2d architecture for trapped IONS-based quantum computing

Abstract

An apparatus and methods are disclosed for quantum computing based on a two-dimensional architecture for trapped ion systems. The apparatus includes a vacuum chamber including an ion trap and drive circuitry, and a radiation source. The ion trap includes a substrate and electrodes formed thereon to define a matrix of first channels and second channels running between the electrodes across the substrate in a first direction and a second direction, respectively, angled relative to one another and intersecting at multiple channel junctions. The drive circuitry is coupled to apply electrical potential between the electrodes across the channels so as to trap arrays of ions within the channels. The radiation source is configured to apply coherent radiation to the ions within the channels so as to segment the arrays of ions into multiple multi-ion registers and to drive the ions within the multi-ion registers in parallel to perform quantum computations.

Description

2D ARCHITECTURE FOR TRAPPED IONS-BASED QUANTUM COMPUTINGCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to US Provisional Patent Application No. 63 / 695,877, titled "2D architecture for trapped ions-based quantum computing", filed September 18, 2024, which is hereby incorporated by reference in its entirety.FIELD OF INVENTION

[0002] The present disclosure relates to quantum computing systems, methods and architectures, and more particularly to trapped ion-based quantum computing systems and methods for controlling and manipulating ions in quantum computing applications.BACKGROUND

[0003] Quantum computing represents a paradigm shift in computational technology, leveraging quantum mechanical phenomena to process information in ways that classical computers cannot. Unlike classical bits that exist in definite states of 0 or 1, quantum bits (qubits) can exist in superposition states, allowing quantum computers to explore multiple computational paths simultaneously. This quantum parallelism, combined with quantum entanglement and interference, enables quantum computers to solve certain classes of problems exponentially faster than their classical counterparts.

[0004] Among the various physical platforms for implementing quantum computers, trapped ion systems have emerged as a leading approach due to their high-fidelity quantum operations and long coherence times. In trapped ion quantum computers, individual ions are confined using electromagnetic fields and serve as qubits.

[0005] Traditional trapped ion architectures typically involve linear chains of ions, where quantum operations are performed sequentially or on small groups of ions. While these systems have demonstrated high-fidelity quantum gates and have been used to implement various quantum algorithms, scaling to larger numbers of qubits presentschallenges. As the number of ions in a single chain increases, the complexity of controlling individual ions grows, and the time required to perform quantum operations across the entire system can become prohibitive.

[0006] The quantum computing field faces a scaling challenge as practical quantum advantage for many applications may require thousands or even millions of logical qubits. Each logical qubit typically requires multiple physical qubits for quantum error correction, further increasing the total number of physical qubits needed. Current quantum computing systems, while demonstrating quantum operations on tens to hundreds of qubits, fall short of the scale needed for many practical applications.

[0007] Various approaches have been explored to address the scaling challenge in trapped ion quantum computing. These include techniques for shuttling ions between different trap regions, creating modular architectures with multiple trap zones, and developing methods for parallel quantum operations. However, maintaining high fidelity while scaling to large numbers of qubits remains a significant challenge in the field.

[0008] The development of scalable quantum computing architectures that can maintain high operational fidelity while supporting large numbers of qubits represents an ongoing area of research and development in the quantum computing community.SUMMARY

[0009] This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.

[0010] In accordance with aspects of the present disclosure, an apparatus for quantum computing includes a vacuum chamber and a radiation source. The vacuum chamber includes an ion trap and drive circuitry. The ion trap includes a substrate and electrodes formed on the substrate to define a matrix of first channels running between the electrodesacross the substrate in a first direction and second channels running across the substrate in a second direction, angled relative to the first direction and intersecting at multiple channel junctions with the first channels. The drive circuitry is coupled to apply electrical potential between the electrodes across the first and second channels so as to trap arrays of ions within the first and second channels. The radiation source is configured to apply coherent radiation to the ions within the first and second channels so as to segment the arrays of ions into multiple multi-ion registers and to drive the ions within the multi-ion registers in parallel to perform quantum computations.

[0011] In various embodiments of the apparatus, the ion trap is configured to trap onedimensional array of ions along each channel of the first and second channels.

[0012] In various embodiments of the apparatus, the electrodes are arranged to form a two-dimensional grid of intersecting first and second channels, each channel being capable of hosting an ion array.

[0013] In various embodiments of the apparatus, the first direction of the first channels is perpendicular to the second direction of the second channels.

[0014] In various embodiments of the apparatus, the radiation source is further configured to perform mid-circuit measurements on selected ions of the trapped arrays of ions.

[0015] In various embodiments of the apparatus, the drive circuitry and radiation source are configured to enable parallel application of multi-qubit gates across multiple segments of the trapped ion arrays.

[0016] In various embodiments of the apparatus, each channel of the first and second channels is configured to trap an array of ions which is at least 100 ions long.

[0017] In various embodiments of the apparatus, the apparatus further includes rotatable assemblies, where the matrix of first and second channels is divided into regions. Each region includes channel sections of the first and second channels and at least one channel junction, where each matrix region is mounted on a rotatable assembly of therotatable assemblies and each rotatable assembly is configured to rotate its respective matrix region to couple the respective channel sections with channel sections of adjacent matrix regions.

[0018] In various embodiments of the apparatus, the electrodes are formed on the substrate to define a matrix of the first channels running between the electrodes across the substrate in the first direction, the second channels running across the substrate in the second direction, and at least third channels running across the substrate in a third direction angled relative to the first and second directions and intersecting at the multiple channel junctions with the first and second channels, where each region further includes channel sections of the at least third channels.

[0019] In various embodiments of the apparatus, the drive circuitry is further configured to dynamically reconfigure the electrical potentials to dynamically change the segmentation or connectivity of the trapped ion arrays.

[0020] In various embodiments of the apparatus, the radiation source is configured to optically confine ions of the arrays of ions to form barrier ions segmenting the arrays of ions into the multiple multi-ion registers.

[0021] In various embodiments of the apparatus, the radiation source includes optical tweezers distributed along the first and second channels and configured to optically confine the barrier ions.

[0022] In various embodiments of the apparatus, the apparatus further includes control circuitry configured to dynamically reconfigure the optical tweezers to dynamically change the segmentation and connectivity of the trapped ion arrays.

[0023] In various embodiments of the apparatus, the control circuitry is configured to couple adjacent multi-ion registers, which are not separated by channel junctions, by reconfiguring the respective optical tweezers.

[0024] In various embodiments of the apparatus, the radiation source includes optical tweezers distributed along the first and second channels, and wherein the apparatus furtherincludes control circuitry configured to shuttle selected ions of the arrays of ions across channel junctions from a source register to a destination register by dynamically adjusting the electrical potential between the respective electrodes and configuring the respective optical tweezers to confine a portion of the shuttled ions along their trajectory or ions in the origin and destination registers.

[0025] In various embodiments of the apparatus, each array of ions trapped within one of the first channels or the second channels includes a gap at each channel junction of the channel junctions at which its respective channel intersects. The control circuitry is then configured to shuttle selected ions of the arrays of ions trapped within the one of the first channels or the second channels to the arrays of ions trapped within the other one of the first channels or the second channels to form continuous arrays of ions along the other one of the first channels or the second channels, thereby facilitating parallel application of quantum operations on the arrays of ions trapped within the other one of the first channels or the second channels.

[0026] In various embodiments of the apparatus, the source register is trapped within a channel of one of the first or second channels and the destination register is trapped within a channel of the other one of the first or second channels.

[0027] In various embodiments of the apparatus, the ion trap is configured to trap ions at a density of at least 20 ions per square millimeters.

[0028] In accordance with aspects of the present disclosure, a method for shuttling ions of ion arrays trapped within a matrix of intersecting first and second channels formed by electrodes of an ion trap and segmented into multiple multi-ion registers from an origin register to a destination register and across an intersection formed thereof, where the ion trap further includes optical tweezers disposed along the first and second channels, is disclosed. The method includes dynamically adjusting electrical potential between respective electrodes of the ion trap and configuring respective optical tweezers of the ion trap to confine a portion of the shuttled ions along their trajectory during their transport or to confine ions in the origin and destination registers.

[0029] In various embodiments of the method, each array of the arrays of ions is a one-dimensional array of ions.

[0030] In various embodiments of the method, the matrix is a two-dimensional grid of the intersecting first and second channels.

[0031] In various embodiments of the method, the first channels are perpendicular to the second channels.

[0032] In various embodiments of the method, each array of the arrays of ions is at least 100 ions long.

[0033] In various embodiments of the method, the matrix is divided into rotatable regions where each region includes channel sections of the first and second channels and at least one of the formed intersections. The method then further includes rotating one or more regions of the matrix to align the channel section within which the origin register is trapped with the channel section within which the destination register is trapped so that the trajectory of the shuttled ions is a straight line.

[0034] In various embodiments of the method, the matrix further includes at least third channels formed by the electrodes of the ion trap and intersecting with the first and second channels at the formed intersections, where each region further includes channel sections of the at least third channels.

[0035] In various embodiments of the method, the method further includes segmenting the arrays of ions into multiple multi-ion registers.

[0036] In various embodiments of the method segmenting the arrays of ions includes configuring the electrical potential generated by the respective electrodes or configuring the optical tweezers to optically confine respective ions of the arrays of ions to form barrier ions.

[0037] In various embodiments of the method, the arrays of ions are dynamically segmented into multiple multi-ion registers by dynamically reconfiguring the respective electrical potential or by dynamically reconfiguring the optical tweezers.

[0038] In various embodiments of the method, the origin register is trapped along a channel of one of the first or second channels and the destination register is trapped within a channel of the other one of the first or second channels.

[0039] In accordance with aspects of the present disclosure, a method for quantum computation includes trapping a first plurality of arrays of ions in respective positions along a first plurality of parallel axes, where each array of ions of the first plurality of arrays of ions is trapped along a respective axis of the first plurality of axes, trapping a second plurality of arrays of ions in respective positions along a second plurality of parallel axes, where each array of ions of the second plurality of arrays of ions is held trapped along a respective axis of the second plurality of axes, where each axis of the second plurality of axes crosses at least a portion of the axes of the first plurality of axes thereby forming a plurality of junctions therebetween, reconfiguring the first and second pluralities of the arrays of ions such that the arrays of ions of a selected plurality of arrays of ions of the first and second pluralities of arrays of ions extend continuously across the plurality of junctions and the plurality of arrays of ions unselected therefrom includes a gap at each junction of the plurality of junctions, and parallelly applying quantum operations on the selected plurality of arrays of ions.

[0040] In various embodiments of the method, the method further includes selecting the plurality of arrays of ions from the first and second pluralities of arrays of ions prior to the parallel application of the quantum operations.

[0041] In various embodiments of the method, each array of the arrays of ions is a one-dimensional array of ions.

[0042] In various embodiments of the method, the first and second pluralities of axes form a two-dimensional grid of intersecting first and second axes.

[0043] In various embodiments of the method, the first direction of the first plurality of axes is perpendicular to the second direction of the second plurality of axes.

[0044] In various embodiments of the method, the method further includes performing mid-circuit measurements on selected ions of the trapped arrays of ions.

[0045] In various embodiments of the method, the method further includes parallelly applying multi-qubit gates across multiple segments of the trapped ion arrays.

[0046] In various embodiments of the method, each array of ions of the selected plurality of arrays of ions is at least 100 ions long.

[0047] In various embodiments of the method, the trapped first and second pluralities of arrays of ions form a layout of trapped ions, the layout of trapped ions is divided into rotatable regions, each region including ion array sections of the first and second arrays of ions and at least one junction of the formed junctions, and the reconfiguring of the first and second pluralities of the arrays of ions includes rotating one or more regions of the layout of trapped ions to couple the respective ion array sections with ion array sections of adjacent regions.

[0048] In various embodiments of the method, the method further includes trapping at least a third plurality of arrays of ions in respective positions along a third plurality of parallel axes, where each array of ions of the third plurality of arrays of ions is held trapped along a respective axis of the third plurality of axes, each axis of the third plurality of axes crosses at least a portion of the axes of the first and second pluralities of axes at the formed plurality of junctions, each region further includes ion array sections of the third arrays of ions, and the method further includes reconfiguring the third plurality of the arrays of ions.

[0049] In various embodiments of the method, the first and second pluralities of arrays of ions are trapped by electrical potential and are segmented into multiple multi-ion registers, where reconfiguring the first and second pluralities of the arrays of ions includes shuttling selected ions of the arrays of ions of the selected plurality of arrays of ions from a source register to a destination register across a junction of the formed plurality of junctions disposed therebetween by dynamically adjusting the electrical potential and optically confining a portion of the shuttled ions along their trajectory or ions in the origin and destination registers.

[0050] In various embodiments of the method, the electrical potential is generated by electrodes disposed so as to form channels extending along the first and second pluralities of parallel axes, and the first and second pluralities of arrays of ions are trapped within these channels, respectively.

[0051] In various embodiments of the method, the optical confinement is performed via a plurality of optical tweezers disposed along the first and second pluralities of parallel axes.

[0052] In various embodiments of the method, the method further includes segmenting the first and second pluralities of arrays of ions into multiple multi-ion registers.

[0053] In various embodiments of the method, the source register is trapped along an axis of one of the first or second pluralities of parallel axes and the destination register is trapped along an axis of the other one of the first or second pluralities of parallel axes.

[0054] In various embodiments of the method, reconfiguring of the first and second pluralities of the arrays of ions includes reconfiguring the spacing between the ions of at least one of the first and second pluralities of the arrays of ions.

[0055] The foregoing general description of the illustrative embodiments and the following detailed description thereof are merely exemplary aspects of the teachings of this disclosure and are not restrictive.BRIEF DESCRIPTION OF FIGURES

[0056] Non-limiting and non-exhaustive examples are described with reference to the following figures.

