Periodic multidimensional atomic object confinement device with curved branches
By designing a multi-dimensional atomic object constraint device, the periodic or quasi-periodic array formed by bending branches solves the problems of poor operation parallelism, high manipulation signal complexity, and low atomic object transmission efficiency in the prior art, realizes parallel capture and manipulation of atomic objects, and reduces system complexity.
Patent Information
- Application Number
- CN202210985658.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Priority Date
- 2022-06-30
- Filing Date
- 2022-08-17
- Publication Date
- 2025-05-13
- Estimated Expiration
- 2042-08-17
AI Technical Summary
When the existing multi-dimensional ion trap captures and manipulates multiple ions, there are problems such as poor operational parallelism, high signal complexity, and low atomic object transmission efficiency.
A multi-dimensional atomic object constraint device is designed, which is a periodic or quasi-periodic array formed by a plurality of bent branches connected via junction points. Through the setting of bent branches, parallel capture and manipulation of atomic objects are realized, and the complexity of manipulation signals is reduced.
Parallel operation and transmission of atomic objects is realized, reducing the cooling time of atomic objects and the number of manipulation sources, and reducing the complexity of manipulating signal delivery systems.
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Figure CN115910741B_ABST
Abstract
Description
[0001] CROSS-REFERENCE TO RELATED APPLICATIONS
[0002] This application claims priority to U.S. Application No. 63 / 235,007, filed on August 19, 2021, the contents of which are incorporated herein by reference in their entirety. Technical Field
[0003] Various embodiments are directed to multidimensional atomic object confinement devices with curved branches and systems including multidimensional ion trap devices with curved branches. For example, various embodiments are directed to multidimensional atomic object confinement devices having periodic and / or quasi-periodic arrays of branches connected by junctions, the branches including curved branches. Background Art
[0004] An ion trap can use a combination of electric and magnetic fields to capture multiple ions in a potential trap. Ions can be captured for a variety of purposes, which may include, for example, mass spectrometry, research and / or control of the quantum state of the trapped ions. In various scenarios, a multidimensional (e.g., two-dimensional) ion trap can be used to capture multiple ions. Typically, a multidimensional ion trap includes a plurality of one-dimensional trap segments connected to each other via one or more junctions. Through application effort, ingenuity and innovation, many defects of such existing ion traps and systems comprising such ion traps have therefore been solved by developing solutions constructed according to embodiments of the present invention, many examples of which are described in detail herein. Summary of the invention
[0005] Example embodiments provide a multidimensional atomic object confinement device and / or a system including a multidimensional atomic object confinement device, which is formed by a periodic or quasi-periodic array of one-dimensional confinement segments connected via junctions. In various embodiments, the periodic or quasi-periodic array includes curved one-dimensional confinement segments, which are referred to as branches in this article. For example, the curved branches can take the form of sine or cosine functions, odd functions or even functions and / or any other curved one-dimensional segments. In various embodiments, the atomic object confinement device is an ion trap or other confinement device configured to confine multiple atomic objects. In various embodiments, the atomic objects are ions, atoms, polyions or polyatomic groups or crystals, neutral or ionic molecules, etc.
[0006] According to a first aspect, an atomic object confinement device comprises: a plurality of branches, each of the plurality of branches defining a one-dimensional well segment; and a plurality of junctions, each of the plurality of junctions connecting at least two of the plurality of branches. The plurality of branches and the plurality of junctions are arranged into a periodic or quasi-periodic array of connected one-dimensional well segments. The periodic array or quasi-periodic array comprises one or more minimum array elements. Each of the one or more minimum array elements comprises at least one curved branch.
[0007] In example embodiments, the at least one curved branch has a first end disposed at the first junction and a second end disposed at the second junction, and a length of the at least one curved branch is greater than a linear distance between the first junction and the second junction.
[0008] In an example embodiment, each branch of the plurality of branches is a curved branch.
[0009] In an example embodiment, the array is configured such that a straight line drawn tangent to a branch of the plurality of branches at a first point is tangent to another branch of the plurality of branches at a period or a subharmonic of the period of the array and (a) intersects the remaining branches of the plurality of branches at discrete points or (b) does not intersect the remaining branches of the plurality of branches.
[0010] In an example embodiment, the array is configured such that a straight line is drawn perpendicular to a branch of the plurality of branches and perpendicular to further branches at a period or a subharmonic of a period of the array.
[0011] In an example embodiment, the array is configured such that a straight line is drawn tangent to a set of branches at a period or a subharmonic of the period of the array, the set of branches forming a row or column, and the straight line does not intersect any branch in the set of branches at any other point along the branch.
[0012] In an example embodiment, the array is configured such that a straight line drawn tangentially to a branch of the plurality of branches, from that branch, is not tangential to any other branch of the plurality of branches within a given number of periods of the array.
[0013] In an example embodiment, the array is configured such that a straight line drawn perpendicular to a branch of the plurality of branches at a point from that branch is neither (a) tangential to any other branch of the plurality of branches nor (b) perpendicular to a point of another branch of the plurality of branches within a given number of periods of the array.
[0014] In an example embodiment, each minimum array element of the one or more minimum array elements includes at least one straight branch.
[0015] In an example embodiment, the array is configured such that at least one of the following is satisfied: (i) a first straight line drawn tangent to a branch of the plurality of branches at a first point is tangent to a first set of additional branches of the plurality of branches at a period or a subharmonic of the period of the array and (a) intersects the remaining branches of the plurality of branches at a discrete point or (b) does not intersect the remaining branches of the plurality of branches, (ii) a second straight line is drawn perpendicular to the branch and perpendicular to a second set of additional branches of the plurality of branches at a period or a subharmonic of the period of the array, (iii) a second straight line is drawn perpendicular to the branch and perpendicular to a second set of additional branches of the plurality of branches at a period or a subharmonic of the period of the array A third straight line is drawn tangent to a set of branches at the wave, the set of branches forming a row or column, and the third straight line does not intersect any branch in the set of branches at any other point along the branch, (iv) a fourth straight line is drawn tangent to the branch from the branch and is not tangent to any other branch in the plurality of branches within a given number of periods of the array, or (v) a fifth straight line is drawn perpendicular to the branch at a point from the branch and is neither (a) tangent to any other branch in the plurality of branches nor (b) perpendicular to another branch in the plurality of branches within a given number of periods.
[0016] In an example embodiment, the array is configured such that at least two of the following are satisfied: (i) a first straight line drawn tangent to a branch of the plurality of branches at a first point is tangent to a first set of additional branches of the plurality of branches at a period or a subharmonic of the period of the array and (a) intersects the remaining branches of the plurality of branches at a discrete point, or (b) does not intersect the remaining branches of the plurality of branches, (ii) a second straight line is drawn perpendicular to the branch and perpendicular to a second set of additional branches of the plurality of branches at a period or a subharmonic of the period of the array, (iii) a second straight line is drawn perpendicular to the branch and perpendicular to a second set of additional branches of the plurality of branches at a period or a subharmonic of the period of the array, A third straight line is drawn tangent to a set of branches at the wave, the set of branches forming a row or column, and the third straight line does not intersect any branch in the set of branches at any other point along the branch, (iv) a fourth straight line is drawn tangent to the branch from the branch and is not tangent to any other branch in the plurality of branches within a given number of periods of the array, or (v) a fifth straight line is drawn perpendicular to the branch at a point from the branch and is neither (a) tangent to any other branch in the plurality of branches nor (b) perpendicular to another branch in the plurality of branches within a given number of periods.
[0017] According to another aspect, a quantum computer is provided. In an example embodiment, the quantum computer includes a controller; and an atomic object confinement device. The controller is configured to cause one or more voltage signals to be applied to corresponding electrodes of the atomic object confinement device. The atomic object confinement device includes: a plurality of branches, each of the plurality of branches defining a one-dimensional well segment; and a plurality of junctions, each of the plurality of junctions connecting at least two of the plurality of branches. The plurality of branches and the plurality of junctions are arranged into a periodic or quasi-periodic array of connected one-dimensional well segments. The periodic array or quasi-periodic array includes one or more minimum array elements. Each of the one or more minimum array elements includes at least one curved branch.
[0018] In an example embodiment, the controller is configured to cause (almost and / or approximately) parallel operations to be performed on the atomic objects constrained by the atomic object constraining means.
[0019] In an example embodiment, the (almost and / or approximately) parallel operations include a first operation performed in a first minimum array element of the one or more minimum array elements and a second operation performed in a second minimum array element of the one or more minimum array elements, the first operation and the second operation being performed by one or more manipulation signals propagating along the same beam path.
[0020] In an example embodiment, the quantum computer further includes one or more manipulation sources configured to be controlled by the controller to generate one or more manipulation signals.
[0021] In example embodiments, the at least one curved branch has a first end disposed at the first junction and a second end disposed at the second junction, and a length of the at least one curved branch is greater than a linear distance between the first junction and the second junction.
[0022] In an example embodiment, each branch of the plurality of branches is a curved branch.
[0023] In an example embodiment, each minimum array element of the one or more minimum array elements includes at least one straight branch.
