of the magnetic field Bextwith respect to a polarization direction of the optical trap array is selected such as to render the optical trap array operated at the trapping wavelength Xtra magic-wavelength optical trap for the second metastable excited state |3P2> and the first metastable excited state |3P0> and / or for the second metastable excited state |3P2> and the ground state |1S0>.

2. System of claim 1, wherein the direction and a strength of the magnetic field Bext, the polarization direction of the optical trap array, and the wavelength Xtrof the optical trap array are selected such that a differential light shift induced by the optical trap array on the second metastable excited state |3P2> with respect to the first metastable excited state|3P0> or with respect to the ground state |1S0>, or with respect to both states affects a fidelity of a single particle quantum operation of the quantum manipulation protocol by less than 10%, preferably by less than 5% and more preferably by less than 1%.

3. System of claim 2, wherein an angle 0 between the polarization direction of the optical trap array and the direction of the magnetic field Bextis selected such that, for a given trapping wavelength Xtrof the optical trap array, the differential light shift induced by the optical trap array on the second metastable state with respect to the first metastable state or with respect to the ground state or with respect to both states affects a fidelity of a single particle quantum operation of the quantum manipulation protocol by less than 10%, preferably by less than 5% and more preferably by less than 1%.

4. System of claim of any of claims 1 to 3, wherein the neutral atoms are88Sr atoms.

5. System of claim 4, dependent on claim 3, wherein the angle 0 is selected between 78° and 790, and the wavelength Xtrof the optical trap array is selected to be 813 nm.

6. System of claim 4, dependent on claim 3, wherein the polarization direction of the optical trap array is essentially vertical, the angle 0 is selected between 89° and 910, preferably 90°, and the wavelength Xtrof the optical trap array is selected to be between 1000 nm and 1020 nm.

7. System of claim 6, wherein the optical trap array is formed by an optical lattice, preferably by a folded optical lattice; and / or the system further comprising: one or more auxiliary optical traps having an auxiliary trap wavelength Xauxand a polarization direction that is essentially horizontal; wherein the auxiliary trap wavelength Xauxand the polarization direction of the one or more auxiliary optical traps with respect to the direction of the magnetic field Bextare selected such that a differential light shift induced by the one or more auxiliary optical traps on the second metastable excited state with respect to the first metastableexcited state or with respect to the ground state or with respect to both does not affect a fidelity of the quantum manipulation protocol.

8. System of any of claims i to 7, wherein the laser radiation generated by the atomic state manipulation laser system is applied to the plurality of neutral atoms via a single single-mode, polarization maintaining optical fiber, that, preferably, is length and temperature stabilized; the system optionally further comprising multi-wavelength waveplates which rotate the polarization a first wavelength of the laser radiation but leave a second wavelength essentially unaffected.

9. Neutral atom quantum computer comprising the system of any of claims 1 to 8, and optionally: an interface, for receiving, via a network (270) from a remote user device (260), instructions of a quantum algorithm, and for sending, via the network, a result of the quantum algorithm to the remote user device.

10. Method for quantum computing comprising: obtaining (1110) a set of instructions of a quantum algorithm; forming (1120) a quantum register by trapping a plurality of neutral atoms in an optical trap array inside a vacuum chamber; wherein a ground state, a first metastable excited state and a second metastable excited state of the neutral atoms form a qutrit and / or qubits used for quantum computing; performing (1130) , based on the obtained set of instructions of the quantum algorithm, a sequence of quantum gates on a subset of the plurality of neutral atoms, wherein performing the sequence of quantum gates comprises generating a magnetic field Bextat a location of the optical trap array for inducing a Zeeman splitting for magnetic sub-states of the second metastable excited state; and illuminating the subset of the plurality of neutral atoms with laser radiation coupling, via a multi-photon transition, the ground state to the first metastable excited state, and / or the ground state to the second metastable excited state.

11. Method of claim 10, further comprising: applying two-photon coherent depumping for controlled qubit state reset.

12. Method of claim 11, further comprising laser cooling the plurality of neutral atoms in an optical trap array based at least in part on applying the two-photon coherent depumping for the controlled qubit state reset.

13. Method of any of claims 10 to 12, further comprising obtaining, via a network form a remote user device, the set of instructions of the quantum algorithm; and sending a result of the quantum algorithm via the network to the remote user device.

14. Computer program comprising instructions for controlling a quantum computing device to carry out the steps of the method of any of claims 10 to 13.

15. Quantum computing system (1300) comprising: a trapping laser system (210) for trapping neutral atoms in an optical trap array (110) inside a vacuum chamber (115) for forming a quantum register of qubits; wherein qubits states |o> and |i> of the qubits are encoded as a first metastable excited state ( 13P0>) and a second metastable excited state ( 13P2>) of the neutral atoms; a state manipulation laser system (220) for generating laser radiation (130) for coupling the first metastable excited state to the second metastable excited state, preferably via a Raman transition involving an intermediate state ( 13Sj>) of the neutral atoms; a qubit entangling laser system (222) for generating laser radiation for coupling selected pairs of neutral atoms in the first metastable excited state to a Rydberg state (|r>) or selected pairs of neutral atoms in the second metastable excited state to the Rydberg state or a different one; a quantum state readout system (250) for determining a quantum state of at least a subset of the plurality of neural atoms adapted for generating laser radiation for:(i) selectively transferring neutral atoms in the second metastable excited state to a ground state (|1S0>) of the neutral atoms;(ii) transferring neutral atoms in the first metastable excited state to the ground state of the neutral atoms; and(iii) generating a fluorescence signal from neutral atoms in the ground state; and a control system (240) for controlling operation of the state manipulation laser system, the qubit entangling laser system and the quantum state readout system to perform a plurality of quantum gates of a quantum algorithm and to determine a result of the quantum algorithm by: selectively detecting neutral atoms in the second metastable excited state; and, subsequently, selectively detecting neutral atoms in the first metastable excited state of the neutral atoms.

