Frequency selected shelving in low quantization fields using microwave dressing fields

Abstract

A controller causes performance of a shelving operation by causing, at an initial time, a dressing field source to provide a dressing field characterized by a dressing field frequency that is detuned from a transition frequency corresponding to a transition between a qubit state and a shelving state of the quantum object. The controller causes a magnetic field source to provide an oscillating magnetic field oscillating with a magnetic field frequency that corresponds to a first dressed frequency. The controller causes the magnetic field source to stop providing the oscillating magnetic field; and at a final time, the dressing field source to stop providing the dressing field. At the final time, at least one of a population of the qubit state at the initial time has been transferred to the shelving state or a population of the shelving state at the initial time has been transferred to the qubit state.

Description

FREQUENCY SELECTED SHELVING IN LOW QUANTIZATION FIELDS USINGMICROWAVE DRESSING FIELDSCROSS-REFERENCE TO RELATED APPLICATION(S)

[0001] This application claims priority to U.S. Application No. 19 / 075,176, filed March 10, 2025, and U.S. Application No. 63 / 635,228, filed April 17, 2024, the contents of which are incorporated herein by reference in their entireties.TECHNICAL FIELD

[0002] Various embodiments relate to shelving quantum objects from a first subset of quantum states into a second subset of quantum states. For example, various embodiments relate to shelving quantum objects using microwave dressing fields to enable frequency- selected shelving when degenerate transitions between the first subset of quantum states and the second subset of quantum states are present.BACKGROUND

[0003] In various scenarios, it is desirable to shelf quantum objects. For example, confined quantum objects may be shelved from a first subset of quantum states (e.g., possibly a magnetic field insensitive subset of states) into a second subset of quantum sates (e.g., possibly a magnetic field sensitive subset of states) for performance of a magnetic field mediated interactions. In another example, a confined quantum object may be shelved during performance of a state detection or measurement operation. Through applied effort, ingenuity, and innovation many deficiencies of conventional shelving techniques have been solved by developing solutions that are structured in accordance with the embodiments of the present invention, many examples of which are described in detail herein.BRIEF SUMMARY OF EXAMPLE EMBODIMENTS

[0004] Example embodiments provide methods, systems, apparatuses, computer program products and / or the like for performing shelving operations. During a shelving operation a quantum object is transitioned from a first sub-space of the energy space of the quantum object into a second sub-space of the energy space of the quantum object. For example, the first sub-space may be a qubit sub-space comprising magnetic field insensitive states (e.g., clock states) and the second sub-space may comprise magnetic field sensitive states. In various embodiments, the shelving transition (e.g., from the first sub-space to the second sub-space) or a deshelving transition (e.g., from the second sub-space to the first sub-space) is performed in a frequency-selected manner using a dressing field.

[0005] In various embodiments, a dressing field is applied to quantum object such that various dressed states of the quantum object are formed. The dressed states include a first dressed state that is a superposition of a first state of the first sub-space and a first state of the second sub-space. A transition between the first state of the first sub-space and the first state of the second sub-space is driven, while the dressing field is begin applied to the quantum object, by application of an oscillating magnetic field that oscillates with a magnetic field frequency that corresponds to a frequency characteristic of the first dressed state.

[0006] In an example embodiment, a controller is configured to control operation of a confinement apparatus configured to confine one or more quantum objects, one or more dressing field sources configured to generate and provide respective dressing fields, and one or more magnetic field sources configured to generate and provide respective oscillating magnetic fields to cause performance of a shelving operation on at least one of the one or more quantum objects. To perform the shelving operation, the controller causes, at an initial time, a dressing field source to start to provide a dressing field characterized by a dressing frequency and an amplitude. The frequency is detuned by a detuning from a transition frequency corresponding to a first transition between a first state of the first sub-space of the quantum object and a first state of the second sub-space of the quantum object. The dressing field is polarized in a first direction and is caused to be incident on the quantum object. The controller further causes a magnetic field source to start to provide an oscillating magnetic field in a second direction. The second direction is orthogonal to the first direction. The oscillating magnetic field oscillates with a magnetic field frequency that corresponds to a first dressed state frequency. The controller further causes the magnetic field source to stop providing the oscillating magnetic field; and, at a final time, the dressing field source to stop providing the dressing field. At the final time, at least one of a population of the first qubit state at the initial time has been transferred to the first shelving state or a population of the first shelving state at the initial time has been transferred to the first qubit state.