[0024] In an example embodiment, the array is configured such that at least one of the following is satisfied: (i) a first straight line drawn tangent to a branch of the plurality of branches at a first point is tangent to a first set of additional branches of the plurality of branches at a period or a subharmonic of the period of the array and (a) intersects the remaining branches of the plurality of branches at a discrete point or (b) does not intersect the remaining branches of the plurality of branches, (ii) a second straight line is drawn perpendicular to the branch and perpendicular to a second set of additional branches of the plurality of branches at a period or a subharmonic of the period of the array, (iii) a second straight line is drawn perpendicular to the branch and perpendicular to a second set of additional branches of the plurality of branches at a period or a subharmonic of the period of the array A third straight line is drawn tangent to a set of branches at the wave, the set of branches forming a row or column, and the third straight line does not intersect any branch in the set of branches at any other point along the branch, (iv) a fourth straight line is drawn tangent to the branch from the branch and is not tangent to any other branch in the plurality of branches within a given number of periods of the array, or (v) a fifth straight line is drawn perpendicular to the branch at a point from the branch and is neither (a) tangent to any other branch in the plurality of branches nor (b) perpendicular to another branch in the plurality of branches within a given number of periods of the array.
[0025] In an example embodiment, the array is configured such that at least two of the following are satisfied: (i) a first straight line drawn tangent to a branch of the plurality of branches at a first point is tangent to a first set of additional branches of the plurality of branches at a period or a subharmonic of the period of the array and (a) intersects the remaining branches of the plurality of branches at a discrete point, or (b) does not intersect the remaining branches of the plurality of branches, (ii) a second straight line is drawn perpendicular to the branch and perpendicular to a second set of additional branches of the plurality of branches at a period or a subharmonic of the period of the array, (iii) a second straight line is drawn perpendicular to the branch and perpendicular to a second set of additional branches of the plurality of branches at a period or a subharmonic of the period of the array, A third straight line is drawn tangent to a set of branches at the wave, the set of branches forming a row or column, and the third straight line does not intersect any branch in the set of branches at any other point along the branch, (iv) a fourth straight line is drawn tangent to the branch from the branch and is not tangent to any other branch in the plurality of branches within a given number of periods of the array, or (v) a fifth straight line is drawn perpendicular to the branch at a point from the branch and is neither (a) tangent to any other branch in the plurality of branches nor (b) perpendicular to another branch in the plurality of branches within a given number of periods of the array.
[0026] In an example embodiment, the quantum computer further includes at least one voltage source configured to be controlled by the controller to generate one or more voltage signals.
[0027] According to another aspect, a multidimensional atomic object confinement device is provided. The multidimensional atomic object confinement device comprises a plurality of branches arranged in a multidimensional periodic array. The plurality of branches comprises curved branches respectively arranged according to the period of the periodic array. BRIEF DESCRIPTION OF THE DRAWINGS
[0028] Having thus generally described the invention, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale, and in which:
[0029] Figure 1 illustrates an example array layout of an atomic object constraint device according to an example embodiment;
[0030] Figure 2 illustrates a number of periodic and quasi-periodic array layouts according to various example embodiments;
[0031] Figure 3A is a schematic diagram illustrating an example layout of an atomic object confinement apparatus and some example beam paths of a quantum processor according to an example embodiment;
[0032] Figure 3B is a schematic diagram illustrating a conventional straight-branch atomic object constraint device;
[0033] Figure 4 is a schematic diagram of a portion of an atomic object constraint apparatus according to an example embodiment;
[0034] Figure 5 is a schematic diagram illustrating an example quantum computing system according to various embodiments, the example quantum computing system including a multi-dimensional atomic object confinement device and configured to transport a polyatomic object crystal through at least one junction of the multi-dimensional atomic object confinement device;
[0035] Figure 6 A schematic diagram of an example controller of a quantum computer configured to perform one or more deterministic reshaping and / or reordering functions according to various embodiments is provided; and
[0036] Figure 7 A schematic diagram of an example computing entity of a quantum computer system that may be used in accordance with example embodiments is provided. DETAILED DESCRIPTION
[0037] The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which some but not all embodiments of the present invention are shown. In fact, the present invention can be implemented in many different forms and should not be construed as being limited to the embodiments set forth herein; on the contrary, these embodiments are provided so that the present disclosure satisfies applicable legal requirements. Unless otherwise stated, the term "or" (also represented as " / ") is used herein in both alternative and combined meanings. The terms "illustrative" and "exemplary" are used for examples and do not indicate quality levels. Unless otherwise stated, the terms "approximately" and "approximately" refer to within engineering and / or manufacturing limitations and / or within user measurement capabilities. The same reference numerals always refer to the same elements.
[0038] In various embodiments, a multidimensional atomic object constraint device is provided. The multidimensional atomic object constraint device includes a plurality of branches. Each branch of the plurality of branches is a one-dimensional constraint segment configured to capture an atomic object in a substantially one-dimensional capture region. The multidimensional atomic object constraint device includes a periodic or quasi-periodic array formed by a plurality of branches connected via junctions. The plurality of branches include curved branches. For example, the curved branches may take the form of a sine function or a cosine function, an odd function or an even function, and / or any other curved one-dimensional segment. In an example embodiment, the plurality of branches further include one or more straight branches or non-curved branches. In an example embodiment, each branch of the plurality of branches is a curved branch. For example, in various embodiments, the periodic or quasi-periodic array is formed by one or more minimum array elements, wherein each minimum array element includes at least one curved branch.
[0039] Each embodiment provides a system including a multidimensional atomic object constraint device. For example, each embodiment provides a quantum processor or quantum computer including a multidimensional atomic object constraint device, the multidimensional atomic object constraint device including a periodic or quasi-periodic array of branches connected by junctions, wherein at least some of the branches are curved. In such an embodiment, the quantum bit (qubit) (e.g., quantum bit) of the quantum processor or quantum computer is an atomic object constrained in the multidimensional atomic object constraint device. In each embodiment, the atomic object is an ion, an atom, an ion group or a crystal, etc. In each embodiment, a periodic array of branches with the same geometry is useful to allow a shared capture and / or transmission (TT) electrode manipulation signal set to be shared between similar types of TT electrodes across branches, thereby reducing the total number of signals and control complexity. In addition, in each embodiment, the branches of the multi-atomic object constraint device are curved to allow the system to perform parallel processing. For example, the system can be a quantum processor configured to perform parallel operations to reduce the running time of a quantum circuit, so that a deeper quantum circuit can be implemented within the coherence time of the quantum bit (e.g., quantum bit) of the quantum processor.
[0040] Large quantum computers are expected to solve problems that are difficult to solve with today's technology, such as in the fields of chemistry, materials science, and biology. Solving such problems will require calculations performed using quantum algorithms implemented using deep quantum circuits. The performance of these deep quantum circuits will require a sufficient number of qubits to be available for quantum processors and operations that can be used for deep quantum circuits (e.g., including transmission of qubits, cooling of qubits, gating of qubits, etc.) to be performed within the coherence time of the qubits. In order to enable the quantum processor to perform a larger number of operations (e.g., deeper quantum circuits) within a time period defined by the coherence time of the qubits, each embodiment provides a multidimensional atomic object constraint device configured to implement (almost and / or approximately) parallelization of operations. For example, the multidimensional atomic object constraint device of each embodiment is configured so that multiple operations can be performed almost and / or approximately in parallel. In each embodiment, when the manipulation signal propagates across the atomic object constraint device, almost and / or approximately parallel operations are performed serially at different points in the atomic object constraint device. As used herein, the term manipulation refers to the application of a manipulation signal (e.g., a laser beam, a microwave signal, a magnetic field, etc.) to a polyatomic object to cause a controlled evolution of the quantum state of one or more atomic objects as qubits (e.g., cooling, gating, shelving, reading, etc.). In various embodiments, atomic objects can also be transported in parallel within a multi-dimensional atomic object confinement device.
[0041] In addition, the curved branches of the multidimensional atomic object constraint device enable the use of a shared manipulation signal (e.g., a laser beam) to process multiple operating areas, regardless of whether the multiple operating areas are connected in series or in parallel. Therefore, the number of manipulation sources required to perform the operation is reduced, and the complexity of the manipulation signal transmission system is also reduced. In addition, the total laser power usage can be reduced (e.g., fewer beam paths are required, beam control hardware is eliminated, etc.). In addition, the curved branches of the multidimensional atomic object constraint device enable atomic objects to be moved into or out of corresponding beam paths without the need to transport the atomic objects through a junction, which reduces the time required to perform such atomic object transport and subsequent cooling of the transported atomic objects.
[0042] Thus, embodiments provide technical solutions to technical problems associated with how to execute deep quantum circuits, where a large number of operations need to be performed within the coherence time of the qubits of a quantum processor executing the deep quantum circuits. For example, embodiments provide improvements in the field of atomic object confinement devices and quantum computers and / or processors including atomic object confinement devices by providing atomic object confinement devices that are configured to enable parallel execution of various operations and / or atomic object transfers, reduce the required cooling of atomic objects due to certain transfer events, and reduce the number of manipulation sources and the complexity of the manipulation signal delivery system.
[0043] As described above, each embodiment provides a multidimensional atomic object constraint device, each of which includes a periodic or quasi-periodic array formed by multiple branches connected via junctions, wherein the multiple branches include curved branches. For example, in each embodiment, at least one branch of each minimum array element is a curved branch. As used herein, the minimum array element of the atomic object constraint device is a minimum set of branches and junctions that can be used for tiling and / or forming a tessellation of the layout of the atomic object constraint device. In an example embodiment, each of the multiple branches of the atomic object constraint device is a curved branch. In an example embodiment, the minimum array element of the atomic object constraint device includes straight branches and / or non-curved branches.