[0057] FIG. 1 illustrates a block diagram of a quantum computing system architecture, in accordance with aspects of the disclosure.

[0058] FIG. 2 depicts a schematic diagram of a quantum computing system architecture showing an ion trap with electrodes arranged on a substrate, along with various radiation and detection sources, in accordance with aspects of the disclosure.

[0059] FIG. 3 illustrates a schematic two-dimensional (2D) grid-like layout of an ion trap comprising an exemplary array of electrodes, in accordance with aspects of the disclosure.

[0060] FIG. 4 depicts a schematic diagram of a segmented 2D ion array trapped within a 2D grid-like ion trap, in accordance with aspects of the disclosure.

[0061] FIGS. 5A-5B show diagrams depicting segment coupling within an exemplary simplified 2D ion trap, in accordance with aspects of the disclosure.

[0062] FIGS. 5C-5D show diagrams depicting segment coupling across junctions within the 2D ion trap of FIGS. 5A-5B, in accordance with aspects of the disclosure.

[0063] FIG. 6 illustrates a schematic diagram of ion arrays trapped within an ion trap having a 2D grid layout and including electrodes mounted on rotating assemblies, in accordance with aspects of the disclosure.

[0064] FIG. 7 depicts a schematic diagram of ion arrays trapped within another ion trap having a 2D grid layout and including electrodes mounted on rotating assemblies, in accordance with aspects of the disclosure.

[0065] FIG. 8 shows a flowchart depicting a method for manipulating trapped arrays of ions, in accordance with aspects of the disclosure.

[0066] FIG. 9 illustrates a flowchart depicting a method for quantum computation based on trapped 2D ion arrays, in accordance with aspects of the disclosure.DETAILED DESCRIPTION

[0067] The following description sets forth exemplary aspects of the present disclosure. It should be recognized, however, that such description is not intended as a limitation on the scope of the present disclosure. Rather, the description also encompasses combinations and modifications to those exemplary aspects described herein.

[0068] Although the disclosure is not limited in this regard, by using the term “or” when listing two or more items or options, it is meant that each item, and each plausible orfeasible combination of the listed items including a combination of all listed items may be considered.

[0069] Quantum computing systems based on trapped ions have emerged as a promising approach for implementing large-scale quantum computations. Traditional onedimensional ion trap architectures, while effective for smaller systems, face scalability challenges when attempting to reach the thousands or millions of qubits that may be needed for practical quantum advantage. The present disclosure addresses these scalability limitations through a two-dimensional architecture that extends beyond conventional linear ion chain configurations.

[0070] The disclosed architecture employs a matrix of intersecting channels formed by electrodes on a substrate creating a grid-like structure capable of trapping multiple arrays of ions simultaneously. The grid-like structure includes junctions or intersections where the channels intersect. According to some aspects, these channels run in perpendicular directions. The two-dimensional arrangement allows for significantly higher qubit densities compared to linear architectures while maintaining the ability to perform parallel quantum operations across multiple ion arrays. The disclosed system may incorporate optical tweezers distributed along the channels to provide additional confinement and control over individual ions or groups of ions within the arrays.

[0071] Ion arrays trapped within the intersecting channels may be dynamically segmented into multiple registers through the application of optical potentials. These optical potentials, generated by coherent radiation sources, can create barriers that effectively divide long ion chains into smaller, more manageable segments. The segmentation process enables parallel quantum operations to be performed on multiple registers simultaneously, thereby increasing computational throughput. According to some aspects, the optical tweezers may be reconfigured dynamically during operation to change the segmentation pattern and connectivity between different registers.

[0072] The architecture supports various methods for coupling ions across channel intersections. Ion shuttling techniques may be employed to transport selected ions from one register to another, even across junctions where channels intersect. During such shuttling operations, optical tweezers may be configured to follow the trajectory of the transported ions, maintaining tight confinement and reducing heating effects that could otherwise degrade quantum coherence. This approach allows for the creation of continuous ion arrays along selected channels, e.g., each at least 100 ions long, while maintaining gaps in others, enabling selective parallel operations on chosen subsets of the trapped ions.

[0073] An alternative approach to coupling ion segments involves the use of rotatable electrode assemblies that can mechanically reorient channel sections to create direct pathways between different regions of the ion trap. In this configuration, circular or polygonal electrodes, for example, may be mounted on rotating mechanisms that allow them to be oriented in different angular positions. By rotating these electrode assemblies, channel sections that were previously disconnected can be aligned to form continuous pathways, enabling ions to be shuttled without requiring complex right-angle turns at channel intersections. This mechanical reconfiguration approach may eliminate the need for precise optical tweezer control during junction crossings and can simplify the shuttling process by providing direct linear paths between distant regions of the trap. The rotatable assemblies may be actuated through separate control mechanisms that can be operated individually without affecting the position or orientation of other rotatable assemblies in the system, allowing for dynamic reconfiguration of the trap connectivity to support different computational workflows or to optimize ion transport efficiency for specific quantum algorithms.

[0074] According to some aspects, scalability may be further enhanced through the use of such rotatable assemblies in addition. The additional dynamic reconfiguration of the connectivity between different regions of the ion trap may provide additional flexibility inhow quantum operations are performed across the system. The combination of electrical control through electrode potentials, optical control through tweezers, and mechanical control through rotation may create a highly versatile platform for quantum computation that can adapt to different algorithmic requirements and operational constraints.

[0075] Reference is now made to FIG. 1, which shows a quantum computing system 100. System 100 may include a vacuum chamber 110, a radiation source 140, control circuitry 150 and a detection and imaging system 160. Vacuum chamber 110 may include an ion trap 120 and drive circuitry 130.

[0076] Vacuum chamber 110 may provide an ultra-high vacuum environment necessary for maintaining ion stability and coherence during quantum operations. Within the vacuum chamber 110, ion trap 120 may be positioned to confine and manipulate arrays of ions that serve as quantum bits or qubits for computational purposes. Vacuum chamber 110 may maintain pressures sufficiently low to minimize collisions between trapped ions and background gas molecules, which could otherwise cause decoherence and loss of quantum information.

[0077] Ion trap 120 may be contained within the vacuum chamber 110 and may include a substrate upon which the electrodes are formed to create the trapping structure. The trapping structure may include intersecting channels in a grid-like or matrix layout. Drive circuitry 130 may be coupled to the electrodes of the ion trap 120 to apply electrical potentials between the electrodes across the channels, thereby generating the electric fields necessary to trap arrays of ions within the channels.

[0078] A radiation source 140 may be positioned to direct coherent radiation toward the ions trapped within the channels of ion trap 120. Radiation source 140 may be configured to apply coherent radiation to the ions so as to segment the arrays of ions into multiple multi-ion registers and to drive the ions within the multi-ion registers in parallel to perform quantum computations. According to some aspects, the arrays of ions may besegmented to also include a single-ion register. Radiation source 140 may include various types of laser systems capable of generating the specific wavelengths and intensities needed for ion manipulation, state preparation, and quantum gate operations. According to some aspects, radiation source 140 may include multiple laser systems operating at different wavelengths to address different atomic transitions in the trapped ions.

[0079] Detection and imaging system 160 may be configured to monitor and measure the quantum states of the trapped ions. Detection and imaging system 160 may perform readout operations that determine the final quantum states after computational processes have been completed. According to some aspects, detection and imaging system 160 may include a readout laser, charge-coupled device cameras, photomultiplier tubes, or other sensitive photodetectors capable of detecting fluorescence from individual ions. Detection and imaging system 160 may also provide real-time monitoring capabilities that allow for feedback control during quantum operations. According to some aspects, detection and imaging system 160 may include multiple laser systems operating at different wavelengths to address different atomic transitions in the trapped ions.

[0080] Control circuitry 150 may coordinate the operation of all system components to execute quantum algorithms and maintain system stability. As shown in FIG. 1, control circuitry 150 may interface with the drive circuitry 130, radiation source 140, and detection and imaging system 160 to synchronize their operations according to predetermined quantum computation protocols. Control circuitry 150 may include digital signal processors, field-programmable gate arrays, or other computational hardware capable of generating the precise timing sequences needed for quantum gate operations. According to some aspects, the control circuitry 150 may implement feedback loops that use information from detection and imaging system 160 to adjust the parameters of drive circuitry 130 and radiation source 140 in real-time, enabling error correction and optimization of quantum operations.

[0081] Reference is now made to FIG. 2, which shows a portion of a quantum computing system architecture 200 similar to quantum computing system 100. System 200 includes tweezer beams 210, gate beams 220, readout beams 230, an ionization laser 240, a cooling laser 250, a substrate 260, and an electrode grid 270. Substrate 260 may provide a planar foundation upon which electrode grid 270 may be formed to create the ion trapping structure. Electrode grid 270 may include multiple electrodes arranged in a two- dimensional matrix configuration that defines intersecting channels for ion confinement. Ionization laser 240 may be positioned to direct coherent radiation toward electrode grid 270 for, e.g., ion generation and loading operations. Cooling laser 250 may be positioned opposite to ionization laser 240 to provide laser cooling capabilities for maintaining low ion temperatures prior to quantum operations.

[0082] According to some aspects, electrode grid 270 may be fabricated directly onto substrate 260 using semiconductor processing techniques to create a precise geometric arrangement of conductive elements. According to some aspects, the electrodes may be arranged to form a two-dimensional grid of intersecting first and second channels, with each channel being capable of hosting an ion array. The first channels may run in a first direction across substrate 260, while the second channels may run in a second direction that may be angled relative to the first direction. According to some aspects, the first direction of the first channels may be perpendicular to the second direction of the second channels, creating a rectangular grid pattern, as exemplified in FIG. 3. Electrode grid 270 may generate the electrical potentials needed to create trapping regions within the channels where ions may be confined and manipulated. According to some aspects, the ion trap may be configured to trap one-dimensional arrays of ions along each of the channels formed by electrode grid 270.

[0083] Tweezer beams 210 may be directed upward toward electrode grid 270 from below substrate 260 to provide optical confinement capabilities for individual ions orgroups of ions within the trapped arrays. According to some aspects, tweezer beams 210 may be implemented using integrated photonics technology to carry the optical radiation within the traps as a complete unit, which may increase the modularity of the system. Gate beams 220 may also be directed toward ions trapped by electrode grid 270 to provide coherent radiation for quantum gate operations and state manipulation of trapped ions. Gate beams 220 may include, for example, Raman beams, which operate on Zeeman or hyperfine qubits using two-photon transitions, or narrow linewidth lasers, which operate on optical qubits. According to some aspects, gate beams 220 may include Raman beams, which may include multiple laser beams with specific frequency differences that can drive transitions between different quantum states of the trapped ions. Readout beams 230 may be positioned to illuminate the trapped ions for fluorescence detection and quantum state measurement operations.

[0084] Tweezer beams 210 are required to have an optical k-vector that is perpendicular to the plane of electrode grid 270, in order to confine the ions in both axial and radial directions. In the disclosed architecture, the radial axes of the ion confinement may be tilted at will with respect to the axial direction by applying appropriate electrical potentials to the trap electrodes of electrode grid 270. This capability may allow the tweezer confinement from tweezer beams 210 to overlap with both modes of motion of the trapped ions, or only one of the radial directions, if required, thus providing enhanced control over ion positioning and dynamics. Ionization laser 240 may generate the initial ions that are subsequently loaded into the trapping regions created by electrode grid 270, while cooling laser 250 may maintain the ions at sufficiently low temperatures to preserve quantum coherence throughout computational operations.

[0085] The spatial arrangement of the beam systems relative to electrode grid 270 may enable simultaneous operation of multiple laser systems without interference between different optical functions. Gate beams 220, tweezer beams 210, and readout beams 230may each access the trapped ions from below substrate 260, while ionization laser 240 and cooling laser 250 may provide lateral access to the trapping region. This configuration may allow for independent control of ion loading, cooling, quantum gate operations, optical confinement, and state readout processes. Electrode grid 270 may include openings or transparent regions that permit optical access to the trapped ions while maintaining the electrical field configurations needed for ion confinement within the intersecting channel structure.

[0086] Reference is now made to FIG. 3, which shows a schematic grid layout of an ion trap 300. Ion trap 300 includes a perpendicular matrix layout of 5*5 electrode assemblies (will also be referred to as “electrodes” for simplicity) referenced 310u-3105,5 respectively. Ion trap 300 further includes column channels 320A1-320A4, row channels 320B1-320B4, and junctions 3301,1-3304,4. Column channels 320A1-320A4 and row channels 320B1-320B4 are also indicated by dotted lines. Column channels 320A1- 320A4 extend in a first direction between adjacent columns of electrodes 3101,1-3105,5, while row channels 320B1-320B4 extend in a second direction, perpendicular to the first direction, between adjacent rows of electrodes 3101,1-3105,5. Junctions 3301,1-3304,4 may be formed at the intersections where column channels 320A1-320A4 and row channels 320B1-320B4 cross each other, creating connection points that enable ion movement between different channel orientations.

[0087] Each channel of channels 320A1-320A4 and 320B1-320B4 is capable of hosting an ion array. The electrode layout creates a rectangular grid structure that enhances the utilization of available substrate area while providing systematic utilization of all trapping regions. The perpendicular arrangement may enable independent control of ion arrays along different axes, allowing for parallel operations to be performed simultaneously on multiple ion chains without interference between different channel orientations. The grid structure shown in FIG. 3 may be extended beyond the illustrated 5x5 electrodearrangement to accommodate larger numbers of ion arrays, e.g., according to the computational requirements of specific quantum algorithms.