[0007] According to one aspect, method of performing a shelving or deshelving operation is provided. In an example embodiment, the method is performed by a controller of an atomic system or a quantum system and includes causing a dressing field source to start to provide a dressing field characterized by a dressing field frequency and a dressing field amplitude. The dressing field frequency is detuned by a detuning from a transition frequency corresponding to both (a) a first transition between a first qubit state of a quantum object and a first shelvingstate of the quantum object and (b) a second transition between a second qubit state of the quantum object and a second shelving state of the quantum object. The dressing field is polarized in a first direction, and the dressing field is caused to be incident on the quantum object. The method further includes causing a magnetic field source to start to provide an oscillating magnetic field in a second direction. The second direction is orthogonal to the first direction. The oscillating magnetic field oscillates with a magnetic field frequency. The magnetic field frequency corresponds to one of a first dressed frequency or a second dressed frequency. The method further includes causing the magnetic field source to stop providing the oscillating magnetic field; and causing the dressing field source to stop providing the dressing field. The dressing field being incident on the quantum object causes (a) the first qubit state and the first shelving state to form a first pair of dressed states and (b) the second qubit state and the second shelving state to form a second pair of dressed states. The first dressed frequency corresponds to the first pair of dressed states and the second dressed state frequency corresponds to the second pair of dressed states. When the magnetic field frequency corresponds to the first dressed frequency, at least one of a population of the first qubit state is transferred to the first shelving state or a population of the first shelving state is transferred to the first qubit state. When the magnetic frequency corresponds to the second dressed frequency, at least one of a population of the second qubit state is transferred to the second shelving state or a population of the second shelving state is transferred to the second qubit state.

[0008] In an example embodiment, the first dressed frequency is not equal to the second dressed frequency or a harmonic thereof.

[0009] According to another aspect, another method for performing a shelving operation is provided. In an example embodiment, the method is performed by a controller configured to control operation of at least a dressing field source and a magnetic field source. In an example embodiment, the method includes causing, at an initial time, a dressing field source to start to provide a dressing field characterized by a dressing field frequency and a dressing field amplitude. The dressing field frequency is detuned by a detuning from a transition frequency corresponding to a transition between a selected qubit state of a quantum object and a selected shelving state of the quantum object. The dressing field is polarized in a first direction, and the dressing field is caused to be incident on the quantum object. The method further includes causing a magnetic field source to start to provide an oscillating magnetic field in a second direction. The second direction is orthogonal to the first direction. The oscillating magnetic field oscillates with a magnetic field frequency that corresponds to adressed frequency. The method further includes causing the magnetic field source to stop providing the oscillating magnetic field; and causing, at a final time, the dressing field source to stop providing the dressing field. At the final time, at least one of a population of the selected qubit state at the initial time has been transferred to the selected shelving state or a population of the selected shelving state at the initial time has been transferred to the selected qubit state.

[0010] In an example embodiment, at least one of starting to provide the dressing field or stopping providing the dressing field is done adiabatically.

[0011] In an example embodiment, the dressing field being incident on the quantum object causes the selected qubit state and the selected shelving state to from a pair of dressed state and the dressing frequency is corresponds to a frequency difference between dressed states of the pair of dressed states.

[0012] In an example embodiment, starting to provide the dressing field adiabatically comprises causing the dressing field amplitude to increase from a minimum dressing field amplitude to a maximum dressing field amplitude over a time period that is longer than at least one of (a) one divided by the detuning or (b) one divided by the dressed state frequency, and stopping providing the dressing field adiabatically comprises causing the dressing field amplitude to decrease from the maximum dressing field amplitude to the minimum dressing field amplitude over a time period that is longer than at least one of (a) one divided by the detuning or (b) one divided by the dressed state frequency.