[0044] In general, each branch of the atomic object confinement device is defined by one or more radio frequency tracks and / or electrodes (referred to herein as RF tracks) and at least one capture and / or transmission (TT) electrode sequence or a series of capture and / or transmission (TT) electrodes. When an RF voltage signal is applied to the RF track, a capture potential configured to capture and / or confine an atomic object within a one-dimensional capture region is generated. In particular, applying the RF voltage signal to the RF track generates a pseudopotential. The one-dimensional capture region includes an RF zero point. The RF zero point is a one-dimensional path defined by the direction of the weakest pseudopotential gradient. At certain points along the RF zero point, the pseudopotential is substantially equal to zero. Therefore, the RF zero point creates a stable one-dimensional capture region. The branches of the atomic object confinement device are substantially defined by the RF zero point. In a curved branch, the RF zero point is curved in the same manner as the branch, so that the atomic object captured and / or confined within the branch of the atomic object confinement device can be transmitted along the RF zero point of the corresponding branch. The TT electrode is configured to have a series of voltage signals applied thereto, wherein the time evolution of the series of voltage signals is slow compared to the time evolution of the radio frequency voltage signal applied to the RF rail (due at least in part to the use of a low pass filter). In an example embodiment, the term slow means that the highest frequency Fourier component having a substantially non-zero amplitude is slower than the frequency of the signal applied to the RF rail.
[0045] Figure 1 The meaning of a bent branch and / or an array comprising bent branches as used herein is illustrated. Figure 1 An example arrangement of the branches 208 of the atomic object constraints in the array 205 is illustrated according to an example embodiment. Figure 1The example array 205 shown in FIG. 2 is a periodic array of curved branches 208. Each branch 208 extends from a first end 209A that is adjacent to, adjacent to, and / or forms at least a portion of a first junction 202A to a second end 209B that is adjacent to, adjacent to, and / or forms at least a portion of a second junction 202B. The shortest distance (e.g., straight-line distance and / or Euclidean distance) between the first junction 202A and the second junction 202B is the array distance The length of the curved branch 208 is greater than the array distance In an exemplary embodiment, the length of the curved branch 208 is at least wait.
[0046] Figure 1 Five arrays with curved branch criteria are further illustrated as shown by lines 150A, 150B, 150C, 150D, and 150E. As used herein to describe arrays with curved branch criteria, the terms "tangent" and "perpendicular" refer to the plane of the atomic object constraint (e.g., in Figure 1 The angle of the two-dimensional projection shown in the plane).
[0047] In various embodiments, a periodic or quasi-periodic array of branches including at least one curved branch in each minimum array element satisfies at least one of the five arrays with a curved branch criterion. In an exemplary embodiment, a periodic or quasi-periodic array of branches including at least one curved branch in each minimum array element satisfies all five arrays with a curved branch criterion.
[0048] The first array with a curved branch standard is shown by line 150A. Line 150A is a straight line that is tangent to at least one branch 208 at a certain point, and is also tangent to another branch of the array at a period of the atomic object confinement device (or a period of a certain subharmonic), and intersects other branches of the array only at discrete points (or not at all). The circles along line 150A show the areas where line 150A is tangent to the corresponding branch 208.
[0049] A second array with a bent branch standard is shown by line 150B. Line 150B is a straight line that is perpendicular to at least one branch and also perpendicular to another branch at a period of a certain subharmonic of the array.
[0050] A third array with a curved branch standard is shown by line 150C. Line 150C is a straight line that is tangent to some of the branches of the array along the columns or rows of the array at the period of the array and / or some subharmonic period, but does not intersect those same branches at any out point along those branches.
[0051] A fourth array with a curved branch criterion is illustrated by line 150D. Line 150D is a straight line that is tangent to a branch at a point and is not tangent to any other portion of any branch over a given number of periods of the array. For example, if the curved branches are defined by a periodic function corresponding to a period length, then line 150D is not tangent to any other portion of any branch within a distance of a given multiple of the period length of branch 150D at which point the straight line is tangent to branch 150D.
[0052] A fifth array having a curved branch criterion is illustrated by line 150E. Line 150E is a straight line that is perpendicular to a branch at a point and, in a given number of periods of the array, is neither (a) tangent to any other branch of the array nor (b) perpendicular to the same point of the branch in other periods of the array. For example, if a curved branch is defined by a periodic function corresponding to the period length, then line 150E is not perpendicular to the same point of the branch in other periods of the array at a distance from a given multiple of the period length of the branch at which line 150E is tangent to the branch.
[0053] As described above, the atomic object constraint device includes multiple branches connected to form a periodic or quasi-periodic array via a junction. As used herein, a periodic array is an array for which a minimum array element can be defined, which is smaller than the entire array. For example, the minimum array element can be used to generate an array via tiling and / or mosaicking (e.g., by one or more rotations and / or translations of the minimum array element). In other words, a periodic array is an array in which the topological structure and / or geometric structure of the array is repeated with a defined period. A quasi-periodic array is an array in which the period of the array is disturbed by global distortion. In other words, a quasi-periodic array is almost periodic, but the periodicity is disturbed in one or more dimensions.
[0054] Therefore, each embodiment provides an atomic object constraint device (and / or a system including such an atomic object constraint device) including multiple branches, the multiple branches including one or more curved branches, the multiple branches are connected via junctions and arranged in a periodic or quasi-periodic array. The curved branches and / or the periodic or quasi-periodic array are configured so that the array satisfies one or more arrays with curved branch standards. For example, the curved branches and / or the periodic or quasi-periodic array can be configured so that the atomic object constraint device can be used to perform periodic operations and / or transmissions on atomic objects constrained by the atomic object constraint device.
[0055] Figure 2A plurality of possible periodic or quasi-periodic arrays 205 (e.g., 205A to 205L) are illustrated in which branches of atomic object confinement devices may be arranged according to various embodiments. Various other arrays 205 that include at least one curved branch in a minimum array element and / or that meet at least one of the arrays having curved branches criteria may be used in other embodiments. It should be understood that the use of terms such as horizontal and vertical and / or row and column refers to how the array is shown in the corresponding figure. It should be understood that the array may be arranged around a well normal (e.g., a normal to a well surface that is in the z-direction, such as Figure 3A to any angle.
[0056] The first array 205A is a square array in which each branch is one period of a periodic odd or even function. For example, the junction point is located at a harmonic and / or period of a periodic odd or even function. For example, the first array 205A includes a branch row that is each one period of a sine function and a branch column that is each one period of a sine function (e.g., rotated 90 degrees relative to the branch row). The minimum array element of the first array 205A is formed by a connected group of two branches 208 connected by a junction point 202.
[0057] For example, in an example embodiment, the atomic object restraint 200 includes a plurality of branches 208. Each branch of the plurality of branches is a curved branch substantially described by one period of a sine function (sin(x), for x=[0,2π)). The plurality of branches are arranged into a first array 205A including a four-way junction, wherein a branch 208 ending at a junction 202 is substantially perpendicular to at least one other branch at the junction. In other words, the first array 205A includes junctions 202 that connect branches arranged in substantially vertical rows and vertical columns. This example embodiment of the atomic object restraint satisfies all five array criteria for having curved branches, such as Figure 1 shown.
[0058] The second array 205B is an alternating distortion array in which each branch is half of the period of a periodic odd or even function, and alternating rows and / or columns are inverted. For example, each row and each column is a periodic function (e.g., a periodic odd or even function), wherein the junction is set at each half-period of the periodic function. For example, row 290A includes branches that are each half a period of a sine function, wherein the junction is located at a half-period of a periodic odd or even function (such as the sine function shown here). Row 290B, which is adjacent and / or adjacent to row 290A, is inverted relative to row 290A (e.g., flipped around a horizontal axis / horizontal line). Row 290C, which is adjacent and / or adjacent to row 290B so that row 290B is the only row set between rows 290A and 290C, is inverted relative to row 290B (e.g., flipped around a horizontal axis / horizontal line) and is substantially the same as row 290A. Similarly, column 292A includes branches that are each half a period of a sine function, with junctions located at half a period of a periodic odd or even function (such as the sine function shown here). Column 292B, which is adjacent and / or adjacent to column 292A, is inverted relative to column 292A (e.g., flipped about a vertical axis / vertical line). Column 292C, which is adjacent and / or adjacent to column 292B so that column 292B is the only column disposed between columns 292A and 292C, is inverted relative to column 292B (e.g., flipped about a vertical axis / vertical line) and is substantially identical to column 292A. The smallest array element of the second array 205B is formed by a connected group of twelve branches, which are connected via nine junctions formed by the intersection of rows 290A, 290B, 290C with columns 292A, 292B, 292C.
[0059] The third array 205C and the fourth array 205D are examples of arrays in which the arrays include both curved branches and straight branches. As shown in the figure, the horizontal branches of the third array 205C and the fourth array 205D are around the well normal (e.g., the normal to the well surface in the z direction, such as Figure 3A The third array 205C and the fourth array 205D are periodic functions rotated at any angle. The vertical branches of the third array 205C and the fourth array 205D are straight branches, wherein the junction is located at the period of the function. The junction can be located at any desired interval along the vertical branch. In other words, the vertical branch can have any desired length suitable for the intended application. The third array 205C includes a horizontal branch described by a function cos(x)+cos(2x) without rotation and a vertical branch with a length matching the period of the function describing the horizontal branch. The other arrays 205D include a horizontal branch described by a function cos(x) rotated 16 degrees around the well normal and a vertical branch with a length matching the period of the function describing the horizontal branch. The minimum array element of the third array 205C or the fourth array 205D is formed by two connected branches connected by a junction.