[0088] Row channels 320B1-320B4 are formed by the spacing between adjacent rows of electrodes 3101,1-3105,5, creating linear trapping regions that extend across the entire width of the substrate. Column channels 320A1-320A4 may be formed by the spacing between adjacent columns of electrodes 3101,1-3105,5, creating linear trapping regions that extend perpendicular to the row channels 320B1-320B4. According to some aspects, each channel may host a one-dimensional array of ions that can be independently controlled and manipulated through the application of appropriate electrical potentials to the surrounding electrodes. Column channels 320A1-320A4 intersect with row channels 320B1-320B4 at the junctions 3301,1-3304,4, respectively, creating a network of interconnected pathways that may enable complex ion routing and manipulation operations.

[0089] Each column channel 320A1-320A4 may provide electrical field configurations that confine ions in the radial directions while allowing controlled movement along the axial direction of the column channel. Similarly, each row channel 320B1-320B4 may provide electrical field configurations that confine ions in the radial directions while allowing controlled movement along the axial direction of the channel. Optical tweezers (not shown) may be distributed along column channels 320A1-320A4 and row channels 320B1-320B4 (e.g., below the ion trap) to provide additional localized confinement and manipulation capabilities for individual ions or groups of ions within the trapped arrays. These optical tweezers may create dynamic potential barriers that can segment ion arrays into smaller registers or facilitate controlled ion transport during shuttling operations between different channels.

[0090] The spacing between ions within each channel may be controlled through the balance of electrical confinement forces and Coulomb repulsion between adjacent ions.The width of the horizontal and column channels may be determined by the spacing between adjacent electrode rows or columns, respectively, which may be optimized to provide stable ion confinement while allowing sufficient optical access for laser-based operations. According to some aspects, the inter-ion distance may be set to five micrometers to provide improved system performance while maintaining stable ion confinement and enabling high-fidelity quantum operations. According to some aspects, channel widths may be set to 100 micrometers to provide optimal system performance while maintaining adequate separation between adjacent ion arrays.

[0091] Junctions 3301,1-3304,4 may serve as critical connection points where ions can be transferred between column channels 320A1-320A4 and row channels 320B1-320B4 through controlled shuttling operations. Each junction or intersection is formed at the intersection of one row channel and one column channel, creating a region where the electrical field configurations from both channel orientations overlap. Junctions 330i,i- 3304,4 may enable the reconfiguration of ion array connectivity by allowing selected ions to be moved from their original channel into a perpendicular channel, thereby changing the overall topology of the trapped ion system.

[0092] Reference is now made to FIG. 4, which shows a schematic diagram of a segmented 2D ion array trapped within a two-dimensional grid-like ion trap 400. Ion trap 400 includes multiple square-shaped electrode structures (will be also referred to as "electrodes") 410I,I-410M,N arranged in a grid pattern forming column channels 420A1- 420AN-1 and row channels 420BI-420BM-1 intersecting at junctions 430I,I-430M-1,N-1, respectively. M, N are natural numbers equal to or higher than 2. Column channels 420A1- 420AN-1 are formed between adjacent columns of electrodes 410I,I-410M,N, extending in a first direction across the substrate. Row channels 420BI-420BM-1 are formed between adjacent rows of electrodes 410I,I-410M,N, extending in a second direction that is perpendicular to the first direction. Junctions 430I,I-430M-1,N-1 are formed at theintersections where column channels 420AI-420AN-1 and row channels 420BI-420BM-1 cross each other. Channels 420AI-420AN-I and 420BI-420BM-I are also indicated by dotted lines.

[0093] Ion trap 400 may enable significantly higher qubit densities compared to linear ion trap architectures. According to some aspects, the system may achieve a qubit density of at least 20 qubits per square millimeter, between 4.5 and 135 qubits per square millimeter, between 100 and 130 qubits per square millimeter or between 115 and 125 qubits per square millimeter through the efficient utilization of the two-dimensional electrode arrangement. According to some aspects, specific implementations may demonstrate densities up to 400 qubits per square millimeter by optimizing the spacing between electrodes 410I,I-410M,N and the number of ions trapped within each channel. The grid pattern may accommodate large numbers of ion arrays according to the computational requirements of specific quantum algorithms. Each channel of column channels 420AI-420AN-1 and row channels 420BI-420BM-1 traps a one-dimensional array of ions that can be independently controlled and manipulated through the application of appropriate electrical potentials to the surrounding electrodes 410I,I-410M,N or by applying optical potential to ions of the array. The two-dimensional arrangement may allow for parallel operations to be performed simultaneously on multiple ion arrays or chains without interference between different channel orientations.

[0094] A one-dimensional ion array is trapped within each channel of channels 420A1- 420AN-1. Each trapped ion array includes multiple sequential or concatenated array sections or is segmented into multiple sequential array sections separated by gaps or spaces formed at junctions or intersections 430I,I-430M-1,N-1. According to some aspects, gaps at the intersections may provide a clear, unobstructed path for ions to be shuttled between segments in different directions. According to some aspects, gaps at intersections may prevent unwanted interactions at the crossing point. According to some aspects, gaps atintersections may enable scalable, reliable, and parallel quantum operations in the 2D ion trap architecture. According to some aspects, channels oriented in a selected direction may be populated with ion arrays that are continuous across their respective intersections, while channels oriented in other directions may contain ion arrays that are interrupted by gaps at the intersections, as illustrated, for example, in FIG. 7 with respect to a rotating ion trap configuration. Furthermore, ions may be dynamically shuttled or repositioned within a channel, or transferred between channels, to create various gap patterns or configurations at different times, depending on operational requirements and desired functionalities. As shown in FIG. 4, channel 420A1, for example, is composed of array sections 460Ai,i- 460 AM, 1 that are separated by gaps at junctions 430I,I-430M-1,1, respectively. Each array section may include a predetermined number of ions that can be manipulated as a cohesive unit during quantum operations. The array sections are further segmented into smaller registers through the strategic placement of barrier ions that create additional divisions within the ion arrays. For example, barrier ions 440A-440D (colored white) segment array section 46OA2,1 of ion array 420A2 into segments or registers 450A-450C of three ions each (colored black, also termed "data qubits"), respectively. According to some aspects, barrier ions 440A-440D may be optically confined using coherent radiation from optical tweezers distributed along the channels, creating localized potential barriers that effectively separate adjacent groups of ions within the same array section.

[0095] The segmentation of ion arrays into multiple registers may enable parallel quantum operations to be performed across different multiple portions of the trapped ion system simultaneously. As illustrated in FIG. 4, array section 460A2,l may be divided into segments 450A-450C through the placement of barrier ions 440A-440D at specific positions along the channel. Segment 450A may include a first group of ions that can be manipulated independently from the ions contained within segments 450B and 450C. According to some aspects, the radiation source (e.g., radiation source 140 of system 100of FIG. 1) may be configured to optically confine selected ions of the arrays to form the barrier ions 440A-440D, thereby segmenting the arrays of ions into multiple multi-ion registers. According to some aspects, the arrays of ions may be segmented to include single ion registers as well. The optical confinement may be achieved through the use of optical tweezers (e.g., tweezer beams 210 of FIG. 2) that create localized trapping potentials at specific positions along the channels, effectively isolating different groups of ions from one another while maintaining their overall confinement within the channel structure. According to some aspects, each segment may encode one or more logical qubits, where multiple physical qubits within a segment are used to implement quantum error correction protocols that protect the logical quantum information from decoherence and operational errors.

[0096] A drive circuitry, such as drive circuitry 130 of FIG. 1, may be configured to generate and coordinate the electrical potentials applied to electrodes 410I,I-410M,N, thereby establishing the trapping conditions and spatial arrangement of segments such as segments 450A-450C of trapped ion section 460A2,I (e.g., via electrodes 4101,2 and 4101,3 (not shown)). These electrical potentials facilitate the conditions necessary for gate beams 220 to manipulate the trapped ions and enable the parallel application of multi-qubit gates across multiple segments. According to some aspects, the drive circuitry may be further configured to dynamically reconfigure the electrical potentials to dynamically change the segmentation or connectivity of the trapped ion arrays during quantum computation operations. A radiation source, such as radiation source 140 of FIG. 1 may include optical tweezers distributed along column channels 420AI-420AN-1 and row channels 420B1- 420BM-1 that are configured to optically confine the barrier ions and maintain the segmentation pattern. According to some aspects, the radiation source may be further configured to perform mid-circuit measurements on selected ions of the trapped arrayswithout disturbing the quantum states of ions in other segments, thereby enabling error correction and feedback control during quantum algorithm execution.

[0097] According to some aspects, the disclosed systems and methods may maintain an overhead of 10% in the inter-ion distance, to accommodate an increase or decrease of 10% in the number of ions per segment, or an overhead of a few inter-ion distances (e.g., three inter-ion distances) per segment to enable arbitrary shuttling operations without requiring ions to make way for arriving ions from other segments. This spacing overhead may allow ions to be transferred between different segments or registers of the ion arrays through the junctions while dynamically accommodating for the increase in the number of ions. The overhead spacing may be implemented by ensuring that the segments terminate a predetermined distance before reaching the boundaries of their respective channel section defined by the trapping electrodes and extending between the respective adjacent junctions, creating buffer zones that may accommodate the presence of shuttled or merged ions. Thus, according to some aspects, each channel may be configured to trap an array of ions that includes a sufficient number of ions to support the encoding of multiple logical qubits while maintaining the spacing overhead for shuttling operations. The scalable architecture shown in FIG. 4 may accommodate quantum computing systems that include thousands or millions of physical qubits distributed across the two-dimensional electrode grid, enabling the implementation of quantum algorithms that may provide computational advantages over classical computing approaches.

[0098] Segment coupling represents a fundamental capability of the disclosed two- dimensional ion trap architecture that enables quantum information to be shared and processed across different regions of the trapped ion system. The coupling mechanism may allow segments that are initially isolated by barrier ions to be connected or temporarily connected, creating larger computational units that can support multi-segment quantum operations. According to some aspects, segment coupling may be achieved by dynamicallyreconfiguring the optical tweezers that create the barrier ions, effectively removing or repositioning the potential barriers to allow direct interaction between previously separated ion groups. This coupling functionality may enable the implementation of quantum algorithms that require entanglement or information transfer between distant qubits, as ions from different segments can be brought into proximity for gate operations and then returned to their original isolated states. The ability to dynamically couple and decouple segments may provide significant advantages for quantum error correction protocols, where logical qubits encoded across multiple segments may need to interact for syndrome extraction and error correction operations. According to some aspects, the coupling process may be performed selectively, allowing specific pairs or groups of segments to be connected while maintaining isolation of other segments, thereby enabling parallel execution of different computational tasks within the same ion trap system. The temporal control of segment coupling may also facilitate the implementation of quantum communication protocols between different regions of the trap, supporting distributed quantum computing architectures where different segments may perform specialized computational roles. Thus, segment coupling may enable large-scale quantum computation, support error correction and parallelism and provide scalability. Reference is now made to FIGS. 5A-5D which illustrate the dynamic reconfiguration capabilities enabled by optical tweezers and electrical potential control.

[0099] FIGS. 5A-5B illustrate segment coupling within an exemplary simplified 2D ion trap. FIG. 5A shows a first ion array configuration 500A of segmented ion arrays trapped within the ion trap, while FIG. 5B shows a second ion array configuration 500B of segmented ion arrays trapped within the same ion trap structure. The ion trap includes four square electrodes 510A, 51 OB, 510C, and 510D arranged in a 2x2 grid pattern. A column channel 520A and a row channel 520B are formed between the square electrodes 510A- 510D, with the channels intersecting at a junction 530. Column channel 520A extendsbetween opposing pairs of square electrodes 510A and 510D, and 51 OB and 5 IOC. Row channel 520B extends between opposing pairs of square electrodes 510A and 51 OB, and 510D and 5 IOC. Row channel 520B extends perpendicular to column channel 520A, creating a cross-shaped intersection pattern that enables ion movement and manipulation in both directions (e.g., horizontal and vertical).

[0100] Square electrodes 510A-510D provide the electrical potentials for ion confinement and manipulation within column channel 520A and row channel 520B, e.g., through the application of radiofrequency and direct current voltages. Each square electrode may be independently controlled to create the specific electric field configurations needed for stable ion trapping and controlled ion transport. Optical tweezers (not shown) providing tweezer beams such as tweezer beams 210 of FIG. 2, may be distributed along column channel 520A and row channel 520B to facilitate or support the confinement and manipulation of ions within the channel structure. According to some aspects, the optical tweezers may be utilized to optically confine selected ions to form barrier ions that segment the ion arrays into multiple multi-ion registers.

[0101] The configurations shown in FIGS. 5A-5B demonstrate segment coupling between segments or registers which are not separated by a junction (e.g., junction 530) through optical tweezers and electrical potential control. In first ion arrays configuration 500A of FIG. 5A, the ion array trapped by column channel 520A includes a vertical onedimensional array of 26 ions 540A1-540A26, arranged in a linear chain along the channel. The ion array is composed of two consecutive array sections 550A1 and 550A2 formed due to and separated by an ion array gap formed at junction 530 of the ion trap disposed at the intersection of channel 520A and channel 520B. Array section 550A1 includes ions 540A1- 540A13 and array section 550A2 includes ions 540A14-540A26. Array section 550A1 is trapped in a section of column channel 520A formed by opposing square electrodes 510Aand 510D, while array section 550A2 is trapped in a section of column channel 520A formed by opposing square electrodes 51 OB and 5 IOC.