[0013] In an example embodiment, starting to provide the oscillating magnetic field comprises smoothly increasing a magnetic field envelope amplitude of an envelope of the oscillating magnetic field from a minimum magnetic field envelope amplitude to a maximum magnetic field envelop amplitude and stopping providing the oscillating magnetic field comprises smoothly decreasing the magnetic field envelope amplitude from the maximum magnetic field envelope amplitude to the minimum magnetic field envelope amplitude.

[0014] In an example embodiment, the magnetic field envelope amplitude is increased from the minimum magnetic field envelope amplitude to the maximum magnetic field envelope amplitude adiabatically and the magnetic field envelope amplitude is decreased from the maximum magnetic field envelope amplitude to the minimum magnetic field envelope amplitude adiabatically.

[0015] In an example embodiment, the quantum object is confined by a confinement apparatus and the confinement apparatus defines a plane, the first direction being parallel to the plane.

[0016] In an example embodiment, the dressed frequency corresponds to a Rabi frequency of the transition between the qubit state and the shelving state.

[0017] In an example embodiment, the dressed frequency is substantially equal to the square root of the sum of the Rabi frequency of the transition between the qubit state and the shelving state squared and the detuning squared.

[0018] In an example embodiment, the second direction is a quantization direction used to define the qubit state and the shelving state.

[0019] In an example embodiment, the method further includes performing one or more shelved operations on at least one of the quantum object or another quantum object, wherein the quantum object and the other quantum object are both confined by a confinement apparatus, and performing a deshelving operation on the quantum object.

[0020] In an example embodiment, performing the deshelving operation on the quantum object comprises causing the dressing field source to start to provide the dressing field; causing the magnetic field source to start to provide the oscillating magnetic field in the second direction; causing the magnetic field source to stop providing the oscillating magnetic field; and causing the dressing field source to stop providing the dressing field, such that at least one of (a) the population of the first qubit state is transferred to the first shelving state or (b) the population of the first shelving state is transferred to the first qubit state.

[0021] According to another aspect, a system is provided. In an example embodiment, the system comprises a confinement apparatus configured to confine one or more quantum objects at one or more target locations; a dressing field source configured to generate and provide a dressing field polarized in a first direction at a respective target location of the one or more target locations; a magnetic field source configured to generate and provide an oscillating magnetic field in a second direction at the respective target location, the first direction being orthogonal to the second direction; and a controller configured to control operation of the confinement apparatus, the dressing field source, and the magnetic field source. The controller is configured to cause, at an initial time, a dressing field source to start to provide a dressing field characterized by a dressing field frequency and a dressing field amplitude. The dressing field frequency is detuned by a detuning from a transition frequency corresponding to a transition between a qubit state of a quantum object and a shelving state of the quantum object. The dressing field is polarized in a first direction, and the dressing field is caused to be incident on the quantum object. The controller is further configured to cause a magnetic field source to start to provide an oscillating magnetic field in a second direction. The second direction being orthogonal to the first direction. The oscillating magnetic fieldoscillating with a magnetic field frequency that corresponds to a dressed frequency. The controller is further configured to cause the magnetic field source to stop providing the oscillating magnetic field; and cause, at a final time, the dressing field source to stop providing the dressing field. At the final time, at least one of a population of the qubit state at the initial time has been transferred to the shelving state or a population of the shelving state at the initial time has been transferred to the qubit state.

[0022] In an example embodiment, at least one of starting to provide the dressing field or stopping providing the dressing field is done adiabatically.

[0023] In an example embodiment, the dressing field being incident on the quantum object causes the selected qubit state and the selected shelving state to from a pair of dressed state and the dressing frequency is corresponds to a frequency difference between dressed states of the pair of dressed states.

[0024] In an example embodiment, starting to provide the dressing field adiabatically comprises causing the dressing field amplitude to increase from a minimum dressing field amplitude to a maximum dressing field amplitude over a time period that is longer than at least one of (a) one divided by the detuning or (b) one divided by the dressed state frequency, and stopping providing the dressing field adiabatically comprises causing the dressing field amplitude to decrease from the maximum dressing field amplitude to the minimum dressing field amplitude over a time period that is longer than at least one of (a) one divided by the detuning or (b) one divided by the dressed state frequency.