[0060] The fifth array 205E and the sixth array 205F are examples of odd function arrays. The branches are described by any periodic odd function or periodic even function rotated by any angle around the well normal at the corresponding junction. The branches have a length corresponding to the period of the odd function or even function describing the branches. The array is formed by reflecting the cross axis across the horizontal axis or horizontal line. For example, the branches of the fifth array 205E are described by sin(x) rotated 45 degrees around the well normal. The smallest array element of the fifth array 205E or the sixth array 205F is formed by four connected branches connected by two junctions.
[0061] The seventh array 205G is an anisotropic alternating distortion array. The horizontal branch is any periodic function rotated at any angle around the well normal. Each horizontal branch has a length corresponding to the period of the periodic function describing the horizontal branch. The vertical branch is a straight line with any desired length suitable for the intended application. For example, the junction point can be located at any desired interval along the vertical branch. The adjacent, adjacent and / or alternating horizontal branch rows are reversed (for example, flipped around the horizontal axis or horizontal line). The illustrated seventh array includes horizontal branches described by cos (x) that are not rotated around the well normal and vertical branches with a length that matches the period of the function describing the horizontal branch.
[0062] The eighth array 205H is a star-shaped and cross-shaped array, in which each branch is a half period of a periodic odd function or an even function. For example, each row and each column is a periodic function (e.g., a periodic odd function or an even function), in which a junction point is set at each half period of the periodic function. Similar to the second array 205B, adjacent rows / columns are reversed relative to each other (e.g., flipped around a horizontal / vertical axis or a horizontal / vertical line). Also similar to the second array 205B, the smallest array element of the eighth array 205H is formed by a connection group of eight branches, which are connected via four junction points formed by the intersection of three adjacent rows and three adjacent columns.
[0063] The ninth array 205I, the tenth array 205J and the eleventh array 205K show periodic arrays in which the junction is formed by the confluence of three branches. The first array, the second array, the third array, the fourth array, the fifth array, the sixth array, the seventh array and the eighth array 205A to 205H each show a periodic array in which the junction is formed by the confluence of four branches.
[0064] For example, for the ninth array 205I, the smallest array element consists of an irregular hexagon with 180 degree rotational symmetry. One or more sides of the hexagon are replaced by a warp function so that the resulting array includes a warp branch.
[0065] In another example, for the tenth array 205J, the smallest array element consists of a regular hexagon, where each branch is replaced by the same odd or even function (where the function is odd or even near the center of the branch). For example, a regular hexagon has a 60-degree rotational symmetry about the center point of the hexagon. In the illustrated embodiment, the sides of the regular hexagon are replaced by curved branches described by a sine function whose period matches the length of the hexagon side.
[0066] For the eleventh array 205K, the smallest array element consists of a hexagon with folded symmetry on both the x-axis and the y-axis, the vertical branches are straight, and the other branches are curved branches described by odd or even functions. This is similar to the fifth array 205E, but each four-way junction is replaced by a pair of three-way junctions connected by short straight branches. It should be understood that various other octagons, hexagons, squares, and / or other grids with three-way junctions, four-way junctions, and / or more than four-way junctions can be adapted with curved branches to provide a periodic array with curved branches.
[0067] The twelfth array 205L is a quasi-periodic array with four-way junctions. In the twelfth array 205L, the period of the array is perturbed by global distortion in two dimensions to provide a quasi-periodic array.
[0068] Figure 3AAn example array 205 of an atomic object confinement device 200 is illustrated. In the illustrated embodiment, a beam path 220 is plotted along the y direction to indicate how a beam (e.g., a laser beam and / or other manipulation signal) can propagate across the narrower dimension of the atomic object confinement device 200. In various embodiments, the beam path is defined to substantially span the narrower dimension of the atomic object confinement device (or in some cases along a diagonal line) so that the manipulation signal propagating along the beam path passes through the atomic object confinement device while the manipulation signal is still well collimated (e.g., the full width half maximum of the beam cross section of the manipulation signal is at most a specific width). The solid dots indicate positions within the array 205 where, when an atomic object is located, the beam propagating along the beam path 220 will be incident on the atomic object substantially parallel to the RF null of the corresponding branch at the location of the atomic object (location 210) or substantially perpendicular to the RF null of the corresponding branch at the location of the atomic object (location 212). Therefore, the array 205 and the beam path 220 are configured so that a single manipulation beam can be incident on multiple atomic objects simultaneously. In addition, a single manipulation beam can be simultaneously incident on an atomic object that is substantially parallel and substantially perpendicular to the RF zero point of the corresponding branch at the location of the corresponding atomic object. This feature of the atomic object confinement device 200 enables multiple parallel operations to be performed by, for example, a quantum processor including the atomic object confinement device 200. This feature further enables the use of a single manipulation source to process multiple operating regions and / or atomic objects to reduce the manipulation source power and / or the number of manipulation sources and / or the complexity of the manipulation source and / or manipulation signal transmission system. In addition, each branch includes a location, such as a hollow point 214, at which the atomic object can be transmitted out of the path of the beam path 220 without having to be transmitted through a junction. This enables the removal of atomic objects from parallel operations without the need to perform junction transmission and subsequent cooling in a timely manner.
[0069] Figure 3A Also illustrated is how the atomic object constraint device 200 can achieve the execution of almost and / or approximately parallel operations. For example, along the beam path 220A, the atomic object can be located at positions 250A, 250B. The atomic object located at position 250B can be moved out of the beam path 220A (without having to pass through the junction 202), so that when a manipulation signal is applied to perform parallel operations on the atomic object located at position 250A, the motion and / or internal state of the atomic object located near position 250B is not disturbed. The atomic object can then be moved back to the position, and the atomic object located at position 250A can be moved out of the beam path 220A (without having to pass through the junction 202), so that when a manipulation signal is applied to perform parallel operations on the atomic object located at position 250B, the motion and / or internal state of the atomic object located near position 250A is not disturbed.
[0070] Thus, various embodiments enable minimization of resources (e.g., the number of beams required for gating) while compensating for variations in local trap and beam characteristics (e.g., divergence and clipping of the laser beam, variations in trap potential, etc.) that do not allow full parallelization of the operation. For example, using a total manipulation signal flux (J / mm) incident on the atomic object 2 ) proportionally changes the internal state of the atomic objects. When the manipulation signal is incident on all four atomic objects (those at positions 250A, 250B), the divergence of the manipulation signal (e.g., laser beam) means that each atomic object will experience a different light intensity (W / mm 2 ) and therefore slightly different gating operations. This effect can be compensated by performing gating in series on each atomic object, adjusting the length of each laser pulse to achieve equal total flux on each manipulation signal. When the beam waist of the manipulation signal appears and / or is just located at the midpoint between position 250A and / or position 250B, the partially parallel situation is possible (as described above about positions 250A, 250B). In this case, the atomic objects at position 250A all see the same light intensity. In addition, the atomic objects at position 250B see the same light intensity, although different from the atomic objects at position 250A.
[0071] Figure 3B A conventional straight branch array 5 is shown comprising a plurality of branches 8, each of which is straight (eg, not bent and / or has a distance equal to the array distance). Length) and joined at junction 2. Beamline 20 shows how, in a conventional straight branch array 5, the entire series of branches 8 are illuminated by beam path 20 when the beam path is intended to be incident on position 10, so that beam path 20 is substantially parallel to the RF null at position 10. When an atomic object is located at position 6, which is along the same series of branches 8 as position 10 to be illuminated by beam path 20, but the atomic object should not be illuminated by beam path 20 (e.g., not to have beam path 20 perform operations on it), the atomic object must be transferred to position 14 through junction 2. Transferring an atomic object through junction 2 is a slower process than transferring an atomic object along branches of similar length, and significant cooling of the atomic object may be required after the transfer occurs. Therefore, it is desirable to minimize the transfer of atomic objects through junction 2. In addition, when it is desired to irradiate position 12, the beam path 20 is substantially perpendicular to the RF null at that position, and a different beam path 20 must be used. In other words, a single beam path 20 cannot simultaneously illuminate both the location 10 where the beam path 20 is substantially parallel to the RF null and the location 12 where the beam path 20 is substantially perpendicular to the RF null. Therefore, additional optical circuitry is required. By comparison Figure 3AAn example embodiment of a periodic array comprising curved branches as shown in and Figure 3B As can be seen from the conventional periodic array including straight branches shown in , various embodiments of the atomic object confinement device 200 provide significant technical advantages over conventional devices.