[0102] The vertical ion array trapped within channel 520A is segmented into six segments 560A1-560A6, of three ions each through the strategic placement of barrier ions 540A1, 540A5, 540A9, 540A13, 540A14, 540A18, 540 A22, and 540A26, which are optically confined using coherent radiation from the optical tweezers. These barrier ions create localized potential barriers that effectively separate adjacent groups of ions within the ion array, enabling independent manipulation of each segment during quantum operations. A horizontal ion array trapped within row channel 520B includes a one-dimensional array of 26 ions 540B1-540B26, which is similarly divided into two consecutive array sections 550B1 and 550B2 due to and by the ion array gap at junction 530. The horizontal ion array includes ions 540B1-540B13 and is similarly segmented into six segments of three ions each through barrier ions 540B1, 54OBs, 540B9, 540B13, 540B14, 540B18, 540B22, and 540B26.

[0103] Ion array configuration 500B of FIG. 5B shows the populated ion trap of FIG. 5A following segment coupling performed between adjacent segments of the trapped ion arrays which are not separated by a junction, e.g., between segments of the same ion array section. The barrier ions in configuration 500B are positioned at different locations compared to configuration 500A. For example, the ion array trapped within column channel 520A includes barrier ions now positioned at ions 540A1, 540A3, 540 A7, 540A11, 540A13, 540A14, 540A16, 540A20, 540A24 and 540A26, creating segments with different numbers of ions per segment: segments 560Ar and 560A4' including a single ion and segments 560 A2' and 560 A3' including three ions. Similar segment coupling was performed between adjacent segments of the horizontal ion array trapped within row channel 520B, as shown in FIG. 5B.

[0104] According to some aspects, the illustrated segment coupling may be performed by optical tweezers. The optical tweezers may be dynamically reconfigured to change the segmentation pattern by moving the positions of the barrier ions or by changing the number of barrier ions within each array section. The reconfiguration process may involve switching the optical tweezers between different positions along the channels, allowing for rapid changes in the connectivity and segmentation of the trapped ion arrays. According to some aspects, multi-qubit connectivity reconfiguration may be performed in a few microseconds, which allows for real-time adaptation of the ion array structure to support different quantum algorithm requirements. According to some aspects, such segment coupling may be performed on all such segments of an ion array layout in parallel. For example, such segment coupling may be used to mediate qubit-qubit interaction between adjacent logical qubits that reside between adjacent intersections.

[0105] Traditional shuttling methods in Paul traps often rely on time-varying electrical potentials, which can induce heating effects as ions traverse RF nulls and junctions. These effects are especially pronounced during separation and recombination processes, where potential barriers are removed and zero-curvature points are encountered, and are further exacerbated when manipulating relatively long ion arrays (e.g., ion arrays having 10 to 20 ions each). The optical shuttling approach disclosed herein may overcome these limitations by utilizing optical tweezer potentials to maintain continuous trapping curvature on the ions throughout the shuttling process and to guarantee that the phonon spectrum of relatively long ion arrays or crystals remains stiff during transport. The optical tweezers may be configured to follow the instantaneous equilibrium position of the ions as they move through the time-varying trap potentials, thereby preserving tight confinement and minimizing heating effects that could otherwise degrade quantum coherence. This approach may eliminate or reduce the need for sympathetic cooling of the ion crystal after or during shuttling operations, which may reduce the requirement for additional ion speciesdedicated to cooling functions. According to some aspects, this reduction in cooling requirements may decrease the total number of ions needed for quantum operations by approximately a factor of two, thereby relaxing physical and engineering constraints on chip design while maintaining high operational fidelity. The optical tweezers may be steered along the trajectory of the shuttled ions using, e.g., acousto-optical or movable micro-mirrors steering mechanisms that provide dynamic positioning control, or alternatively, may be implemented using fixed tweezer positions along predetermined ion trajectories with temporal switching between these positions at appropriate times during the shuttling process. According to some aspects, the fixed-position approach may be compatible with photonic integration technology within the ion chip architecture, eliminating the need for acoustic-based steering systems while maintaining effective confinement during ion transport operations.

[0106] Reference is now made to FIGS. 5C-5D, which illustrate ion shuttling across junctions in the populated ion trap following the configurations shown in FIG. 5B. FIG. 5C shows a third ion array configuration 500C according to which ions are shuttled in a straight line, while FIG. 5D shows a fourth ion array configuration 500D according to which ions are shuttled along a right-angle trajectory. Square electrodes 510A-510D continue to provide the electrical potentials for ion confinement and manipulation within the channels, while the optical tweezers disposed along the channels facilitate and support the confinement and manipulation of ions during the shuttling process. The shuttling operations illustrated in FIG. 5D demonstrate how junction 530 enables dynamic reconfiguration of ion array connectivity by allowing selected ions to be moved between different channel orientations, thereby changing the overall topology and segmentation of the trapped ion system. According to some aspects, junction 530 serves as a connection point where ions can be transferred between column channel 520A and row channel 520Bthrough controlled shuttling operations that may involve precise coordination of electrical potentials and optical confinement.

[0107] Third ion array configuration 500C of FIG. 5C illustrates the formation of a reconfigured ion arrangement through straight-line shuttling of ion 540B12 which formed origin single ion segment 560B4' (shown in FIG. 5B) and ion 540B13 of array section 550B1 to destination segment 560B4' of array section 550B2 of the same horizontal ion array trapped by row channel 520B. Ions 540B12 and 540B13 are shuttled in a straight line across junction 530 to be coupled to segment 560B41, thereby altering the segmentation and connectivity of the ion arrays. According to some aspects, the control circuitry (e.g., control circuitry 150 of FIG. 1) may be configured to shuttle selected ions of the arrays across channel junctions from a source register to a destination register by dynamically adjusting the electrical potential between the respective electrodes and configuring the respective optical tweezers to confine a few of the shuttled ions (e.g., between 10 and 20 ions (inclusive)) along their trajectory or ions in the origin and destination registers. The straight-line shuttling process may involve the coordinated reduction of electrical barriers at junction 530 while maintaining optical confinement of the shuttled ions to prevent heating and decoherence during transport.

[0108] This disclosed optical confinement approach for ion shuttling techniques may maintain quantum coherence by minimizing heating effects during transport, enable precise control over ion positioning throughout the shuttling process, and allow for simultaneous manipulation of multiple ion groups across different regions of the trap. The optical tweezers can be dynamically reconfigured in nanosecond timescales, enabling rapid adaptation to changing computational requirements and supporting high-throughput quantum operations. Additionally, this approach facilitates complex ion routing patterns that would be difficult to achieve using electrical potentials alone, thereby enhancing the connectivity and reconfigurability of the quantum computing architecture.

[0109] According to some aspects, the optical tweezers may be steered along the trajectory of the shuttled ions, e.g., using acousto-optical means for dynamic positioning, allowing the optical confinement to follow the ions as they move from the source register to the destination register. The acousto-optical steering may provide precise control over the position and intensity of the optical tweezers throughout the shuttling process, maintaining tight confinement of the transported ions while minimizing disturbance to ions that remain in their original positions. According to some aspects, the optical tweezers may be positioned at fixed locations along the ion trajectory and switched between these positions at appropriate times instead of continuous steering, which may simplify the optical control system while still providing effective confinement during ion transport. The switching approach may involve activating different optical tweezers in sequence as the ions move along their predetermined path, creating a series of localized confinement regions that guide the ions from the source to the destination.

[0110] Fourth ion arrays configuration 500D of FIG. 5D illustrates the formation of a reconfigured ion arrangement through right-angle shuttling of ion 540B12 (of origin single ion segment 560B4' (shown in FIG. 5B)) and ion 540B13 of array section 550B1 of the ion array trapped within row channel 520B to destination segment 560A4' of array section 550A2 of the vertical ion array trapped within column channel 520 A. Ions 540B12 and 540B13 are shuttled at a right angle across junction 530 to be coupled to segment 560A4', demonstrating the capability of the junction to enable ion movement between different channel orientations, such as perpendicular channel orientations. The right-angle shuttling process may involve more complex electrical potential control compared to straight-line shuttling, as the ions must navigate the intersection region where the electric field configurations from both channel orientations overlap. According to some aspects, the optical tweezers may have dynamically modifiable properties including intensity, frequency, and spatial configuration during operation, allowing the optical confinementparameters to be adjusted in real-time to accommodate the changing requirements of the shuttling process as ions transition from one channel orientation to another.[oni] The formation of junction 530 by the 2D channel layout of the ion trap allows for ion movement and interaction along and between the channels, enabling complex reconfiguration operations that can adapt the ion array structure to support different quantum computational workflows. According to some aspects, each array of ions trapped within selected channels of the same orientation, e.g., the row channels (or the column channels) may include a gap at each channel junction where the respective channel intersects, and the control circuitry may be configured to shuttle (e.g., by right-angle shuttling) selected ions of the arrays trapped within the other channels of the other orientations, e.g., the column channels (or the row channels) to fill the gaps of the arrays trapped within the selected row channels (or column channels) to form continuous arrays of ions within the selected row channels. This gap-filling process may facilitate parallel application of quantum operations on the arrays of ions trapped within the selected channels (e.g., the row channels) by creating continuous ion chains that span multiple array sections.

[0112] The dynamical confinement of a few selected shuttled ions along their trajectory, as well as ions in the original and destination segments, may affect all shuttled ions within the transport group due to the Coulomb forces between the ions. This approach may ensure accurate and smooth motion of the shuttled ions while reducing recoil of the origin and destination segments, thereby minimizing unwanted heating or decoherence to the ions in the segments and to the shuttled ions regardless of whether they are individually optically confined.

[0113] According to some aspects, the optically confined ions may be actively cooled during the shuttling operation without disturbing other ions in the system. For example, to couple logical qubits across junctions or intersections, a limited number of data qubits mayneed to be shuttled, e.g., six data qubits, which may provide sufficient connectivity while maintaining operational efficiency.

[0114] According to some aspects, the shuttling operations may be performed independently at each intersection of the electrode two-dimensional grid structure. According to some aspects, by using identical operations throughout multiple intersections in the ion trap, shuttling can be multiplexed, thereby reducing the number of required control signals to the system. This multiplexing approach may simplify the control architecture while enabling parallel shuttling operations across different regions of the trap simultaneously. By repeating the disclosed configurations of segment coupling and ion shuttling, high-fidelity logical operations may persist while entanglement and information can be distributed throughout the entire quantum processor. The scalable nature of these operations may enable the implementation of complex quantum algorithms that require extensive qubit connectivity and information transfer across large numbers of logical qubits distributed throughout the two-dimensional ion trap architecture.

[0115] According to some aspects, the shuttling operations may maintain the overhead of a few inter-ion distances per segment as discussed previously, which may accommodate the dynamic reconfiguration requirements while preserving the high qubit density advantages of the two-dimensional architecture. This spacing overhead may enable the shuttling and coupling operations described above without requiring significant expansion of the physical footprint of the ion trap, thereby supporting scalable quantum computation while maintaining efficient utilization of the available substrate area.

[0116] According to some aspects, FIGS. 5A-5D illustrate a simplified ion trap structure for demonstrative purposes, and the principles, methods, and configurations described with respect to this simplified structure may be applied to much larger grid-like electrode structures of ion traps and their corresponding trapped ion arrays. The scalable nature of the disclosed architecture may enable the extension of the segment coupling andion shuttling techniques to ion trap systems comprising, e.g., hundreds or thousands of electrodes arranged in extensive two-dimensional grid patterns, where each channel may accommodate significantly longer ion arrays and where multiple junctions may be distributed throughout the expanded electrode matrix to support complex quantum computational workflows across the enlarged system.

[0117] According to some aspects, the disclosed two-dimensional ion trap architecture may be characterized through exemplary dimensional analysis and property estimation based on the intersection approach illustrated in FIGS. 3-5D. The system parameters may be defined to include B segments trapped between every two adjacent intersections, C channels in both the horizontal and vertical directions along which ions are trapped, S ions per segment, s positions reserved for shuttled ions per segment, 1 logical qubits per segment, L total logical qubits, an inter-ion distance of d, and a channel width of w. These parameters may be related through the following relationships:• L = 21C(C+1)B• Chip Length = (S+s)B(C+l)d + CwThe number of intersections in such a configuration may be C .

[0118] According to some aspects, specific implementations may utilize parameter values such as d = 5 pm, w = 100 micrometers (pm), and 1 = 2 logical qubits per segment. For systems targeting approximately L ~ 10,000 logical qubits, various configurations may be considered with different values of B, S, and s. For example, a configuration with B = 1 segment between intersections, S = 60 ions per segment, s = 0 reserved ion positions, and C = 50 channels may yield 10,000 logical qubits with a chip area of 20x20 square millimeters (mm ). Alternatively, a configuration with B = 3 segments between intersections, S = 60 ions per segment, s = 2 reserved ion positions, and C = 29 channels may produce 10,440 logical qubits with a chip area of 29.7x29.7 mm . A third exampleconfiguration with B = 10 segments between intersections, S = 60 ions per segment, s = 2 reserved ion positions, and C = 16 channels may generate 9,792 logical qubits with a chip area of 50.03x50.03 mm2.

[0119] These examples may illustrate a trade-off relationship where increasing the value of B may increase the chip area and reduce ion density on the chip, while simultaneously reducing the number of intersections, which may yield a simpler chip structure and enable faster operations due to fewer shuttling operations being required. The dimensional analysis may provide guidance for optimizing system parameters based on specific performance requirements, fabrication constraints, and computational objectives for different quantum computing applications.