[0025] In an example embodiment, starting to provide the oscillating magnetic field comprises smoothly increasing a magnetic field envelope amplitude of an envelope of the oscillating magnetic field from a minimum magnetic field envelope amplitude to a maximum magnetic field envelop amplitude and stopping providing the oscillating magnetic field comprises smoothly decreasing the magnetic field envelope amplitude from the maximum magnetic field envelope amplitude to the minimum magnetic field envelope amplitude.

[0026] In an example embodiment, the magnetic field envelope amplitude is increased from the minimum magnetic field envelope amplitude to the maximum magnetic field envelope amplitude adiabatically and the magnetic field envelope amplitude is decreased from the maximum magnetic field envelope amplitude to the minimum magnetic field envelope amplitude adiabatically.

[0027] In an example embodiment, the quantum object is confined by a confinement apparatus and the confinement apparatus defines a plane, the first direction being parallel to the plane.

[0028] In an example embodiment, the dressed frequency corresponds to a Rabi frequency of the transition between the qubit state and the shelving state.

[0029] In an example embodiment, the dressed frequency is substantially equal to the square root of the sum of the Rabi frequency of the transition between the qubit state and the shelving state squared and the detuning squared.

[0030] In an example embodiment, the second direction is a quantization direction used to define the qubit state and the shelving state.

[0031] In an example embodiment, the controller is further configured to cause performance of one or more shelved operations on at least one of the quantum object or another quantum object, wherein the quantum object and the other quantum object are both confined by a confinement apparatus, and performing a deshelving operation on the quantum object.

[0032] In an example embodiment, performing the deshelving operation on the quantum object comprises causing the dressing field source to start to provide the dressing field; causing the magnetic field source to start to provide the oscillating magnetic field in the second direction; causing the magnetic field source to stop providing the oscillating magnetic field; and causing the dressing field source to stop providing the dressing field, such that at least one of (a) the population of the first qubit state is transferred to the first shelving state or (b) the population of the first shelving state is transferred to the first qubit state.

[0033] According to another aspect, a controller is provided. In an example embodiment, the controller comprises at least one processing device and at least one non-transitory memory storing computer-executable instructions. The memory and computer-executable instructions are configured to, when executed by the at least one processing device, to cause the controller to perform at least causing, at an initial time, a dressing field source to start to provide a dressing field characterized by a dressing field frequency and a dressing field amplitude. The dressing field frequency is detuned by a detuning from a transition frequency corresponding to a transition between a selected qubit state of a quantum object and a selected shelving state of the quantum object. The dressing field is polarized in a first direction, and the dressing field is caused to be incident on the quantum object. The memory and computer-executable instructions are further configured to, when executed by the at least one processing device, to cause the controller to perform at least causing a magnetic field source to start to provide an oscillating magnetic field in a second direction. The second direction is orthogonal to the first direction. The oscillating magnetic field oscillates with a magnetic field frequency that corresponds to a dressed frequency. The memory andcomputer-executable instructions are further configured to, when executed by the at least one processing device, to cause the controller to perform at least causing the magnetic field source to stop providing the oscillating magnetic field; and causing, at a final time, the dressing field source to stop providing the dressing field. At the final time, at least one of a population of the selected qubit state at the initial time has been transferred to the selected shelving state or a population of the selected shelving state at the initial time has been transferred to the selected qubit state.

[0034] According to another aspect a computer program product is provided. In an example embodiment, the computer program product comprises at least one non-transitory memory storing computer-executable instructions. The computer-executable instructions are configured to, when executed by a processing device of a controller configured to control operation of a confinement apparatus and one or more manipulation sources, cause the controller to perform causing, at an initial time, a dressing field source to start to provide a dressing field characterized by a dressing field frequency and a dressing field amplitude. The dressing field frequency is detuned by a detuning from a transition frequency corresponding to a transition between a selected qubit state of a quantum object and a selected shelving state of the quantum object. The dressing field is polarized in a first direction, and the dressing field is caused to be incident on the quantum object. The computer-executable instructions are further configured to, when executed by the processing device, cause the controller to perform causing a magnetic field source to start to provide an oscillating magnetic field in a second direction. The second direction is orthogonal to the first direction. The oscillating magnetic field oscillates with a magnetic field frequency that corresponds to a dressed frequency. The computer-executable instructions are further configured to, when executed by the processing device, cause the controller to perform causing the magnetic field source to stop providing the oscillating magnetic field; and causing, at a final time, the dressing field source to stop providing the dressing field. At the final time, at least one of a population of the selected qubit state at the initial time has been transferred to the selected shelving state or a population of the selected shelving state at the initial time has been transferred to the selected qubit state.BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