16. Quantum computing system (1300) of claim 15, wherein the laser radiation for selectively transferring neutral atoms in the second metastable excited state to the ground state of the neutral atoms is adapted to transfer neutral atoms in the second metastable excited state to a third metastable excited state (|3Pi>) which subsequently decays into the ground state of the neutral atoms, wherein, optionally, the second metastable excited state is coupled to the third metastable excited state via a two- photon transition or via optical pumping using an intermediate state ( 13D2>) that, preferably, decays into the first metastable excited state with a probability of less than 1%, more preferably of less than 0.05%.

17. Quantum computing system (1300) of claim 15 or 16, wherein the laser radiation for transferring neutral atoms in the first metastable excited state to the ground state of the neutral atoms is adapted to transfer neutral atoms in the first metastable excited state and the second metastable excited state to the third metastable excited state which subsequently decays into the ground state of the neutral atoms, wherein, optionally, the first metastable excited state is coupled to the third metastable excited state via a two-photon transition or via optical pumping using an intermediate state (|3Si>).

18. Quantum computing system (1300) of any of claims 15 to 17, wherein the quantum state readout system (250) comprises:a fluorescence generation laser system (1310) adapted to illuminate neutral atoms in the ground state of the neutral atoms with a pair of essentially counterpropagating laser beams coupling the ground state to an excited state (| ‘P,>) of the neutral atoms.

19. Quantum computing system (1300) of claim 18, wherein the fluorescence generation laser system comprises an optical switching device for each laser beam of the pair of beams adapted to illuminate the neutral atoms in the ground state of the neutral atoms with the pair of essentially counterpropagating laser beams; and wherein the control system is adapted to control the switching devices such that the neutral atoms in the ground state of the neutral atoms are illuminated in an alternating manner.

20. Quantum computing system (1300) of claim 18 or 19, wherein the fluorescence generation laser system is further adapted to illuminate the neutral atoms in the ground state of the neutral atoms with the pair of essentially counterpropagating laser beams such that a polarization of the laser beams is oriented with respect to a quantization axis defined by an external magnetic field such that a n-transition between the ground state and the excited state is driven.

21. Quantum computing system (1300) of any of claims 18 to 20, wherein the quantum state readout system (250) comprises an imaging objective for collecting the fluorescence, wherein the imaging objective comprises a numerical aperture >= 0.5, preferably >=0.65; and / or wherein the imaging objective is oriented perpendicular to a quantization axis defined by an external magnetic field.

22. Neutral atom quantum computer comprising the system of any of claims 15 to 21, and optionally: an interface, for receiving, via a network (270) from a remote user device (260), instructions of a quantum algorithm, and, for sending, via the network, a result of the quantum algorithm to the remote user device.

23. Method for quantum computing, comprising obtaining (1410) a set of instructions of a quantum algorithm; forming (1420) a quantum register of qubits by trapping a plurality of neutral atoms in an optical trap array inside a vacuum chamber, wherein qubits states |o> and |i> of the qubits are encoded as a first metastable excited state (|3P0>) and a second metastable excited state (|3P2>) of the neutral atoms; performing (1430), based on the obtained set of instructions of the quantum algorithm, a sequence of quantum gates on a subset of the plurality of neutral atoms, wherein performing the sequence of quantum gates comprises: coupling the first metastable excited state to the second metastable excited state, preferably via a Raman transition involving an intermediate state ( 13Sj>) of the neutral atoms, and coupling selected pairs of neutral atoms in the first metastable excited state to a Rydberg state ( | r>) or selected pairs of neutral atoms in the second metastable excited state to a Rydberg state; and determining (1440) a result of the quantum algorithm comprising selectively detecting neutral atoms in the second metastable excited state, and, subsequently, selectively detecting neutral atoms in the first metastable excited state of the neutral atoms.

24. Method for quantum computing of claim 23, wherein determining (1440) the result of the quantum algorithm comprises: selectively transferring neutral atoms in the second metastable excited state to a ground state (|1S0>) of the neutral atoms; and generating a fluorescence signal from the neutral atoms transferred from the second metastable excited state to the ground state, and, optionally, transferring neutral atoms in the first metastable excited state to the ground state of the neutral atoms and generating a fluorescence signal from the neutral atoms transferred from the first metastable excited state to the ground state.

25. Method of claim 24, wherein generating the fluorescence signal from the neutral atoms comprises illuminating the neutral atoms in the ground state of the neutral atoms with a pair of essentially counterpropagating laser beams coupling the ground state to an excited state (| ‘P,>) of the neutral atoms, optionally, in an alternating manner, and, optionally,such that a polarization of the laser beams is oriented with respect to a quantization axis defined by an external magnetic field such that a n-transition between the ground state and the excited state is driven.

26. Method of any of claims 23 to 25 wherein determining (1440) the result of the quantum algorithm further comprises: collecting the generated fluorescence with an imaging objective that comprises a numerical aperture >= 0.5, preferably >=0.65; and / or that is oriented perpendicular to a quantization axis defined by an external magnetic field.

27. Method of any of claims 23 to 26, further comprising obtaining, via a network form a remote user device, a set of instructions of the quantum algorithm; and sending a result of the quantum algorithm via the network to the remote user device.

28. Computer program comprising instructions for controlling a quantum computing device to cariy out the steps of the method of any of claims 23 to 27.

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