[0120] According to some aspects, an alternative approach to coupling ion segments involves the use of rotatable electrode assemblies that can mechanically reorient channel sections to create direct pathways between different regions of the ion trap. In this configuration, electrodes such as circular or polygonal electrodes may be mounted on rotating mechanisms that allow them to be oriented in different angular positions. By rotating these electrode assemblies, channel sections that were previously disconnected can be aligned to form continuous pathways, enabling ions to be shuttled without requiring complex right-angle turns at channel intersections. This mechanical reconfiguration approach can simplify the shuttling process by providing direct linear paths between distant regions of the trap. The rotatable assemblies may be actuated through separate control mechanisms that can be operated individually without affecting the position or orientation of other rotatable assemblies in the system, allowing for dynamic reconfiguration of the trap connectivity to support different computational workflows or to optimize ion transport efficiency for specific quantum algorithms. Furthermore, scalability may be enhanced through the use of such rotatable assemblies, as the additional dynamic reconfiguration of the connectivity between different regions of the ion trap may provide enhanced flexibilityin how quantum operations are performed across the system. The combination of electrical control through electrode potentials, or optical control through tweezers, and mechanical control through rotation may create a highly versatile platform for quantum computation that can adapt to different algorithmic requirements and operational constraints.

[0121] Reference is now made to FIG. 6, which shows a schematic diagram of a rotatable assembly architecture for a two-dimensional ion trap 600. Ion trap 600 includes a 2D layout of N circular electrode assemblies (will also be referred to as "circular electrodes" or just "electrodes" for simplicity), generally referenced 610, such as circular electrodes 610A-D shown in FIG. 6, where N is a natural number, for example, of the order of several hundreds to a few thousands. According to some aspects, each electrode assembly or circular electrode may include a plurality of electrodes. The circular electrodes are mounted on respective rotating assemblies, generally referenced 660, such as rotating assemblies 660A-D shown in FIG. 6. The layout of circular electrodes includes a 2D layout of intersecting channels of different orientations, , e.g., a network layout, generally referenced 620. The channels may include a plurality of parallel channels at each orientation. The channels are further indicated by dotted lines to show the pathways along which ion arrays may be trapped and manipulated. Each channel includes multiple channel sections. Each channel section is configured to trap a section of the ion array trapped within the respective channel. Each array section may include multiple ions that are segmented into smaller segments or registers through the application of optical tweezers that create barrier ions at specific positions along the channel sections. Barrier ions are colored white while data ions are colored black. Each segment or register can be manipulated as a cohesive unit during quantum operations.

[0122] In the specific example of FIG. 6, the electrodes are arranged in a grid-like layout of M*N electrodes which includes a grid-like layout of channels of two perpendicular orientations: column channels, generally referenced 620A, such as columnchannels 620A1 and 620 A2, shown in FIG. 6, and row channels, generally referenced 620B, such as row channels 620B1 and 620B2, shown in FIG. 6. Junctions are formed at the intersections where the channels cross each other, generally referenced 630, such as junctions 630A-D shown in FIG. 6.

[0123] In the specific configuration of FIG. 6, each circular electrode is divided into four quarters while the channels extend therebetween and the respective junction is disposed at the center of each electrode. Each electrode, such as electrode 610A, includes two channel sections of each channel, such as channel sections 650A1-650A4 of electrode 610A, while channel sections 650A1 and channel sections 650A3 are sections of column channel 620A1 and channel sections 650A2 and 650A4 are sections of channel 620B1 at the shown orientation of electrode 610A. The channel sections of each electrode are separated by the respective junction, such as junction 630A of electrode 610A. Each channel section is confined by two opposing electrode quarters and may be configured to trap a section of an ion array generally referenced 640. Accordingly, each circular electrode assembly traps four ion array sections, such as ion array sections 640A1-640A4 trapped by electrode assembly 610A. For example, channel section 650A1 traps array section 640A1, channel section 650A2 traps array section 640 A2, channel section 650A3 traps array section 640A3 and channel section 650A4 traps array section 640A4. The trapped ion arrays are segmented to form multi-ion segments or registers. In the exemplary configuration of FIG. 6, each array section is segmented into three segments, such as segments 670AI,I-670AI,3 of array section 670A1 trapped within channel section 650A1 of circular electrode 610A, while each segment includes three ions.

[0124] The rotating assemblies, such as rotating assemblies 660 A-D shown in FIG. 6, may be configured to rotate the circular electrodes, such as respective circular electrodes 610A-D to different angular positions, thereby changing the orientation of the channel sections of the circular electrodes relative to the channel sections of adjacent circularelectrodes. According to some aspects, the rotating assembly may include mechanical or electro-mechanical actuators that provide precise angular control over the position of the respective circular electrode during quantum computation operations. According to some aspects, each rotating assembly may enable its respective circular electrode to be rotated independently of other adjacent, circular electrodes, allowing for selective coupling between different channel sections of adjacent electrode structures. The rotating assemblies, such as rotating assemblies 660 A-D shown in FIG. 6, may provide independent rotational control over their respective circular electrodes, enabling complex reconfiguration patterns across the entire electrode array.

[0125] The ion arrays trapped within the channels may be reconfigured through the rotation of the circular electrodes, which may change the connectivity between array sections trapped within a channel. The rotational capability may enable different array sections to be coupled or decoupled depending on the angular positions of the circular electrodes, providing dynamic control over the connectivity and segmentation of the trapped ion arrays throughout the system. Accordingly, segments of adjacent circular electrodes may be coupled or decoupled by rotation of one or more respective circular electrodes. For example, at the electrode orientations shown in FIG. 6 of circular electrodes 610A and 610D, array section 640A4 is coupled with array section 640D2 and segment 670A4,3 of array section 640A4 is coupled with segment 670D2,l of array section 640D2.

[0126] According to some aspects, the segmentation, shuttling and segment coupling operations, e.g., across junctions, described with respect to FIGS. 3, 4 and 5A-5D may be performed in the rotatable assembly configuration of FIG. 6, mutatis mutandis. The optical tweezers may be utilized to dynamically segment the ion arrays trapped within the channel sections of the circular electrodes, and ions may be shuttled between different array sections through the junctions formed at the centers of the circular electrodes as disclosed hereinabove. According to some aspects, shuttling between two adjacent electrodeassemblies may be realized by the following steps. Voltage on electrodes located at the electrode assembly edges may be adjusted to ensure the continuity of the trapping potential between the electrode assemblies. The voltage at the electrode assembly edges may then be lowered, allowing shuttling of ions between the electrode assemblies. To avoid unnecessary heating rate and potential qubit decoherence during this step, the above- mentioned steps may be mediated by holding the ions at the electrode assembly's edges by optical tweezers and moving them across the newly formed electrode assembly segments. This step may be followed by reconfiguring the voltages along the electrode assembly’s axis after the tweezers’ mediated shuttling is accomplished. According to some aspects, the junctions or intersection of each circular electrode, e.g., of each of junctions 630A- D, may be electrically blocked. According to some aspects, an electrical junction may be allowed, thereby combining both coupling techniques on the same platform (e.g., by mechanical rotation and by electrical potential).

[0127] According to some aspects, the rotatable assembly architecture may provide several advantages over fixed electrode configurations for quantum computing applications. The mechanical reconfiguration approach may eliminate the need for complex right-angle shuttling operations at channel intersections by allowing channel sections to be aligned in straight-line configurations through rotation. Ion shuttling may be performed along straight lines between rotated electrode assemblies, which may simplify the electrical control requirements and reduce the heating effects that can occur during complex ion transport operations. The rotational capability may also enable the creation of different connectivity patterns that can be optimized for specific quantum algorithms or error correction protocols, providing enhanced flexibility in how quantum operations are distributed across the ion trap system. According to some aspects, hexagonal packing arrangements may be used for the rotatable assemblies instead of square packing, whichmay provide additional angular orientations and connectivity options for the channel sections and trapped ion arrays.

[0128] The rotatable assembly system may support various rotation angles including 90-degree, 180-degree, and 270-degree rotations that can be performed in parallel throughout the system to couple segments across neighboring circular electrodes. According to some aspects, the circular electrodes may include more than four channel sections, such as eight channel sections, which may provide a wider set of rotation angles and allow some channel sections to remain uncoupled while others are aligned for ion transport operations. The increased number of channel sections per circular electrode may enable more complex connectivity patterns and may provide greater flexibility in routing ion arrays between different regions of the trap system.

[0129] Reference is now made to FIG. 7, which shows a diagram of a rotatable grid structure for a two-dimensional ion trap 700. Ion trap 700 may include N circular electrode assemblies (will be also referred to as "circular electrodes" or "electrodes"), generally referenced 710, such as circular electrodes 710A-D shown in FIG. 7, where N is a natural number, e.g., of the order of several hundreds to a few thousands. The circular electrodes, such as electrodes 710A-D are mounted on respective rotating assemblies, generally referenced 760, such as rotating assemblies 760A-D shown in FIG. 7. The circular electrodes grid includes intersecting channels in two perpendicular orientations, forming columns and rows generally referenced 720A and 720B, respectively. The channels include a plurality of parallel channels at each orientation such as column channels 720A1 and 720 A2 and row channels 720B1 and 720B2, as partially shown in FIG. 7. According to some aspects, each rotating assembly may rotate its respective circular electrode independently of the other rotating assemblies, allowing selective coupling between specific channel sections without affecting the orientation of adjacent electrode structures.

[0130] Each circular electrode includes a plurality of channel sections or arms, (e.g., eight channel sections in the configuration of FIG. 7), generally referenced 750, that extend radially from the center of the electrode structure at various orientations, including the column and row orientations of the channels. For example, circular electrode 710A includes channel sections 750A1 through 75OAs. Similarly, circular electrode 71 OB includes channel sections 750B1 through 75OBs, circular electrode 710C includes channel sections 750C1 through 75OCs, and circular electrode 710D includes channel sections 750D1 through 75ODs. Each channel section is configured to trap a section of an ion array, generally referenced 740, with circular electrode 710A trapping array sections 740A1 through 74OAs, circular electrode 71 OB trapping array sections 740B1 through 74OBs, circular electrode 710C trapping array sections 740C1 through 74OCs, and circular electrode 710D trapping array sections 740D1 through 74ODs.

[0131] A configuration of the circular electrodes having a higher number of arms, eight arms for example, as shown in FIG. 7, may provide enhanced flexibility compared to a configuration having fewer arms, e.g., a four-arm design (as shown in FIG. 6, for example), by offering a wider set of rotation angles and connectivity options. Each circular electrode may be rotated to various angular positions, e.g., including 45-degree increments as in the eight-arm configuration shown in FIG. 7, enabling precise alignment between channel sections of adjacent electrodes. The increased number of channel sections per electrode may allow some arms to remain uncoupled while others are aligned for ion transport operations, providing greater control over the connectivity patterns within the ion trap system. Thus an eight-arm design as of structure 700 may enable more complex routing patterns for ion arrays and may support advanced quantum algorithms that require specific connectivity topologies between different regions of the trap.

[0132] Each channel section of the circular electrodes may be configured to trap a section of an ion array that extends across multiple electrode assemblies or structures whenthe channel sections are properly aligned to form one of the channels. For example, when channel sections 750A1 and 750A? of circular electrode 710A are aligned with channel sections 750B1 and 750B? of circular electrode 71 OB, the ion array sections 740A1, 740 As, 740Bi and 74OBs are coupled to form a continuous ion chain that spans both electrode structures and forms a portion of an ion array trapped within a respective portion of channel 720 Ai. The alignment process may be achieved through coordinated rotation of rotating assemblies 760A and 760B to bring the respective channel sections into the same orientation, the column orientation, along which a channel is formed. According to some aspects, the channels may intersect at the electrodes’ centers at intersections or junctions generally referenced 730, such as junctions 730A-D of electrodes 710A-D, respectively, shown in FIG. 7.

[0133] Accordingly, each channel of the ion trap is formed by and includes a plurality of consecutively aligned channel sections. For example, having the alignment shown in FIG. 7, and as indicated above, the portion of channel 720A1 shown in FIG.7 includes and is formed by aligned channel sections 750A1, 75OAs, 750B1 and 75OBs, while channel sections 750A1 and 75OAs are of electrode 710A and channel sections 750B1 and 75OBs are of electrode 710B. As another example, the portion of channel 720B1 shown in FIG.7 includes and is formed by aligned channel sections 750A3, 750A?, 750D3 and 750D?, while channel sections 750A3 and 750A? are of electrode 710A and channel sections 750D3 and 750D? are of electrode 710D. The channels intersect at the center of each electrode thereby forming junctions 730, which may be utilized for shuttling of ions, as herein disclosed.

[0134] In the configuration of electrode 710A shown in FIG. 7, channel sections 750A2, 750A4, 750A6, and 75OAs are not aligned, and thus are not part of a channel. Accordingly, their trapped ion array sections are not coupled with other ion array sections and do not form an ion array trapped within a channel.

[0135] The ion array sections trapped within each channel section may be segmented into multiple segments or registers, generally referenced 770, e.g., through the application of optical tweezers that create localized confinement regions along the channel sections. As shown in FIG. 7, each array section may be divided into smaller segments that can be manipulated independently during quantum operations. For example, in the configuration shown in FIG. 7, each array section is divided into two segments of three ions each. Accordingly, array section 740A1 trapped within channel section 750A1 of electrode 710A is segmented into segments or registers 770Ai,i, and 770AI,2 of three ions each while data ions are colored black and barrier ions are colored white. According to some aspects, the segmentation pattern may be dynamically reconfigured through the coordinated control of optical tweezers or electrical potentials applied to the circular electrodes.