[0035] Having thus described the invention in general terms, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale, and wherein:

[0036] Figure 1 provides block diagram of an example quantum computing system, in accordance with an example embodiment.

[0037] Figure 2 provides a partial energy space diagram of an example quantum object, in accordance with an example embodiment.

[0038] Figure 3 provides a plot illustrating the time evolution of the respective amplitudes of the dressing field and the envelope of the oscillating magnetic field used to perform a shelving or deshelving operation, in accordance with an example embodiment.

[0039] Figure 4 provides a schematic diagram of an example controller of a quantum computer comprising a confinement apparatus configured for confining quantum objects therein, in accordance with an example embodiment.

[0040] Figure 5 provides a flowchart illustrating various processes and / or procedures performed by a controller to cause an atomic system and / or quantum computer to perform a shelving operation, in accordance with an example embodiment.

[0041] Figure 6 provides a schematic diagram of an example computing entity of a quantum computer system that may be used in accordance with an example embodiment.DETAILED DESCRIPTION OF SOME EXAMPLE EMBODIMENTS

[0042] The present invention now will be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the invention are shown. Indeed, the invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. The term “or” (also denoted “ / ”) is used herein in both the alternative and conjunctive sense, unless otherwise indicated. The terms “illustrative” and “exemplary” are used to be examples with no indication of quality level. The terms “generally” and “approximately” refer to within applicable engineering and / or manufacturing tolerances and / or within user measurement capabilities, unless otherwise indicated. Like numbers refer to like elements throughout.

[0043] In various scenarios, quantum objects are confined by a confinement apparatus. In various embodiments, the quantum objects are ions, atoms, ionic or neutral molecules, multipolar molecules, quantum dots, and / or other confined quantum particles and the confinement apparatus is an ion trap, such as a surface ion trap, Paul ion trap, optical trap, magnetic trap, and / or other apparatus configured for confining quantum objects.

[0044] In various embodiments, the internal structure of the quantum objects confined by the confinement apparatus define respective energy spaces. For example, the energy space ofa quantum object may be defined, at least in part by hyperfine splitting in the case of a quantum object being an ion with a non-zero nuclear spin. A first sub-space and a second sub-space may be defined within the energy space of the quantum object. For example, the first sub-space may be defined to include a pair of states with an energy splitting therebetween that is insensitive to magnetic fields (e.g., clock states), which are referred to herein as magnetic field insensitive states. The second sub-space may be defined to include a pair of states with an energy splitting therebetween that is sensitive to magnetic fields, which are referred to herein as magnetic field sensitive states. For example, in some embodiments, the quantum objects may be moved between the magnetic field insensitive states of the first sub-space and the magnetic field sensitive states of the second sub-space for performance of various operations of the system.

[0045] In an example embodiment where the quantum objects are used as qubits of a quantum computer, the first sub-space may be a qubit sub-space with the states therein being the qubit states of the qubit. The second sub-space may be a shelving sub-space. For example, the quantum objects may be shelved to the second sub-space that includes magnetic field sensitive states for performance of a quantum logic gate (e.g., single-qubit gate, two-qubit gate, and / or the like) or other interaction that is caused or mediated by a magnetic field or magnetic field gradient. For example, in an example embodiment, one or more quantum objects may be shelved (or deshelved) in accordance with an example embodiment for performance of a geometric phase gate, as disclosed by U.S. Application No. 63 / 487,076, filed February 27, 2023, the content of which is incorporated herein by reference in its entirety. In various embodiments, the quantum objects may be shelved into the second subspace for performance of a quantum state detection and / or measurement operation.