[0072] Figure 4 A schematic top view of a portion of an example atomic object confinement device 200 is provided. The example atomic object confinement device 200 includes a plurality of branches 208, the plurality of branches 208 including curved branches, the plurality of branches 208 being arranged in a periodic array 205 and connected via a junction 202. In an example embodiment, the atomic object confinement device 200 is a multi-dimensional (e.g., two-dimensional or three-dimensional) surface ion trap, surface Paul trap, etc. configured to capture a plurality of atomic objects (e.g., ions, ion crystals, etc.). Each branch 208 of the atomic object confinement device 200 extends a corresponding length between two corresponding ends 209A, 209B. Typically (e.g., except possibly along the edge of the atomic object confinement device 200), each end 209 of each branch 208 is connected to at least one other branch 208 via a junction 202. In general, the branches 208 of the atomic object confinement device 200 are one-dimensional segments and / or portions of the atomic object confinement device 200. In particular, the branches 208 of the atomic object confinement device 200 define a substantially one-dimensional confinement region within which an atomic object can be confined. In general, the junction 202 is formed by the confluence, joining and / or abutment of two or more branches 208. At least two of the two or more branches 208 define a one-dimensional confinement region that is transverse to each other at least near the junction. For example, branch 208A is transverse to branches 208B and 208D at least near the junction 202A.
[0073] In various embodiments, the atomic object confinement device 200 includes a plurality of branches 208, the plurality of branches 208 including curved branches and arranged in a periodic or quasi-periodic array. The shortest distance (e.g., straight-line distance and / or Euclidean distance) between two adjacent junctions 202 (e.g., the shortest path between two adjacent junctions does not pass through and / or include any other junctions) is the array distance When the path length along the branch is greater than the array distance , the branch 208 disposed between two adjacent junctions 202 (e.g., having a first end 209A at one of the two adjacent junctions and a second end 209B at the other of the two adjacent junctions) is a curved branch. In an exemplary embodiment, the length of the curved branch 208 is at least wait.
[0074] In various embodiments, the atomic object confinement device 200 includes a plurality of branches 208 including curved branches and arranged in a periodic or quasi-periodic array such that the array 205 satisfies at least one array with curved branches criterion, as described above.
[0075] In an example embodiment, the atomic object confinement device 200 is manufactured as part of an atomic object confinement device chip and / or as part of an atomic object confinement device package. In an example embodiment, the atomic object confinement device 200 is at least partially defined by a plurality of radio frequency (RF) tracks 230. In various embodiments, the atomic object confinement device 200 is at least partially defined by a plurality of capture and / or transmission (TT) electrode 235 sequences. In various embodiments, various TT electrode geometries, placements, layouts, etc. may be used. The geometries, placements, layouts, etc. of the TT electrodes 235 shown are provided for illustrative purposes, and in various embodiments, will be determined and / or configured based on the intended application of the atomic object confinement device 200. In various embodiments, the upper surface of the atomic object confinement device 200 has a flattened topology. For example, the upper surface of each RF track 230 in the plurality of RF tracks and the upper surface of each TT electrode 235 in the plurality of TT electrode sequences may be substantially coplanar. In an example embodiment, the surface of the atomic object confinement device 200 is not flat, and defines a plane from which the height of the atomic object above the "surface" of the atomic object confinement device 200 is measured.
[0076] In various embodiments, each branch 208 of the atomic object restraint 200 includes a plurality of (e.g., one or more) RF rails 230 and / or is at least partially defined by a plurality of (e.g., one or more) RF rails 230. In an exemplary embodiment, the branches 208 of the atomic object restraint 200 are formed with substantially parallel longitudinal axes. For example, when the branch 208 is defined by two or more RF rails 230, the two or more RF rails 230 extend substantially parallel to each other along the length of the branch 208. As used herein, substantially parallel indicates that the RF rails 230 that are substantially parallel to each other do not intersect or cross each other. For example, the RF rails 230 can be formed by starting with a rectangular geometry and then by adding interfering geometries such as kinks, bends, etc.
[0077] In various embodiments, two adjacent RF rails 230 may be separated (e.g., insulated) from each other by a longitudinal gap 231. For example, the longitudinal gap may define (in one or two dimensions) a confinement channel or region of the atomic object confinement device 200, in which one or more atomic objects may be confined and / or captured at different locations within the atomic object confinement device. In various embodiments, the longitudinal gap defined thereby may extend substantially parallel to the adjacent RF rails 230 along the length of the corresponding branch 208. In example embodiments, the longitudinal gap may be at least partially filled with an insulating material (e.g., a dielectric material). In various embodiments, the dielectric material may be silicon dioxide (e.g., formed by thermal oxidation) and / or other dielectric and / or insulating materials. In various embodiments, the longitudinal gap has a width (e.g., the distance between adjacent RF rails 230) of approximately 40 μm to 500 μm. In various embodiments, one or more TT electrode sequences 236.2 are disposed and / or formed within the longitudinal gap.
[0078] In various embodiments, the atomic object confinement device 200 (and / or the branches 208 and / or their junctions 202) can be at least partially defined by a plurality of TT electrode sequences 236 (e.g., 236.1, 236.2, 236.3), each of which includes a plurality of TT electrodes 235. In an example embodiment, each of the TT electrode sequences 236 associated with and / or at least partially defining the branches 208 is formed to extend substantially parallel to one or more RF rails 230, which at least partially define the corresponding branches 208 along at least a portion of the length of the branches 208. For example, three sequences 236.1, 236.2, and 236.3 of TT electrodes at least partially define Figure 4 208C shown in . Each of the three TT electrode sequences 236.1, 236.2, and 236.3 includes a plurality of TT electrodes 235. In various embodiments, the number of TT electrode sequences 236 that at least partially define each branch 208 includes two, three, four, and / or other numbers of TT electrode sequences. In an example embodiment, the atomic object confinement device 200 includes a plurality of TT electrode sequences 236, wherein each of the plurality of TT electrode sequences at least partially defines a branch 208 and / or a junction 202 of the atomic object confinement device 200. In some embodiments, each of the TT electrodes 235 is formed with a substantially coplanar upper surface that is substantially coplanar with an upper surface of the RF track 230.
[0079] In example embodiments, a lateral gap may exist between adjacent and / or neighboring TT electrodes 235. In example embodiments, the lateral gap may be an empty space and / or at least partially filled with a dielectric material to prevent electrical communication between adjacent and / or neighboring electrodes 235. In example embodiments, the lateral gap between adjacent and / or neighboring electrodes 235 may be about 1 μm to 10 μm.
[0080] In an example embodiment, a longitudinal gap exists between the TT electrode sequence 236 and the adjacent and / or neighboring RF track 230. In an example embodiment, the longitudinal gap may be at least partially filled with a dielectric material and / or an insulating material to prevent electrical communication between the TT electrodes 235 of the TT electrode sequence 326 and the RF track 230. In an example embodiment, the longitudinal gap between adjacent and / or neighboring electrodes may be about 1 μm to 10 μm.
[0081] In an example embodiment, a plurality of RF tracks 230 (e.g., a pair) may be formed between the first TT electrode sequence 236.1 and the third TT electrode sequence 236.3, wherein the second TT electrode sequence 236.2 extends between the RF tracks 230 along the longitudinal channel 201. For example, each sequence of TT electrodes 236 of a particular branch 208 may extend in a direction substantially parallel to the corresponding RF track 230 along at least a portion of the length of the particular branch 208. In various embodiments, the upper surface of the TT electrode 235 is substantially coplanar with the upper surface of the RF track 230.
[0082] In various embodiments, a periodic voltage signal (e.g., a voltage signal having a radio frequency period) may be applied to the RF rail 230 to generate an electric field and / or a magnetic field for maintaining the atomic object confined and / or trapped in the atomic object confinement device 200. For example, the RF rail 230 that at least partially defines a particular branch 208 generates an electric pseudopotential that confines and / or traps the atomic object within the particular branch 208 in a direction transverse to the corresponding one-dimensional segment and / or portion of the atomic object confinement device 200. For example, the RF rail 230 is configured to generate a pseudopotential when a periodic voltage signal is applied thereto, the pseudopotential being along the direction defined by Figure 4 The one-dimensional segments shown by the dashed lines in constrain and / or capture atomic objects. For example, the RF nulls along branch 208 define a transmission path along the branch along which the atomic objects can be transmitted along the length of branch 208.
[0083] In various embodiments, the TT electrode 235 is configured to have a control voltage signal applied thereto such that the TT electrode 235 generates a time-varying electric potential field that causes the atomic object to be transmitted along the transmission path of the branch 208 (e.g., along the RF null). For example, the electric field and / or magnetic field generated at least in part by controlling the voltage signal applied to the TT electrode 235 of a particular branch 208 of the TT electrode sequence 236 can trap at least one atomic object in a potential well above the upper surface of the second TT electrode sequence (e.g., 236.2 for branch 208C) and / or the longitudinal gap 201 of the corresponding branch 208C. In addition, the control voltage signal applied to the electrode 235 can cause the atomic object constrained and / or trapped in the potential well and / or longitudinal gap 201 above the upper surface of the second TT electrode sequence 236.2 to traverse a trajectory that substantially follows and / or follows the RF null of the corresponding branch 208C when the atomic object is located within the branch 208C.
[0084] In various embodiments, a TT electrode 235 is also disposed within the junction 202. In various embodiments, the TT electrode 235 disposed near the junction 202 is configured such that when a control voltage signal is applied to the TT electrode 235 near the junction 202, the TT electrode 235 generates an electric field and / or a magnetic field configured to cause an atomic object to be transported through the junction 202 along a transport path.