[0136] According to some aspects, ions may be shuttled toward the junctions to form a continuous ions array along a selected channel and across the respective junctions. As shown in FIG. 7, channels 720A are selected to be populated with a continuous ions array. Accordingly, channel 720A1, for example, traps a continuous ion array, while the portion of the trapped ion array shown in FIG. 7 includes segments, 770Ai,i and 770 A 1.2 of array section 740A1, formed segment 770AI_3, segments 770A5.1 and 770A5.2 of array section 740A5, segments 770Bi,i and 770BI,2 of array section 740B1, formed segment 770BI_3, segments 770B5.1 and 770B5.2 of array section 74OBs,. Segment 770AI,3 may be formed, for example, by straight line shuttling of three ions, each from a different array section trapped within the other channel sections of electrode 710A, e.g., array sections 740A2- 740A4 and 740Ae-740As trapped within array sections 750A2-750A4 and 750A6-750As, respectively. Ion arrays trapped within channels oriented differently from the selected channels 720 A, such as channels 720B-720D, exhibit gaps at their junctions. Unlike the rotatable ion trap configurations illustrated in FIGS. 6 and 7, these ion array configurationscan be established in non-rotatable ion trap setups, such as those shown in FIGS. 3-5B, through right-angle shuttling of ions.

[0137] The modular design of the rotatable electrode system may enable scalable expansion of the quantum computing architecture through the addition of additional circular electrode assemblies arranged in larger grid patterns. Each rotating assembly may operate independently, allowing for localized reconfiguration of connectivity patterns without disrupting operations in other regions of the trap. The scalability of the architecture may support quantum computing systems that include thousands of electrodes distributed across extended substrate areas, with each electrode contributing multiple channel sections and ion array segments to the overall computational capacity.

[0138] The rotating assemblies may provide precise angular control over their respective circular electrodes through mechanical or electromechanical actuators that can position the electrodes at specific orientations with high accuracy. The rotation process enables dynamic reconfiguration of the trap connectivity to support different computational workflows or to optimize ion transport efficiency for specific quantum algorithms. According to some aspects, the rotation angles may be selected from a discrete set of positions that correspond to optimal alignment between channel sections of adjacent electrodes, ensuring reliable connectivity while minimizing mechanical wear on the rotating components. The eight-arm configuration may provide rotation angles at 45- degree intervals, offering a plurality of distinct orientations for each circular electrode and enabling fine-grained control over the connectivity patterns between different regions of the ion trap system.

[0139] According to some aspects, the rotating assemblies may be configured with specific dimensional parameters that optimize performance while maintaining practical fabrication constraints. The number of segments in each rotating assembly affects various aspects of the system, specifically, chip size (assumed square), number of rotatingassemblies and number of fast optical reconfiguration steps performed after each slower mechanical rotation step. To consider these differences, a fixed number of 250,000 physical qubits is assumed. For simplicity, a configuration utilizing four-arm rotating assemblies as shown in FIG. 6 is exemplified. The system may accommodate varying numbers of segments per arm depending on the computational requirements and technical considerations. According to some aspects, a configuration with one segment per arm may result in rotating assemblies having a trap length of approximately 0.5 millimeters, supporting 200 qubits per trap assembly with a total of 1,250 trap assemblies distributed across a chip area of approximately 18x18 square millimeters. According to some aspects, a configuration with two segments per arm may increase the trap length to approximately 1 millimeter, supporting 400 qubits per trap assembly with 625 trap assemblies across a chip area of approximately 25x25 square millimeters. According to some aspects, larger configurations with ten segments per arm may extend the trap length to approximately 10 millimeters, supporting 2,000 qubits per trap assembly with 125 trap assemblies distributed across a chip area of approximately 112x112 square millimeters.

[0140] The distance between adjacent rotating assemblies may be on the order of 100 micrometers to provide sufficient spacing for the mechanical rotation mechanisms while enabling effective ion shuttling between adjacent trap assemblies. According to some aspects, the choice of segment configuration may influence various operational aspects of the system, where configurations with fewer segments per arm may require more frequent rotational operations but may provide greater modularity, while configurations with more segments per arm may reduce the number of required rotations but may increase the optical field of view requirements for the tweezer beam systems.

[0141] The disclosure may further support the formation of channels running in multiple directions beyond the traditional perpendicular orientations. According to some aspects, the electrodes may be formed to define a matrix that includes first channels runningin a first direction, second channels running in a second direction, and at least third channels running in a third direction that is angled relative to both the first and second directions. The third channels may intersect with both the first and second channels at the multiple channel junctions, creating a more complex network of pathways that can support advanced quantum computation workflows requiring extensive qubit connectivity. For example, a layout of hexagonal electrodes may be arranged so as to form channels along three principal orientations, each separated by 120°, rather than just two perpendicular directions as in a square grid. When referring to the rotating electrode configurations, each rotatable region may include channel sections of the third channels in addition to channel sections of the first and second channels, enabling three-dimensional connectivity patterns within the two-dimensional electrode layout.

[0142] According to some aspects, the disclosed systems may implement photonic interconnects as an additional method to link qubits between distant regions of the trap. These photonic interconnects may be compatible with both the fixed electrode configurations and the rotatable electrode architectures without requiring modifications to the basic electrode designs. The photonic interconnects may provide long-range connectivity options that complement both the electrical shuttling operations in fixed electrode configurations and the mechanical reconfiguration capabilities of the rotating assemblies, enabling hybrid approaches to quantum information transfer across the expanded electrode matrix in any of the disclosed architectures.

[0143] According to some aspects, the disclosed two-dimensional ion trap architecture may be compatible with various atomic species without imposing restrictions on the choice of ions used for quantum computation. The electrode configurations and optical control systems may be adapted to accommodate different ion types, including but not limited to alkaline earth ions such as calcium and barium, ions such as ytterbium (Yb), cadmium (Cd), and mercury (Hg), and other atomic species commonly employed in trapped ionquantum computing systems. The flexibility in atomic species selection may allow optimizing the choice of ions based on specific performance requirements such as coherence times, gate fidelities, or operational wavelengths. The modular design of both the fixed electrode and rotatable electrode architectures may support the implementation of mixed-species ion systems, where different atomic species can be trapped simultaneously within the same electrode matrix to leverage the unique properties of each ion type for specialized quantum operations or enhanced error correction protocols.

[0144] According to some aspects, sympathetic cooling using a different ion species may be employed to enhance the thermal management of long ion arrays. In some embodiments, groups or "magazines" including multiple cooling ions, potentially including tens of ions, can be introduced into the ion arrays. All necessary tweezer beam apparatus may be included to facilitate this process. The cooling ions may be used to sympathetically cool the long ion arrays and may subsequently be removed or transported out after the cooling process is complete. This approach may be applicable to both fixed-electrode ion trap configurations, such as those illustrated in FIGS. 3-5D, and rotatable electrode ion trap configurations, as shown in FIGS. 6 and 7. For instance, in the configuration depicted in FIG. 7, channel sections of a rotatable electrode may serve as a conduit for injecting cooling ions. Similarly, in ion trap 400, a channel may be formed across each electrode assembly specifically for the purpose of injecting cooling ions.

[0145] Reference is now made to FIG. 8, which illustrates a flowchart depicting a method 800 for trapping and manipulating arrays of ions segmented into ion segments or ion registers that are trapped within a 2D ion trap according to the present disclosure. The method may utilize or may be applied by the disclosed systems and architectures and will be exemplified by reference to FIGS. 1 to 7. According to some aspects, the method may be implemented via machine-executable instructions stored in a storage medium configured to be executed by at least one hardware processor or a controller, such as controlcircuitry 150 of system 100 of FIG. 1. According to some aspects, the disclosed systems may include the storage medium or the at least one hardware processor or controller.

[0146] At a step 810, electrical potentials between selected electrodes of the ion trap are dynamically adjusted to shuttle selected ions from an origin register to a destination register and across an intersection or a junction disposed therebetween. The electrical potential adjustment may be performed, e.g., using drive circuitry 130 shown in FIG. 1, which may apply time-varying voltages to specific electrodes to create potential gradients that guide ion movement along predetermined trajectories. The electrical potential adjustment process may accommodate various electrode configurations and intersection geometries.

[0147] At a step 820, respective optical tweezers of the ion trap may be configured to confine a portion of the shuttled ions. The optical tweezers may be positioned along the trajectory of the shuttled ions to maintain tight confinement during transport, preventing heating effects that could otherwise degrade quantum coherence. According to some aspects, the optical tweezers may be steered along the trajectory of the shuttled ions using, e.g., acousto-optical means or steerable opto-mechanical means for dynamic positioning, allowing the optical confinement to follow the ions as they move from the origin register to the destination register. According to some aspects, optical confinement may be applied to ions in the origin and destination registers, providing stability to the remaining ion populations during the shuttling process and minimizing recoil effects that could disturb the quantum states of non-transported ions. The optical tweezer configuration may utilize, for example, the tweezer beams system illustrated in FIG. 2, where tweezer beams 210 are directed toward the electrode grid to provide localized confinement capabilities. According to some aspects, the optical tweezers may be positioned at fixed locations along the ion trajectory and switched between these positions at appropriate times instead of continuous steering, which may simplify the optical control system while maintaining effectiveconfinement during ion transport. The optical confinement approach may eliminate the need for sympathetic cooling of the ion arrays after shuttling operations, reducing the requirement for additional ion species dedicated to cooling functions and decreasing the total number of ions needed for quantum operations. The dynamical confinement of selected shuttled ions may affect all ions within the transport group due to Coulomb forces, ensuring accurate and smooth motion while reducing unwanted heating or decoherence effects throughout the shuttling process.

[0148] According to some aspects, the intersections or junctions are formed by intersecting first and second channels of the ion trap. The intersections may be similar, for example, to junction 530 shown in FIGS. 5C-5D formed between intersecting channels 520A and 520B. According to some aspects, the matrix may include at least third channels formed by the electrodes of the ion trap that intersect with the first and second channels at the formed intersections, creating a more complex network of pathways that support advanced ion routing operations. The rotatable electrode configuration shown in FIG. 6 may provide additional flexibility for the shuttling process, where rotating one or more regions of the matrix may align the channel section within which the source register is trapped with the channel section within which the destination register is trapped so that the trajectory of the shuttled ions follows a straight line. This alignment capability may simplify the electrical control requirements and reduce heating effects that can occur during complex ion transport operations involving right-angle turns at intersections.

[0149] At an optional step 830, the segmentation of the arrays of ions into the multiple multi-ion registers may be performed. The segmentation process may utilize, for example, radiation source 140 shown in FIG. 1 to apply coherent radiation to selected ions within the trapped arrays, creating barrier ions that divide the arrays into smaller, manageable registers. According to some aspects, segmenting the arrays of ions may include configuring the electrical potential generated by the respective electrodes or configuringoptical tweezers to optically confine respective ions of the arrays of ions to form barrier ions. The optical tweezers, such as tweezer beams 210 shown in FIG. 2, may be distributed along the first and second channels to provide localized confinement of selected ions that serve as barriers between different registers.

[0150] According to some aspects, the arrays of ions may be dynamically segmented into multiple multi-ion registers by dynamically reconfiguring the respective electrical potential or by dynamically reconfiguring the optical tweezers during quantum computation operations. The segmentation process may create registers similar, for example, to those shown in FIG. 4, where barrier ions 440A-440D segment array section 460A2.1 into segments 450A-450C of three ions each. According to some aspects, the segmentation may be applied to ion arrays trapped within both fixed electrode configurations as shown in FIGS. 3-5 and rotatable electrode configurations as shown in FIG. 6. According to some aspects, the segmentation may be performed as disclosed with respect to FIGS. 5A-5B. The optical tweezers may create localized potential barriers at specific positions along the channels, effectively isolating different groups of ions from one another while maintaining their overall confinement within the channel structure. The segmentation step may enable parallel quantum operations to be performed across multiple registers simultaneously, thereby increasing computational throughput and supporting complex quantum algorithms that require independent manipulation of different ion groups.

[0151] At an optional step 840, the trapping of the arrays of ions may be performed. The arrays of ions may be trapped within a matrix of intersecting channels (e.g., first and second channels) formed by electrodes of an ion trap having a plurality of optical tweezers disposed along the channels. According to some aspects, trapping the arrays of ions may be performed using the ion trap architectures described with reference to FIGS. 1-7. The trapping process may utilize, for example, ion trap 120 contained within vacuum chamber110 as shown in FIG. 1, where drive circuitry 130 applies electrical potentials between electrodes formed on a substrate creating the matrix of intersecting channels. According to some aspects, the matrix may include a two-dimensional grid of intersecting first and second channels, where the first channels run in a first direction across the substrate and the second channels run in a second direction that may be perpendicular to the first direction. According to some aspects, each array of the trapped arrays of ions may be a one-dimensional array of ions that extends along the respective channel. According to some aspects, the trapping step may utilize the electrode configurations shown in FIGS. 3-7 to create stable confinement regions for the ion arrays. According to some aspects, the matrix may be formed by square-shaped electrodes such as electrodes 410I,I-410M, N shown in FIG. 4, which create column channels 420AI-420AN-I and row channels 420BI-420BM-I that intersect at junctions 430I,I-430M-I, N-I. According to some aspects, the matrix may be divided into rotatable regions using circular electrodes such as circular electrodes 610A- 610D shown in FIG. 6, where each region includes channel sections and at least one intersection. The rotatable electrode assemblies may provide enhanced flexibility for ion manipulation by allowing mechanical reconfiguration of the channel connectivity patterns. According to some aspects, each array of the arrays of ions may be at least a predetermined minimum number of ions long, e.g., at least 100 ions long. According to some aspects, the arrays of ions may be 100 to 400 ions long. According to some aspects, the arrays of ions may be 200 to 300 ions long.