[0046] In various embodiments, the shelving process includes application of a dressing field to the one or more quantum objects. In various embodiments, the dressing field is a microwave signal (e.g., an electromagnetic signal characterized by a microwave frequency). In an example embodiment, the dressing field source is similar to the dressing field source disclosed in U.S. Application No. 63 / 581,017, filed September 7, 2023, the content of which is incorporated herein by reference in its entirety. While the dressing field is being applied to the quantum object such that a first dressed state and a second dressed state of the quantum object are formed, an oscillating magnetic field is applied to the quantum object. The oscillating magnetic field drives the shelving (or deshelving) operation. In various embodiments, the dressing field and / or the oscillating magnetic field are turned on and / or turned off adiabatically.

[0047] In various scenarios, the energy space of a quantum object includes a first subspace of quantum states and a second sub-space of quantum states where multiple transitions between respective first sub-space of states and respective second sub-space states are degenerate. For example, a first transition between a first state of the first sub-space of states (also referred to as a first qubit state herein) and a first state of the second sub-space of states (also referred to as a first shelving state herein) may be degenerate with (e.g., correspond to substantially the same energy change and / or transition frequency as) a second transition between a second state of the first sub-space of states (also referred to as a second qubit state herein) and a second state of the second sub-space of states (also referred to as a second shelving state herein). Conventional shelving / deshelving techniques include applying a laser beam to a quantum object to shelve or deshelve the quantum object using, for example, a Rabi flop. The frequency of the laser beam is used to control which transition of the quantum object is driven. However, since the first transition and the second transition are degenerate (e.g., correspond to substantially the same transition frequency), attempting to perform the first transition to shelve quantum objects from the first qubit state to the first shelving state will also drive the second transition, which may not be desired. Moreover, since the Rabi frequencies of the first transition and the second transition are different, the first transition and second transition cannot be driven simultaneously with high fidelity.

[0048] For example, an example quantum object has a first sub-space including qubit states F = 1, m = 0 and F = 2, m = 0, and a second sub-space including states F = 2, m = 1 and F = 1, m = 1. It may be desired to shelve the F = 1, m = 0 qubit state to the F = 2, m = 1 shelving state and the F = 2, m = 0 qubit state to the F = 1, m = 1 shelving state. However, the frequency difference between the F = 1, m = 0 qubit state and the F = 2, m = 1 shelving state is sufficiently similar to the frequency difference between the F = 2, m = 0 qubit state and the F = 1, m = 1 shelving state that both of the transitions are simultaneously driven with a single laser or microwave tone. The length of time for which the single laser or microwave tone is applied to cause a near 100% population inversion via the Rabi flop is the inverse of the Rabi frequency of the transition. However, the Rabi frequencies of the two transitions are different by a factor of an irrational number. Therefore, the shelving transitions cannot be performed with near 100% probability for both pairs of states. Thus, the probability of performing a complete shelving of both qubit states is not high enough for the performance of high-fidelity quantum logic gate, for example. Moreover, it may be desired to drive only one of the first transition or the second transition, but due to the degeneracy of the two transitions, attempting to drive the first transition results in the driving of the second transition, and viceversa. As such, technical problems exist regarding the shelving and deshelving of quantum objects.

[0049] Various embodiments provide technical solutions to these technical problems. For example, a dressing field is applied to a quantum object to be shelved. The dressing field is characterized by a dressing field frequency that is detuned from the first transition frequency corresponding to a transition from the first qubit state to the first shelving state (or vice versa) and from the second transition frequency corresponding to a transition from the second qubit state to the second shelving state (or vice versa). Notably the first transition frequency and the second transition frequency are approximately equal. The application of the dressing field to the quantum object causes formation of a first pair dressed states, which are dressed states that are superpositions of the first qubit state and the first shelving state, and a second pair dressed states, which are dressed states that are superpositions of the second qubit state and the second shelving state.

[0050] The first pair of dressed state corresponds to a first dressed frequency and the second pair of dressed state corresponds to a second dressed frequency. For example, in various embodiments, the first dressed frequency is parameterized by and / or a function of the Rabi frequency of the transition between the first qubit state and the first shelving state. In various embodiments, the second dressed frequency is parameterized by and / or a function of the Rabi frequency of the transition between the second qubit state and the second shelving state. As the Rabi frequency of the transition between the first qubit state and the first shelving state is not equal to the Rabi frequency of the transition between the second qubit state and the second shelving state, the first dressed frequency is not equal to the second dressed frequency.