[0085] In various embodiments, the control voltage signal applied to the TT electrode 235 and the periodic voltage signal applied to the RF rail 230 are provided by one or more connected devices (e.g., Figure 5 The controller 30 shown in the figure is controlled via leads. For example, the controller 30 can control the voltage source 50 and / or other voltage drivers so that the voltage source 50 and / or the driver apply a control voltage signal to the TT electrode 235 to generate a time-varying potential (e.g., a time-evolving potential) that causes the atomic object captured and / or constrained by the atomic object confinement device 200 to be transported along a specified transport path and / or maintained at a specified position.
[0086] Depending on factors such as the shape and / or size of the charge on at least one atomic object and / or multiple atomic objects of the polyatomic object crystal and / or the combined electric and / or magnetic fields (e.g., generated by applying a periodic voltage signal to the RF rail 230 and applying a control voltage signal to the TT electrode 235), the atomic objects can be stabilized at a specific distance (e.g., about 20 μm to about 200 μm) above the upper surface of the atomic object confinement device 200 (e.g., the coplanar upper surfaces of the TT electrode 235 and the RF rail 230). To further facilitate control of the transport of the atomic objects along a desired trajectory, in various embodiments, the atomic object confinement device 200 can be operated within a cryogenic and / or vacuum chamber capable of cooling the atomic object confinement device to a temperature less than 124 Kelvin (e.g., less than 100 Kelvin, less than 50 Kelvin, less than 10 Kelvin, less than 5 Kelvin, etc.).
[0087] Technical advantages
[0088] Various embodiments provide technical solutions to the technical problem of enabling the execution of (almost and / or approximately) parallel operations in an atomic object confinement device. For example, in various applications, such as using the atomic object confinement device as part of a quantum processor and using atomic objects captured and / or constrained by the atomic object confinement device as qubits of the quantum processor, being able to execute (almost and / or approximately) parallel operations will enable the quantum processor to perform deeper quantum circuits and more complex quantum computations.
[0089] For example, a periodic branch array comprising multiple branches with the same geometry enables global transmission of atomic objects across the array, wherein a small set of common T-electrode control signals are sliced between corresponding TT electrodes of different branches, and each TT electrode of the same type within a branch is manipulated by the same signal as other TT electrodes of the same type in other branches. This enables a significant reduction in the control complexity of the TT electrode operating signals, the number of pins on the chip comprising the atomic object confinement device, vacuum feedthrough (e.g., allowing wires to pass through the interior of a cryogenic and / or vacuum chamber), and the atomic object confinement device system.
[0090] For example, the curved branches of a periodic or quasi-periodic array of atomic object confinement devices enable a manipulation signal emitted along a single beam path to perform operations on multiple atomic objects, wherein the incident manipulation signal propagates substantially parallel to the RF null at some locations along the beam path and propagates substantially perpendicular to the RF null at other locations along the beam path. Therefore, the curved branches of the atomic object confinement devices reduce the number of manipulation sources (e.g., lasers) required to perform various operations. In addition, when an atomic object is positioned along the beam path but the manipulation signal propagating along the beam path is not expected to be incident on the atomic object, the atomic object can be transmitted out of the beam path without the atomic object being transmitted through a junction, which reduces the time required to perform such a transmission operation and subsequently cool the transmitted atomic object.
[0091] Additional technical advantages provided by various embodiments may include: having an operating region along a shared manipulation signal beam path requires fewer manipulation signals - reducing power, cost and complexity. Parallel operation using a shared manipulation signal has been described. In addition to parallel operation, reduced laser power, cost and complexity are additional benefits, even in embodiments that do not perform parallel operation. Another technical advantage provided by various embodiments includes: the atomic object confinement device has both a tangential action region and a perpendicular action region (e.g., a region where gating operations can be performed) along the same beam path, enabling the device to be reconfigured to use axial gating or radial gating and / or both as needed. Axial gating may be preferred for various scenarios due to the low noise voltage source available to the TT electrode relative to the RF track source. Radial gating may be preferred in various scenarios due to the provision of higher frequency motion modes, which can reduce errors and electrical power requirements when the RF track source noise is low enough. Having an atomic object confinement device with these two options enables the quantum computer to be reconfigured so that if a better RF source becomes available, the optimal operating region is used in the future, and if no such low noise RF source is available, axial gating is used.
[0092] Therefore, various embodiments provide technical advantages over conventional two-dimensional atomic object confinement devices and systems including the same.
[0093] Exemplary quantum computer including atomic object confinement device
[0094] As described above, the atomic object confinement device 200 can be part of a quantum processor of a quantum computer. For example, an atomic object captured and / or confined by the atomic object confinement device 200 can be used as a qubit of a quantum processor. The arrangement of multiple branches including curved branches of the atomic object confinement device 200 in a periodic or quasi-periodic array enables the quantum processor to efficiently perform parallel operations. Figure 5A schematic diagram of an example quantum computer system 100 including an atomic object confinement device 200 (e.g., an ion trap) according to example embodiments is provided. In various embodiments, the quantum computer system 100 includes a computing entity 130 and a quantum computer 110. In various embodiments, the quantum computer 110 includes a controller 30 and a quantum processor 115. In various embodiments, the quantum processor 115 includes an atomic object confinement device 200, which is enclosed in a cryostat and / or vacuum chamber 40, one or more voltage sources 50, one or more manipulation sources 60, etc.
[0095] In an example embodiment, the one or more manipulation sources 60 include one or more lasers (e.g., optical lasers, microwave sources, etc.). In various embodiments, the one or more manipulation sources 60 are configured to manipulate and / or cause controlled quantum state evolution of one or more atomic objects within the atomic object confinement device 100. For example, in an example embodiment, wherein the one or more manipulation sources 60 include one or more lasers, the lasers can provide one or more laser beams to the confinement device within the cryogenic and / or vacuum chamber 40. The laser beams can be used to perform various operations (e.g., parallel operations), such as enacting one or more quantum gates, sympathetic cooling, etc. on one or more atomic objects. In various embodiments, the manipulation sources 60 are controlled by corresponding driver controller elements 615 (see Figure 6 )control.
[0096] In various embodiments, the quantum computer 110 includes one or more voltage sources 50. For example, the voltage source 50 may include a plurality of TT voltage drivers and / or voltage sources and / or at least one RF driver and / or voltage source. In an example embodiment, the voltage source 50 may be electrically coupled to a corresponding potential generating element (e.g., TT electrode 235, RF rail 230) of the atomic object confinement device 200. For example, the voltage source 50 is configured to provide a periodic voltage signal to the RF rail 230 and control the voltage signal to the TT electrode 235. In various embodiments, the voltage source 50 is controlled by a corresponding driver controller element 615 of the controller 30.
[0097] In various embodiments, the computing entity 130 is configured to allow a user to provide input to the quantum computer 110 (e.g., via a user interface of the computing entity 130) and to receive, view, etc. output from the quantum computer 110. The computing entity 130 may communicate with the controller 30 of the quantum computer 110 via one or more wired or wireless networks 120 and / or via direct wired and / or wireless communications. In example embodiments, the computing entity 130 may convert, configure, format (etc.) information / data, quantum circuits, quantum computing algorithms, etc. into a computing language, executable instructions, command sets, etc. that the controller 30 may understand and / or implement.
[0098] In various embodiments, the controller 30 is configured to control the voltage source 50, the cryogenic system and / or vacuum system that controls the temperature and pressure within the cryogenic and / or vacuum chamber 40, the manipulation source 60, and / or other systems that control various environmental conditions (e.g., temperature, pressure, etc.) within the cryogenic and / or vacuum chamber 40 and / or are configured to manipulate and / or cause the controlled evolution of the quantum state of one or more atomic objects within the confinement device. For example, the controller 30 can cause the controlled evolution of the quantum state of one or more atomic objects within the confinement device to execute quantum circuits and / or algorithms. In various embodiments, the atomic objects confined within the confinement device are used as qubits of the quantum computer 110. For example, the quantum process 115 can include a plurality of polyatomic object crystals, each polyatomic object crystal including a first atomic object used as a qubit atomic object of a quantum processor and a second atomic object used as an alternating cooling atomic object for cooling the qubit atomic object of the same polyatomic object crystal.
[0099] Exemplary Controller
[0100] In various embodiments, the atomic object confinement device is incorporated into the quantum computer 110. In various embodiments, the quantum computer 110 also includes a controller 30 configured to control various elements of the quantum computer 110. For example, the controller 30 may be configured to control a voltage source 50, a cryogenic system and / or a vacuum system that controls the temperature and pressure within the cryogenic and / or vacuum chamber 40, a manipulation source 60, and / or other systems that control environmental conditions (e.g., temperature, humidity, pressure, etc.) within the cryogenic and / or vacuum chamber 40 and / or are configured to manipulate and / or cause a controlled evolution of the quantum state of one or more atomic objects within the confinement device.
[0101] like Figure 6As shown, in various embodiments, the controller 30 may include various controller elements, including a processing element and / or device 605, a memory 610, a driver controller element 615, a communication interface 620, an analog-to-digital converter element 625, and the like. For example, the processing element and / or device 605 may include a programmable logic device (CPLD), a microprocessor, a co-processing entity, an application-specific instruction set processor (ASIP), an integrated circuit, an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), a programmable logic array (PLA), a hardware accelerator, other processing devices and / or circuits, and / or controllers. The term circuit may refer to a complete hardware embodiment or a combination of hardware and a computer program product. In an example embodiment, the processing element and / or device 605 of the controller 30 includes a clock and / or communicates with a clock. For example, the processing element and / or device 605 is configured to determine how to cause the quantum processor 115 to execute a quantum circuit using parallel (e.g., simultaneous) operations, and then control various aspects of the quantum computer (e.g., by providing instructions to the corresponding driver controller element 615) to cause the quantum processor 115 to execute a quantum circuit using parallel operations.