[0152] Method 800 may enable efficient quantum computation by providing precise control over ion positioning and connectivity within the two-dimensional trap architecture. The execution of steps 810-820 and optionally steps 830 and 840 may support complex quantum algorithms that require dynamic reconfiguration of qubit connectivity and parallel operations across multiple ion registers. According to some aspects, the shuttling operations may be performed independently at multiple intersections throughout theelectrode matrix, enabling parallel ion transport across different regions of the trap simultaneously. The method may accommodate various electrode configurations, including both fixed electrode arrangements as shown in FIGS. 3-5 and rotatable electrode assemblies as shown in FIG. 6, providing flexibility in how the shuttling operations are implemented based on specific computational requirements. The combination of electrical potential control and optical tweezer confinement may create a robust platform for quantum computation that maintains high fidelity during ion transport operations while supporting scalable architectures that can accommodate thousands of qubits distributed across extended electrode matrices.

[0153] According to some aspects, method 800 may also be implemented in a onedimensional ion trap architecture. In this context, the steps of shuttling, segmentation, or optical confinement may be applied along channels having a single orientation, enabling precise control and manipulation of ions within a one-dimensional ions trap for quantum computation.

[0154] Reference is now made to FIG. 9, which illustrates a flowchart depicting a method 900 for quantum computation. Method 900 demonstrates an approach to quantum computation using two-dimensional ion trap architectures. Method 900 may be implemented using the quantum computing systems, ion trap architectures and shuttling methods described with reference to FIGS. 1-8, providing a systematic approach to large- scale quantum computation that leverages the two-dimensional electrode configurations and optical control capabilities disclosed herein. The method may also be applied by the disclosed systems and architectures and will be exemplified by reference to FIGS. 1 to 8. According to some aspects, the method may be implemented via machine-executable instructions stored in a storage medium configured to be executed by at least one hardware processor or a controller, such as control circuitry 150 of system 100 of FIG. 1. Accordingto some aspects, the disclosed systems may include the storage medium or the at least one hardware processor or controller.

[0155] At step 910, a first plurality of arrays of ions may be trapped in respective positions along a first plurality of parallel axes, wherein each array of ions of the first plurality of arrays of ions may be trapped along a respective axis of the first plurality of axes.

[0156] At a step 920, a second plurality of arrays of ions may be trapped in respective positions along a second plurality of parallel axes, wherein each array of ions of the second plurality of arrays of ions may be held trapped along a respective axis of the second plurality of axes. Each axis of the second plurality of axes may cross at least a portion of the axes of the first plurality of axes thereby forming a plurality of junctions therebetween. According to some aspects, the first direction of the first plurality of axes may be perpendicular to the second direction of the second plurality of axes, creating a rectangular grid pattern that enhances the utilization of available substrate area while providing systematic access to all trapping regions. It should be noted that steps 910 and 920 may be performed in any order, or at least partially or wholly simultaneously.

[0157] According to some aspects, the trapping process may utilize a system such as system 100 shown in FIG. 1, where ion trap 120 contained within vacuum chamber 110 provides the controlled environment for ion confinement. Drive circuitry 130 may apply electrical potentials between electrodes formed on a substrate to create the trapping regions along the pluralities of parallel axes. According to some aspects, each array of the arrays of ions may be a one-dimensional array of ions that extends along the respective axis, providing linear chains of qubits that can be manipulated through coordinated electrical and optical control. The first plurality of parallel axes may correspond to channels such as column channels 320A1-320A4 shown in FIG. 3, where each channel provides a linear trapping region that extends between adjacent columns of electrodes. According to someaspects, the second plurality of parallel axes may correspond to channels such as row channels 320B1-320B4 shown in FIG. 3, which extend perpendicular to the column channels and intersect at junctions 330i, 1-3304, 4. The intersection pattern may create a network of interconnected pathways that enable complex ion routing and manipulation operations across the two-dimensional electrode matrix.

[0158] According to some aspects, the electrical potential may be generated by electrodes disposed so as to form channels extending along the first and second pluralities of parallel axes, and the first and second pluralities of arrays of ions may be trapped within these channels, respectively. The electrode configurations may include square-shaped electrodes such as electrodes 410i,i-410m,nshown in FIG. 4, which create stable confinement regions for the ion arrays through the application of radiofrequency and direct current voltages. According to some aspects, the disclosed ion trap architecture creates an integrated trapping system where both channel orientations share common electrode elements while maintaining independent control over ion positioning and manipulation.

[0159] According to some aspects, each array of the first and second arrays of ions may be at least a predetermined minimum number of ions long. According to some aspects, the ion arrays may be segmented into multiple multi-ion registers through the application of optical tweezers that create barrier ions at specific positions along the channels, similar to the segmentation shown in FIG. 4 where barrier ions 440A-440D segment array section 460A2,I into segments 450A-450C. The segmentation process may utilize, for example, radiation source 140 shown in FIG. 1 to apply coherent radiation to selected ions within the trapped arrays, creating localized potential barriers that effectively divide the arrays into smaller, manageable registers. According to some aspects, the trapped pluralities of arrays of ions may form a layout of trapped ions that extends across a two-dimensional electrode matrix, enabling parallel operations to be performed simultaneously on multiple ion arrays without interference between different channel orientations.

[0160] According to some aspects, the first and second pluralities of arrays of ions may be trapped by electrical potential and may be segmented into multiple multi-ion registers through the coordinated application of electrical potentials and optical tweezers. The segmentation process may create registers similar to those shown in FIGS. 5A-5B, where ion arrays are divided into multiple segments through the strategic placement of barrier ions that create localized potential barriers.

[0161] According to some aspects, method 900 may further include trapping at least a third plurality of arrays of ions in respective positions along a third plurality of parallel axes. Each array of ions of the third plurality of arrays of ions may be held trapped along a respective axis of the third plurality of axes, and each axis of the third plurality of axes may cross at least a portion of the axes of the first and second pluralities of axes at the formed plurality of junctions. The third plurality of axes may provide additional connectivity options that support advanced quantum computation workflows requiring extensive qubit connectivity beyond perpendicular orientations. According to some aspects, the electrode configurations may include arrangements that support channels running in multiple directions, such as hexagonal electrode patterns that may create channels along three principal orientations separated by 120 degrees rather than two perpendicular directions.

[0162] At a step 930, the first and second pluralities of the arrays of ions may be reconfigured such that a selected plurality of arrays of ions of the first and second pluralities of arrays of ions extends continuously across the plurality of junctions and the plurality of arrays of ions unselected therefrom includes a gap at each junction of the plurality of junctions, as shown, for example, in FIG. 7. In the ion arrays configuration shown in FIG. 7, channels 720A trap continuous ion arrays while channels 720B-D trap ion arrays, which include gaps at the respective junctions 730. According to some aspects, the method may further include selecting the plurality of arrays of ions from the first and second pluralities of arrays of ions prior to the parallel application of the quantum operations. The selectionprocess may determine which channel orientation will support continuous ion arrays during specific quantum computation phases, while maintaining gaps in the unselected channels, inter alia, to prevent unwanted interactions. According to some aspects, the trapped first and second pluralities of arrays of ions may form a layout of trapped ions that can be dynamically reconfigured to support different connectivity patterns based on the requirements of specific quantum algorithms. According to some aspects, the ion arrays may be dynamically reconfigured, for example, from continuous ion arrays trapped in column channels to continuous ion arrays trapped in row channels, and vice versa, as needed. Such reconfiguration may be performed repeatedly and enables flexible adaptation of the ion array topology to support various quantum operations and algorithmic requirements.

[0163] According to some aspects, reconfiguring the first and second pluralities of the arrays of ions may include shuttling selected ions of the arrays of ions of the selected plurality of arrays of ions from a source register to a destination register across a junction of the formed plurality of junctions disposed therebetween. The shuttling process may involve dynamically adjusting the electrical potential between respective electrodes and optically confining a portion of the shuttled ions along their trajectory or ions in the origin and destination registers, as described in Method 800 of FIG. 8. The optical confinement may be performed via a plurality of optical tweezers disposed along the first and second plurality of parallel axes, similar to the tweezer beams 210 shown in FIG. 2 that provide localized confinement capabilities for individual ions or groups of ions within the trapped arrays. The shuttling operations may be similar to those illustrated in FIGS. 5C-5D, where ions are transported across junction 530 to alter the segmentation and connectivity of the ion arrays through coordinated electrical and optical control.

[0164] At a step 940, quantum operations may be applied in parallel on the selected plurality of arrays of ions. The parallel application of quantum operations may leverage thecontinuous ion arrays created during the reconfiguration step to perform coordinated quantum computations across multiple registers simultaneously. According to some aspects, the method may further include applying multi-qubit gates in-parallel across multiple segments of the trapped ion arrays, utilizing the all-to-all coupling capabilities within segments combined with the ability to controllably and simultaneously execute these couplings using multi-qubit gates. The parallel quantum operations may be implemented for example by using radiation source 140 shown in FIG. 1, which may be configured to apply coherent radiation to the ions within the selected arrays to drive quantum gate operations and state manipulations. According to some aspects, the method may further include performing mid-circuit measurements on selected ions of the trapped arrays of ions without disturbing the quantum states of ions in other segments, thereby enabling error correction and feedback control during quantum algorithm execution.

[0165] The parallel quantum operations may utilize the segmented structure of the ion arrays, where each segment may encode one or more logical qubits through quantum error correction protocols that protect the logical quantum information from decoherence and operational errors. According to some aspects, the method may further include segmenting the first and second pluralities of arrays of ions into multiple multi-ion registers prior to the parallel application of quantum operations. The segmentation may be achieved through the coordinated control of optical tweezers and electrical potentials, creating barrier ions that divide the continuous ion arrays into smaller registers that can be manipulated independently. The parallel execution capability may enable the implementation of complex quantum algorithms that require simultaneous operations across multiple qubit groups, providing computational advantages through the efficient utilization of the two- dimensional ion trap architecture and supporting scalable quantum computation workflows that can accommodate thousands of qubits distributed across extended electrode matrices.

[0166] An outstanding advantage of long ion-chains is the all-to-all coupling within segments combined with the ability to controllably and simultaneously exact these couplings using multi-qubit gates. Unique multi-qubit gates were addressed in PCT patent application PCT / IB2024 / 055007, filed May 23, 2024, which is hereby incorporated by reference in its entirety. PCT / IB2024 / 055007 provides techniques to efficiently engineer appropriate control fields to drive the multi- qubit gates. Additional techniques can be used to make them robust to various sources of error and noise, some of which are addressed in PCT patent application PCT / IB2022 / 061873, filed December 7, 2022, which is hereby incorporated by reference in its entirety. These and other multi-qubit gates were used as part of the architecture presented in PCT patent application PCT / IB2024 / 052100, filed March 5, 2024, which is hereby incorporated by reference in its entirety. These types of gates have been shown to be advantageous in many practical cases such as quantum error correction, and algorithmic primitives. These and expected advances in circuit compilation can substantially improve the rate and quality of operation of the system, for example by speeding up the rate of quantum error correction rounds. The disclosed 2D architecture supports all of these, as well as mid-circuit measurements and reconfiguration steps needed for applying parallel and sequential operations as part of the full quantum circuit design. The disclosed 2D design also inherently supports any single qubit operation. The combination of single-qubit operations and multi-qubit gates may compose a universal set for quantum computation, enabling the implementation of arbitrary quantum algorithms across the disclosed two-dimensional ion trap architecture.

[0167] The disclosed two-dimensional ion trap architecture may enable comprehensive system integration through the coordinated operation of electrical control, optical manipulation, and mechanical reconfiguration components. The electrical control system may provide the foundational trapping potentials through precisely controlled electrode arrays that create stable confinement regions for ion arrays across the two-dimensional substrate. The optical control system may operate in parallel with the electrical system to provide dynamic segmentation capabilities, ion shuttling assistance, and quantum gate operations through coherent radiation sources and optical tweezers distributed throughout the trap structure. According to some aspects, the mechanical control system may provide alternative or additional reconfiguration capabilities through rotatable electrode assemblies that can dynamically alter the connectivity patterns between different regions of the trap without requiring complex electrical shuttling operations. The various integrations of these control modalities may create a versatile quantum computing platform that can adapt to different algorithmic requirements while maintaining high operational fidelity across large numbers of qubits.

[0168] The scalability of the disclosed architecture may be achieved through the modular design of the electrode structures and control systems, which may enable the extension of the basic two-dimensional grid pattern to accommodate significantly larger numbers of qubits. According to some aspects, the system may be scaled up to accommodate one million logical qubits by tiling multiple two-dimensional arrays together in a larger assembly with a footprint of 25 centimeters by 25 centimeters. This scaling approach may utilize the repetitive nature of the electrode grid patterns, where individual two-dimensional arrays can be fabricated as separate modules and then assembled into larger configurations that maintain the same operational principles while expanding the total computational capacity. The modular scaling approach may enable the construction of quantum computing systems that include tens of thousands of individual electrode structures distributed across extended substrate areas, with each electrode contributing multiple channel sections and ion array segments to the overall computational capacity.

[0169] The functional advantages of the two-dimensional architecture may include enhanced qubit density compared to linear ion trap configurations, parallel operation capabilities across multiple ion arrays, and flexible connectivity patterns that can bedynamically reconfigured for quantum computation operations. The two-dimensional electrode arrangement may enable efficient utilization of available substrate area while providing systematic access to multiple or all trapping regions through the intersecting channel structure. According to some aspects, the parallel operation capabilities may allow quantum gates to be applied simultaneously across multiple segments of different ion arrays without interference between different channel orientations, thereby increasing computational throughput and reducing the total time required for complex quantum algorithms. The dynamic reconfiguration capabilities may enable the same physical hardware to support different quantum algorithms with varying connectivity requirements, providing operational flexibility that may be particularly valuable for quantum error correction protocols and distributed quantum computing applications.