[0051] A magnetic field is applied to the quantum object that oscillates at a magnetic field frequency. When it is desired to drive the first transition between the first qubit state and the first shelving state, the magnetic field frequency is set and / or selected to be substantially equal to the first dressed frequency. When it is desired to drive the second transition between the second qubit state and the second shelving state, the magnetic field frequency is set and / or selected to be substantially equal to the second dressed frequency.

[0052] After a period of time, the oscillating magnetic field may be turned off and the dressing field may be turned off such that they are no longer applied to the quantum object. When the quantum object is no longer experiencing the dressing field, the dressed states return to their constituent states. However, when the magnetic field frequency is substantially equal to the first dressed frequency, when the quantum object is no longer experiencing thedressing field, the initial population of the first qubit state has been transferred to the first shelving state and the initial population of the first shelving state has been transferred to the first qubit state. When the magnetic field frequency is substantially equal to the second dressed frequency, when the quantum object is no longer experiencing the dressing field, the initial population of the second qubit state has been transferred to the second shelving state and the initial population of the second shelving state has been transferred to the second qubit state.

[0053] Therefore, various embodiments enable frequency-selected shelving and / or deshelving in a situation in which conventional shelving techniques would drive multiple transitions. Thus, embodiments provide technical improvements and technical advantages to the fields of quantum object shelving (and / or deshelving) and atomic systems and / or quantum computers that use shelving (and / or deshelving) operations.Exemplary Quantum Computer Comprising a Confinement Apparatus

[0054] Various embodiments provide atomic systems and / or quantum computers (e.g., quantum charge-coupled device (QCCD)-based quantum computers) that are configured for performing shelving (and / or deshelving) operations in accordance with various embodiments. Figure 1 provides a schematic diagram of an example quantum computer system 100 configured to perform shelving (and / or deshelving) operations in accordance with various embodiments.

[0055] In the illustrated embodiment, the quantum computer system 100 includes a confinement apparatus 120 (e.g., an ion trap) configured to confine one or more quantum objects. In various embodiments, the quantum computer system 100 comprises a classical (e.g., semiconductor-based) computing entity 10 and a quantum computer 110. In various embodiments, the quantum computer 110 comprises a controller 30, a cryostat and / or vacuum chamber 40 enclosing a confinement apparatus 120, one or more manipulation sources 64 (e.g., 64A, 64B, 64C, 64D, 64E), one or more voltage sources 50, one or more magnetic field generators 70 (e.g., 70A, 70B), 72, an optics collection system 80, and / or the like. In various embodiments, the controller 30 is configured to control the operation of (e.g., control one or more drivers configured to cause operation of) the manipulation sources 64, voltage sources 50, magnetic field generators 70, a vacuum system and / or cryogenic cooling system (not shown), and / or the like. In various embodiments, the controller 30 is configured to receive signals (e.g., electrical signals) generated and provided by one or more photodetectors of the optics collection system 80. In an example embodiment, second substrate 122 may be securedinto relationship with the confinement apparatus 120 and house one or more components of the system (e.g., one or more oscillating magnetic field sources 72, one or more dressing field sources 68, one or more manipulation sources 64E, one or more optical components of a beam path system 66 (e.g., 66A, 66B, 66C), one or more components of the optics collection system 80, and / or the like).

[0056] In an example embodiment, the one or more manipulation sources 64 may comprise one or more lasers (e.g., optical lasers, microwave sources and / or masers, and / or the like) or another manipulation source. In the illustrated embodiment, manipulation sources 64A, 64B, 64C are lasers located outside of the cryogenic and / or vacuum chamber and manipulation source 64D is a laser, microwave source, or other signal generator that is integrated with the confinement apparatus 120 or second substrate 122. In an example embodiment, a manipulation source 64D is a microwave dressing field source 68. For example, the integrated microwave dressing field source 68 (e.g., housed by the confinement apparatus 120 and / or the second substrate 122) may be similar to the dressing field source disclosed in U.S. Application No. 63 / 581,017, filed September 7, 2023, the content of which is incorporated herein by reference in its entirety. In an example embodiment, a manipulation source 64E is an oscillating magnetic field source 72. In various embodiments, the one or more manipulation sources 64 are configured to manipulate and / or cause a controlled quantum state evolution of one or more quantum objects confined by the confinement apparatus 120.