[0102] For example, memory 610 may include non-transitory memory, such as volatile and / or non-volatile storage devices, such as one or more of the following: hard disk, ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, etc. In various embodiments, memory 610 may store qubit records corresponding to qubits of a quantum computer (e.g., stored in a qubit record data storage device, a qubit record database, a qubit record table, etc.), calibration tables, executable queues, computer program code (e.g., one or more computer languages, a dedicated controller language, etc.), one or more libraries, one or more waveform series and associated metadata, etc. In an example embodiment, execution of at least a portion of the computer program code stored in memory 610 (e.g., by processing element and / or device 605) causes controller 30 to perform one or more steps, operations, processes, procedures, etc. described herein for tracking the phase, position, etc. of atomic objects and / or polyatomic object crystals within an atomic system and causing adjustment of the phase of one or more manipulation sources and / or signals generated thereby.
[0103] In various embodiments, the driver controller element 610 may include one or more drivers and / or controller elements, each of which is configured to control one or more drivers. In various embodiments, the driver controller element 615 may include a driver and / or a driver controller. For example, the driver controller may be configured to cause one or more corresponding drivers to operate according to executable instructions, commands, etc. scheduled and executed by the controller 30 (e.g., by the processing element and / or device 605). In various embodiments, the driver controller element 615 may enable the controller 30 to operate the manipulation source 60. In various embodiments, the driver may be a laser driver; or a vacuum element driver; a driver for controlling the flow of current and / or voltage applied to TT electrodes, RF rails, and / or other electrodes for maintaining and / or controlling the capture potential of an atomic object confinement device and / or causing the transmission of one or more atomic objects; a cryogenic and / or vacuum system component driver, etc. For example, the driver may control and / or include a TT and / or RF voltage driver and / or voltage source 50 that provides voltage and / or electrical signals (e.g., periodic voltage signals and / or control voltage signals) to the TT electrode 235 and / or the RF rail 230. In various embodiments, the controller 30 includes a device for sending and / or receiving signals from one or more optical receiver components, such as a camera, a MEMS camera, a CCD camera, a photodiode, a photomultiplier tube, etc. of an optical collection system configured to capture, detect, measure (etc.) an optical signal generated by an atomic object captured and / or constrained by the atomic object confinement device 200. For example, the controller 30 may include one or more analog-to-digital converter elements 625 configured to receive signals from one or more optical receiver components, a calibration sensor, etc.
[0104] In various embodiments, the controller 30 may include a communication interface 620 for interfacing and / or communicating with the computing entity 10. For example, the controller 30 may include a communication interface 620 for receiving executable instructions, command sets, etc. from the computing entity 130 and providing the computing entity 130 with an output received from the quantum computer 110 (e.g., from an optical collection system) and / or a result of processing the output. In various embodiments, the computing entity 130 and the controller 30 may communicate via a direct wired and / or wireless connection and / or one or more wired and / or wireless networks 120.
[0105] Exemplary Computing Entities
[0106] Figure 7An illustrative schematic representation of an example computing entity 130 that may be used in conjunction with embodiments of the present invention is provided. In various embodiments, computing entity 130 is configured to allow a user to provide input to quantum computer 110 (e.g., via a user interface of computing entity 130) and to receive, display, analyze, etc. output from quantum computer 110.
[0107] like Figure 7As shown, the computing entity 10 may include an antenna 712, a transmitter 704 (e.g., a radio), a receiver 706 (e.g., a radio), and a processing element 708 that provides signals to the transmitter 704 and the receiver 706 and receives signals from the transmitter 704 and the receiver 706, respectively. The signals provided to the transmitter 704 and the receiver 706 and received from the transmitter 704 and the receiver 706, respectively, may include signaling information / data according to the air interface standard of the applicable wireless system to communicate with various entities such as the controller 30, other computing entities 130, etc. In this regard, the computing entity 130 is capable of operating with one or more air interface standards, communication protocols, modulation types, and access types. For example, the computing entity 130 can be configured to receive and / or provide communications using a wired data transmission protocol, such as a fiber distributed data interface (FDDI), a digital subscriber line (DSL), Ethernet, an asynchronous transfer mode (ATM), a frame relay, a cable data service interface specification (DOCSIS), or any other wired transmission protocol. Similarly, the computing entity 130 can be configured to communicate via a wireless external communication network using any of a variety of protocols, such as General Packet Radio Service (GPRS), Universal Mobile Telecommunications System (UMTS), Code Division Multiple Access 2000 (CDMA2000), CDMA2000 1X (1xRTT), Wideband Code Division Multiple Access (WCDMA), Global System for Mobile Communications (GSM), Enhanced Data Rates for GSM Evolution (EDGE), Time Division Synchronous Code Division Multiple Access (TD-SCDMA), Long Term Evolution (LTE), Evolved Universal Terrestrial Radio Access Network (E-UTRAN), Evolution Data Optimized (EVDO), High Speed Packet Access (HSPA), High Speed Downlink Packet Access (HSDPA), IEEE 802.11 (Wi-Fi), Wireless Direct (Wi-Fi Direct), 802.16 (WiMAX), Ultra-Wideband (UWB), Infrared (IR) protocol, Near Field Communication (NFC) protocol, Wibree, Bluetooth protocol, wireless Universal Serial Bus (USB) protocol and / or any other wireless protocol.The computing entity 130 can use such protocols and standards to communicate using the following protocols: Border Gateway Protocol (BGP), Dynamic Host Configuration Protocol (DHCP), Domain Name System (DNS), File Transfer Protocol (FTP), Hypertext Transfer Protocol (HTTP), HTTP over TLS / SSL / Secure, Internet Message Access Protocol (IMAP), Network Time Protocol (NTP), Simple Mail Transfer Protocol (SMTP), Remote Login Protocol (Telnet), Transport Layer Security (TLS), Secure Sockets Layer (SSL), Internet Protocol (IP), Transmission Control Protocol (TCP), User Datagram Protocol (UDP), Datagram Congestion Control Protocol (DCCP), Stream Control Transmission Protocol (SCTP), Hypertext Markup Language (HTML), etc.
[0108] Via these communication standards and protocols, computing entity 130 may communicate with various other entities using concepts such as Unstructured Supplementary Service Message / Data (USSD), Short Message Service (SMS), Multimedia Message Service (MMS), Dual Tone Multi-Frequency Signaling (DTMF), and / or Subscriber Identity Module Dialer (SIM Dialer). For example, computing entity 130 may also download changes, add-ons, and updates to its firmware, software (e.g., including executable instructions, applications, program modules), and operating system.
[0109] The computing entity 130 may also include user interface devices including one or more user input / output interfaces (e.g., a display 716 and / or a speaker / speaker driver coupled to the processing element 708 and a touch screen, keyboard, mouse, and / or microphone coupled to the processing element 708). For example, the user output interface may be configured to provide an application, browser, user interface, interface, dashboard, screen, web page, page, and / or similar words used herein, interchangeably executed on the computing entity 130 and / or accessible via the computing entity 130 to enable display or audible presentation of information / data and interaction therewith via one or more user input interfaces. The user input interface may include any of a number of devices that allow the computing entity 130 to receive data, such as a keyboard 718 (hard or soft), a touch display, a voice / speech or motion interface, a scanner, a reader, or other input device. In embodiments including keyboard 718, keyboard 718 may include (or cause to be displayed) conventional numbers (0-9) and related keys (#, *) and other keys for operating computing entity 130 and may include a complete set of alphabetic keys or a set of keys that may be activated to provide a complete set of alphanumeric keys. In addition to providing input, the user input interface may also be used, for example, to activate or deactivate certain features, such as a screen saver and / or sleep mode. Through such input, computing entity 130 may collect information / data, user interaction / input, etc.
[0110] The computing entity 130 may also include volatile storage or memory 722 and / or non-volatile storage or memory 724, which may be embedded and / or may be removable. For example, the non-volatile memory may be ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, etc. The volatile memory may be RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, etc. The volatile and non-volatile storage or memory may store databases, database instances, database management system entities, data, applications, programs, program modules, scripts, source code, object code, byte code, compiled code, interpreted code, machine code, executable instructions, etc. to implement the functions of the computing entity 130.
[0111] in conclusion
[0112] Many modifications and other embodiments of the invention set forth herein will occur to those skilled in the art to which the invention pertains having the benefit of the teachings presented in the foregoing description and the associated drawings. Therefore, it should be understood that the invention is not limited to the specific embodiments disclosed, and modifications and other embodiments are intended to be included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.
[0113] The following additional terms are incorporated as part of this specification:
[0114] 1. An atomic object constraint device, comprising:
[0115] a plurality of branches, each branch of the plurality of branches defining a one-dimensional well segment; and
[0116] a plurality of junctions, each of the plurality of junctions connecting at least two of the plurality of branches,
[0117] wherein the plurality of branches and the plurality of junctions are arranged into a periodic or quasi-periodic array of connected one-dimensional well segments, the periodic array or quasi-periodic array comprising one or more minimum array elements, and
[0118] Each of the one or more minimum array elements includes at least one bent branch.