[0170] The integration of optical tweezers with electrical trapping potentials may provide enhanced control over ion positioning and dynamics throughout the quantum computation process. The optical tweezers may operate independently of the electrical trapping system while providing individual or complementary functionality that includes ion segmentation, shuttling assistance, and localized cooling capabilities. According to some aspects, the optical control system may maintain precise positioning of barrier ions that create the segmentation patterns within ion arrays and provide dynamic confinement for ions during shuttling operations to minimize heating effects and preserve quantum coherence. The optical system may also enable mid-circuit measurement capabilities that can be performed on selected ions without disturbing the quantum states of other ions in the system, supporting quantum error correction protocols and feedback control mechanisms that may be necessary for fault-tolerant quantum computation.

[0171] The electrical control system may provide the foundational infrastructure for ion trapping through the application of radiofrequency and direct current voltages to the electrode arrays, creating the electric field configurations necessary for stable ionconfinement within the intersecting channel structure. According to some aspects, the electrical system may also enable controlled ion transport through the dynamic adjustment of electrode potentials that create potential gradients guiding ion movement along predetermined trajectories. The electrical control system may be designed to accommodate various electrode configurations, including both fixed electrode arrangements and rotatable electrode assemblies, providing flexibility in how the trapping and transport operations are implemented based on specific computational requirements. The integration of the electrical control system with the optical control system may enable coordinated operations where electrical potentials guide ion movement while optical tweezers maintain tight confinement during transport, creating a robust platform for quantum computation that maintains high fidelity during complex ion manipulation operations.

[0172] According to some aspects, the scalable architecture may support quantum computing systems that can accommodate computational workflows requiring extensive qubit connectivity and parallel processing capabilities. The two-dimensional electrode matrix may enable the implementation of quantum algorithms that require simultaneous operations across multiple qubit groups, providing computational advantages through the efficient utilization of the available hardware resources. The scalability may be further enhanced through the use of standardized control interfaces and modular hardware designs that allow individual two-dimensional arrays to be combined into larger assemblies without requiring fundamental changes to the control algorithms or operational procedures. The modular approach may also enable incremental expansion of quantum computing systems, where additional two-dimensional arrays can be added to existing installations to increase computational capacity as algorithmic requirements evolve or as technological improvements enable larger system configurations.

[0173] The disclosed methods of ion shuttling and quantum computation may directly leverage the architectural advantages described above by utilizing the two-dimensionalelectrode matrix to enable parallel ion transport operations across multiple channels while maintaining high-fidelity quantum operations through coordinated electrical and optical control. The shuttling methods may exploit the modular design and standardized control interfaces to perform simultaneous reconfiguration operations across different regions of the trap, while the quantum computation methods may utilize the enhanced qubit density and flexible connectivity patterns to implement complex algorithms that require extensive inter-qubit interactions and parallel processing capabilities across the scalable electrode architecture.

[0174] The electrode layouts or arrays described herein are provided for illustrative purposes and are not intended to limit the scope of the disclosure. The two-dimensional electrode configurations may be implemented in a variety of geometric arrangements, including but not limited to grid-like, or network patterns, and may be adapted or extended to accommodate different computational requirements or physical constraints. Accordingly, the invention encompasses all suitable electrode layouts capable of supporting the trapping, manipulation, and connectivity of ion arrays in two-dimensional quantum computing architectures, beyond the specific examples depicted in the drawings.

[0175] A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the disclosure. Accordingly, other implementations are within the scope of the following claims.

Claims

CLAIMS1. An apparatus for quantum computing, comprising: a vacuum chamber comprising: an ion trap, the ion trap comprises: a substrate; and electrodes formed on the substrate to define a matrix of first channels running between the electrodes across the substrate in a first direction and second channels running across the substrate in a second direction, angled relative to the first direction and intersecting at multiple channel junctions with the first channels; and drive circuitry coupled to apply electrical potentials between the electrodes across the first and second channels so as to trap arrays of ions within the first and second channels; and a radiation source configured to apply coherent radiation to the ions within the first and second channels so as to segment the arrays of ions into multiple multi-ion registers and to drive the ions within the multi-ion registers in parallel to perform quantum computations.

2. The apparatus according to claim 1 , wherein the ion trap is configured to trap onedimensional array of ions along each channel of the first and second channels.

3. The apparatus according to claim 1, wherein the electrodes are arranged to form a two-dimensional grid of intersecting first and second channels, each channel being capable of hosting an ion array.

4. The apparatus according to claim 1 , wherein the first direction of the first channels is perpendicular to the second direction of the second channels.

5. The apparatus according to claim 1, wherein the radiation source is further configured to perform mid-circuit measurements on selected ions of the trapped arrays of ions.

6. The apparatus according to claim 1 , wherein the drive circuitry and radiation source are configured to enable parallel application of multi-qubit gates across multiple segments of the trapped ion arrays.

7. The apparatus according to claim 1 , wherein each channel of the first and second channels is configured to trap an array of ions which is at least 100 ions long.

8. The apparatus according to claim 1, further comprising rotatable assemblies, wherein the matrix of first and second channels is divided into regions, each region comprising channel sections of the first and second channels and at least one channel junction, wherein each matrix region is mounted on a rotatable assembly of the rotatable assemblies and each rotatable assembly is configured to rotate its respective matrix region to couple the respective channel sections with channel sections of adjacent matrix regions.

9. The apparatus according to claim 8, wherein the electrodes are formed on the substrate to define a matrix of the first channels running between the electrodes across the substrate in the first direction, the second channels running across the substrate in the second direction, and at least third channels running across the substrate in a third direction angled relative to the first and second directions and intersecting at the multiple channel junctions with the first and second channels, and wherein each region further comprises channel sections of the at least third channels.

10. The apparatus according to any one of claims 1 to 9, wherein the drive circuitry is further configured to dynamically reconfigure the electrical potentials to dynamically change the segmentation or connectivity of the trapped ion arrays.

11. The apparatus according to any one of claims 1 to 10, wherein the radiation source is configured to optically confine ions of the arrays of ions to form barrier ions segmenting the arrays of ions into the multiple multi-ion registers.

12. The apparatus according to claim 11, wherein the radiation source comprises optical tweezers distributed along the first and second channels and configured to optically confine the barrier ions.

13. The apparatus according to claim 12, wherein the apparatus further comprises control circuitry configured to dynamically reconfigure the optical tweezers to dynamically change the segmentation and connectivity of the trapped ion arrays.

14. The apparatus according to claim 13, wherein the control circuitry is configured to couple adjacent multi-ion registers, which are not separated by channel junctions, by reconfiguring the respective optical tweezers.

15. The apparatus according to any one of claims 1 to 9, wherein the radiation source comprises optical tweezers distributed along the first and second channels, and wherein the apparatus further comprises control circuitry configured to shuttle selected ions of the arrays of ions across channel junctions from a source register to a destination register by dynamically adjusting the electrical potential between the respective electrodes and configuring the respective optical tweezers to confine a portion of the shuttled ions along their trajectory or ions in the origin and destination registers.

16. The apparatus according to claim 15, wherein each array of ions trapped within one of the first channels or the second channels comprises a gap at each channel junction of the channel junctions at which its respective channel intersects, and wherein the control circuitry is configured to shuttle selected ions of the arrays of ions trapped within the one of the first channels or the second channels to the arrays of ions trapped within the other one of the first channels or the second channels to form continuous arrays of ions along the other one of the first channels or the second channels, thereby facilitating parallel application of quantum operations on the arrays of ions trapped within the other one of the first channels or the second channels.

17. The apparatus according to claim 15, wherein the source register is trapped within a channel of one of the first or second channels and the destination register is trapped within a channel of the other one of the first or second channels.

18. The apparatus according to claim 1, wherein the ion trap is configured to trap ions at a density of at least 20 ions per square millimetres.

19. A method for shuttling ions of ion arrays trapped within a matrix of intersecting first and second channels formed by electrodes of an ion trap and segmented into multiple multi-ion registers from an origin register to a destination register and across an intersection formed thereof, the ion trap further comprising optical tweezers disposed along the first and second channels, the method comprising: dynamically adjusting electrical potential between respective electrodes of the ion trap; and configuring respective optical tweezers of the ion trap to confine a portion of the shuttled ions along their trajectory during their transport or to confine ions in the origin and destination registers.

20. The method according to claim 19, wherein each array of the arrays of ions is a one-dimensional array of ions.

21. The method according to claim 19, wherein the matrix is a two-dimensional grid of the intersecting first and second channels.

22. The method according to claim 19, wherein the first channels are perpendicular to the second channels.

23. The method according to claim 19, wherein each array of the arrays of ions is at least 100 ions long.

24. The method according to claim 19, wherein the matrix is divided into rotatable regions, each region comprising channel sections of the first and second channels and at least one of the formed intersections, the method further comprising rotating one or more regions of the matrix to align the channel section within which the origin register is trapped with the channel section within which the destination register is trapped so that the trajectory of the shuttled ions is a straight line.

25. The method according to claim 24, wherein the matrix further comprises at least third channels formed by the electrodes of the ion trap and intersecting with the first and second channels at the formed intersections, and wherein each region further comprises channel sections of the at least third channels.

26. The method according to claim 19, further comprising segmenting the arrays of ions into multiple multi-ion registers.

27. The method according to claim 26, wherein segmenting the arrays of ions comprises configuring the electrical potential generated by the respective electrodes orconfiguring the optical tweezers to optically confine respective ions of the arrays of ions to form barrier ions.

28. The method according to claim 27, wherein the arrays of ions are dynamically segmented into multiple multi-ion registers by dynamically reconfiguring the respective electrical potential or by dynamically reconfiguring the optical tweezers.

29. The method according to claim 19, wherein the origin register is trapped along a channel of one of the first or second channels and the destination register is trapped within a channel of the other one of the first or second channels.

30. A method for quantum computation, comprising: trapping a first plurality of arrays of ions in respective positions along a first plurality of parallel axes, wherein each array of ions of the first plurality of arrays of ions is trapped along a respective axis of the first plurality of axes; trapping a second plurality of arrays of ions in respective positions along a second plurality of parallel axes, wherein each array of ions of the second plurality of arrays of ions is held trapped along a respective axis of the second plurality of axes, wherein each axis of the second plurality of axes crosses at least a portion of the axes of the first plurality of axes thereby forming a plurality of junctions therebetween; reconfiguring the first and second pluralities of the arrays of ions such that the arrays of ions of a selected plurality of arrays of ions of the first and second pluralities of arrays of ions extend continuously across the plurality of junctions and the plurality of arrays of ions unselected therefrom comprises a gap at each junction of the plurality of junctions; andparallelly applying quantum operations on the selected plurality of arrays of ions.

31. The method according to claim 30, wherein the method further comprises selecting the plurality of arrays of ions from the first and second pluralities of arrays of ions prior to the parallel application of the quantum operations.

32. The method according to claim 30, wherein each array of the arrays of ions is a one-dimensional array of ions.

33. The method according to claim 30, wherein the first and second pluralities of axes form a two-dimensional grid of intersecting first and second axes.

34. The method according to claim 30, wherein the first direction of the first plurality of axes is perpendicular to the second direction of the second plurality of axes.

35. The method according to claim 30, further comprising performing mid-circuit measurements on selected ions of the trapped arrays of ions.

36. The method according to claim 30, further comprising parallelly applying multiqubit gates across multiple segments of the trapped ion arrays.

37. The method according to claim 30, wherein each array of ions of the selected plurality of arrays of ions is at least 100 ions long.

38. The method according to claim 30, wherein: the trapped first and second pluralities of arrays of ions form a layout of trapped ions,the layout of trapped ions is divided into rotatable regions, each region comprising ion array sections of the first and second arrays of ions and at least one junction of the formed junctions, and the reconfiguring of the first and second pluralities of the arrays of ions comprises rotating one or more regions of the layout of trapped ions to couple the respective ion array sections with ion array sections of adjacent regions.

39. The method according to claim 38, further comprising trapping at least a third plurality of arrays of ions in respective positions along a third plurality of parallel axes, wherein: each array of ions of the third plurality of arrays of ions is held trapped along a respective axis of the third plurality of axes, each axis of the third plurality of axes crosses at least a portion of the axes of the first and second pluralities of axes at the formed plurality of junctions, each region further comprises ion array sections of the third arrays of ions, and the method further comprises reconfiguring the third plurality of the arrays of ions.

40. The method according to any one of claims 30 to 38, wherein the first and second pluralities of arrays of ions are trapped by electrical potential and are segmented into multiple multi-ion registers, and wherein reconfiguring the first and second pluralities of the arrays of ions comprises shuttling selected ions of the arrays of ions of the selected plurality of arrays of ions from a source register to a destination register across a junction of the formed plurality of junctions disposed therebetween by:dynamically adjusting the electrical potential; and optically confining a portion of the shuttled ions along their trajectory or ions in the origin and destination registers.

41. The method according to claim 40, wherein the electrical potential is generated by electrodes disposed so as to form channels extending along the first and second pluralities of parallel axes, and wherein the first and second pluralities of arrays of ions are trapped within these channels, respectively.

42. The method according to claim 40, wherein the optical confinement is performed via a plurality of optical tweezers disposed along the first and second pluralities of parallel axes.

43. The method according to claim 40, further comprising segmenting the first and second pluralities of arrays of ions into multiple multi-ion registers.

44. The method according to claim 40, wherein the source register is trapped along an axis of one of the first or second pluralities of parallel axes and the destination register is trapped along an axis of the other one of the first or second pluralities of parallel axes.

45. The method according to claim 38, wherein reconfiguring of the first and second pluralities of the arrays of ions comprises reconfiguring the spacing between the ions of at least one of the first and second pluralities of the arrays of ions.

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