[0119] 2. An atomic object restraint device according to item 1, wherein the at least one curved branch has a first end arranged at a first joint point and a second end arranged at a second joint point, and the length of the at least one curved branch is greater than the straight-line distance between the first joint point and the second joint point.
[0120] 3. The atomic object confinement device according to item 1, wherein each of the plurality of branches is a curved branch.
[0121] 4. An atomic object confinement device according to item 1, wherein the array is configured so that a straight line drawn tangent to a branch of the plurality of branches at a first point is tangent to another branch of the plurality of branches at a period of the array or a subharmonic of the period, and (a) intersects with the remaining branches of the plurality of branches at discrete points, or (b) does not intersect with the remaining branches of the plurality of branches.
[0122] 5. An atomic object confinement device according to item 1, wherein the array is configured so that a straight line is drawn perpendicular to a branch among the plurality of branches and perpendicular to another branch at a period of the array or a subharmonic of the period.
[0123] 6. An atomic object confinement device according to item 1, wherein the array is configured so that a straight line is drawn tangent to a set of branches at a period of the array or a subharmonic of the period, the set of branches forming a row or column, and the straight line does not intersect any branch in the set of branches at any other point along the branch.
[0124] 7. An atomic object constraint device according to item 1, wherein the array is configured so that a straight line drawn tangent to a branch of the plurality of branches, starting from the branch, is not tangent to any other branch of the plurality of branches within a given number of cycles of the array.
[0125] 8. An atomic object confinement device according to item 1, wherein the array is configured so that a straight line drawn perpendicular to a branch of the multiple branches at a certain point, from that branch within a given number of cycles of the array, (a) is neither tangent to any other branch of the multiple branches, nor (b) is perpendicular to a point of another branch of the multiple branches.
[0126] 9. An atomic object constraint device according to item 1, wherein each of the one or more minimum array elements includes at least one straight branch.
[0127] 10. The atomic object constraint device according to item 1, wherein the array is configured so that at least one of the following is satisfied:
[0128] a first straight line drawn tangent to a branch of the plurality of branches at a first point, tangent to a first set of additional branches of the plurality of branches at a period of the array or a subharmonic of the period, and (a) intersecting the remaining branches of the plurality of branches at a discrete point, or (b) not intersecting the remaining branches of the plurality of branches,
[0129] drawing a second straight line perpendicular to the branches and perpendicular to a second set of further branches of the plurality of branches at a period of the array or a subharmonic of the period,
[0130] a third straight line is drawn tangentially to a set of branches at a period of the array or a subharmonic of the period, the set of branches forming a row or a column, and the third straight line does not intersect any branch of the set of branches at any other point along the branch,
[0131] a fourth straight line drawn tangent to the branch is not tangent to any other of the plurality of branches within a given number of periods of the array from the branch, or
[0132] A fifth straight line drawn perpendicular to the branch at a point from the branch is neither (a) tangential to any other branch of the plurality of branches nor (b) perpendicular to a point of another branch of the plurality of branches within a given number of cycles of the array.
[0133] 11. A quantum computer comprising:
[0134] a controller configured to cause one or more voltage signals to be applied to respective electrodes of an atomic object confinement device; and the atomic object confinement device comprising:
[0135] a plurality of branches, each branch of the plurality of branches defining a one-dimensional well segment; and
[0136] a plurality of junctions, each of the plurality of junctions connecting at least two of the plurality of branches,
[0137] wherein the plurality of branches and the plurality of junctions are arranged into a periodic or quasi-periodic array of connected one-dimensional well segments, the periodic array or quasi-periodic array comprising one or more minimum array elements, and
[0138] Each of the one or more minimum array elements includes at least one bent branch.
[0139] 12. The quantum computer according to item 11, wherein the controller is configured to perform parallel operations on the atomic objects constrained by the atomic object constraining device.
[0140] 13. A quantum computer according to item 12, wherein the parallel operation comprises a first parallel operation performed in a first minimum array element among the one or more minimum array elements and a second parallel operation performed in a second minimum array element among the one or more minimum array elements, the first parallel operation and the second parallel operation being performed by one or more manipulation signals propagating along the same beam path.
[0141] 14. The quantum computer according to item 13 further comprises one or more manipulation sources, wherein the one or more manipulation sources are configured to be controlled by the controller to generate the one or more manipulation signals.
[0142] 15. A quantum computer according to item 11, wherein the at least one curved branch has a first end arranged at a first junction and a second end arranged at a second junction, and the length of the at least one curved branch is greater than the straight-line distance between the first junction and the second junction.
[0143] 16. A quantum computer according to item 11, wherein each of the plurality of branches is a curved branch.
[0144] 17. The quantum computer according to item 11, wherein each of the one or more minimum array elements comprises at least one straight branch.
[0145] 18. The quantum computer according to item 11, wherein the array is configured so that at least one of the following is satisfied:
[0146] a first straight line drawn tangent to a branch of the plurality of branches at a first point, tangent to a first set of additional branches of the plurality of branches at a period of the array or a subharmonic of the period, and (a) intersecting the remaining branches of the plurality of branches at a discrete point, or (b) not intersecting the remaining branches of the plurality of branches,
[0147] drawing a second straight line perpendicular to the branches and perpendicular to a second set of further branches of the plurality of branches at a period of the array or a subharmonic of the period,
[0148] a third straight line is drawn tangentially to a set of branches at a period of the array or a subharmonic of the period, the set of branches forming a row or a column, and the third straight line does not intersect any branch of the set of branches at any other point along the branch,
[0149] a fourth straight line drawn tangent to the branch is not tangent to any other of the plurality of branches within a given number of periods of the array from the branch, or
[0150] A fifth straight line drawn perpendicular to the branch at a point from the branch is neither (a) tangential to any other branch of the plurality of branches nor (b) perpendicular to a point of another branch of the plurality of branches within a given number of cycles of the array.
[0151] 19. The quantum computer according to item 11 further comprises at least one voltage source, wherein the at least one voltage source is configured to be controlled by the controller to generate the one or more voltage signals.
[0152] 20. A multidimensional atomic object constraint device, comprising:
[0153] A plurality of branches are arranged in a multi-dimensional periodic array, wherein the plurality of branches include bent branches, and the bent branches are respectively arranged according to the period of the periodic array.
Claims
1. An atomic object constraint device, comprising: a plurality of branches, each branch of the plurality of branches defining a one-dimensional well segment; as well as a plurality of junctions, each of the plurality of junctions connecting at least two of the plurality of branches, wherein the plurality of branches and the plurality of junctions are arranged into a periodic or quasi-periodic array of connected one-dimensional well segments, the periodic array or quasi-periodic array comprising one or more minimum array elements, wherein the quasi-periodic array is an array whose period is disturbed by global distortion, and wherein each of the one or more minimum array elements comprises at least one curved branch, Therein, the array is configured such that a straight line drawn perpendicular to a branch of the plurality of branches is also perpendicular to another branch at a period of the array or a subharmonic of the period.
2. The atomic object constraint device according to claim 1, wherein: The at least one curved branch has a first end disposed at a first junction and a second end disposed at a second junction, and a length of the at least one curved branch is greater than a linear distance between the first junction and the second junction.
3. The atomic object constraint device according to claim 1, wherein: Each branch of the plurality of branches is a curved branch.
4. The atomic object constraint device according to claim 1, wherein: The array is configured such that a straight line drawn tangent to a branch of the plurality of branches at a first point is tangent to another branch of the plurality of branches at a period of the array or a subharmonic of the period and (a) intersects the remaining branches of the plurality of branches at discrete points or (b) does not intersect the remaining branches of the plurality of branches.
5. The atomic object confinement device according to claim 1, wherein: The array is configured such that a straight line is drawn tangential to a set of branches at a period of the array or a subharmonic of the period, the set of branches forming a row or column, and the straight line does not intersect any branch of the set of branches at any other point along the branch.
6. The atomic object confinement device according to claim 1, wherein: The array is configured such that a straight line drawn tangentially to a branch of the plurality of branches, from that branch, is not tangential to any other branch of the plurality of branches within a given number of periods of the array.
7. The atomic object confinement device according to claim 1, wherein: The array is configured such that a straight line drawn perpendicular to a branch of the plurality of branches at a point, from that branch, within a given number of cycles of the array, is neither (a) tangential to any other branch of the plurality of branches nor (b) perpendicular to a point of another branch of the plurality of branches.
8. The atomic object confinement device according to claim 1, wherein: Each minimum array element of the one or more minimum array elements includes at least one straight branch.
9. The atomic object confinement device according to claim 1, wherein: The array is configured such that at least two of the following are satisfied: a first straight line drawn tangent to a branch of the plurality of branches at a first point, tangent to a first set of additional branches of the plurality of branches at a period of the array or a subharmonic of the period, and (a) intersecting the remaining branches of the plurality of branches at a discrete point, or (b) not intersecting the remaining branches of the plurality of branches; drawing a third straight line tangential to a group of branches at a period of the array or a subharmonic of the period, the group of branches forming a row or a column, and the third straight line does not intersect any branch of the group of branches at any other point along the branch; a fourth straight line drawn tangentially to the branch is not tangential to any other branch of the plurality of branches within a given number of periods of the array from the branch; or A fifth straight line drawn perpendicular to the branch at a point from the branch is neither (a) tangential to any other branch of the plurality of branches nor (b) perpendicular to a point of another branch of the plurality of branches within a given number of cycles of the array.