[0057] In various embodiments, the confinement apparatus 120 is an ion trap, such as a surface ion trap, Paul ion trap, and / or the like. In various embodiments, the quantum objects are ions, atoms, molecules, and / or the like. For example, the quantum objects define an energy space. A first sub-space is defined within the energy space. In various embodiments, the first sub-space is a qubit or memory sub-space including two qubit states. In various embodiments, the states of the first sub-space (e.g., a first qubit state and a second qubit state) are magnetic field insensitive states (e.g., clock states). A second sub-space is defined with the energy space. In various embodiments, the states of the second sub-space (e.g., a first shelving state and a second shelving state) are magnetic field sensitive states. For example, quantum objects may be shelved from the first sub-space to the second sub-space and / or deshelved from the second sub-space to the first sub-space, in various embodiments.

[0058] In an example embodiment, the one or more manipulation sources 64A, 64B, 64C each provide a manipulation signal (e.g., laser beam, microwave signals, and / or the like) to one or more regions and / or target locations 125 of the confinement apparatus 120 viacorresponding beam path systems 66 (e.g., 66A, 66B, 66C). In various embodiments, at least one beam path system 66 comprises a modulator configured to modulate the manipulation signal being provided to the confinement apparatus 120 via the beam path system 66. In various embodiments, the manipulation sources 64, active components of the beam paths (e.g., modulators, etc.), and / or other components of the quantum computer 110 are controlled by the controller 30.

[0059] In various embodiments, the quantum computer 110 comprises one or more voltage sources 50. For example, the voltage sources may be arbitrary wave generators (AWG), digital analog converters (DACs), and / or other voltage signal generators. For example, the voltage sources 50 may comprise a plurality of control voltage drivers and / or voltage sources and / or at least one RF driver and / or voltage source. The voltage sources 50 may be electrically coupled to the corresponding potential generating elements (e.g., control electrodes and / or RF electrodes) of the confinement apparatus 120, in an example embodiment.

[0060] In various embodiments, the quantum computer 110 comprises one or more magnetic field generators 70 (e.g., 70A, 70B), 72. For example, the magnetic field generator may be an internal magnetic field generator 70A disposed within the cryogenic and / or vacuum chamber 40 and / or an external magnetic field generator 70B disposed outside of the cryogenic and / or vacuum chamber 40. In various embodiments, the oscillating magnetic field sources 72 are housed by the confinement apparatus 120 and / or the second substrate 122 secured into relationship with the confinement apparatus 120. In various embodiments, the magnetic field generators 70 are configured to generate a magnetic field at one or more regions and / or target locations 125 of the confinement apparatus 120 that has a particular magnitude and a particular magnetic field direction (e.g., a quantization direction) in the one or more regions and / or target locations 125 of the confinement apparatus 120. For example, in various embodiments, one or more magnetic field generators 70A, 70B are configured to generate and maintain a quantization field across the confinement apparatus 120 (e.g., at a plurality of region and / or target locations 125 of the confinement apparatus 120) that is substantially spatially uniform across the confinement apparatus 120 and consistent in time (e.g., during operation of the quantum computer 110). In various embodiments, the quantization field is in a low quantization field regime (e.g., greater than 0 Gauss and less 100 Gauss). For example, in various embodiments, the quantization field has an amplitude or magnetic field strength of 2-5 Gauss. In various embodiments, the magnetic field generators 70 comprise permanent magnets, Helmholtz coils, electrical magnets, and / or the like.

[0061] In various embodiments, the quantum computer 110 further includes one or more oscillating magnetic field sources 72 that are configured for generating an oscillating magnetic field at corresponding target locations 125. In an example embodiment, such oscillating magnetic field sources 72 are housed by the confinement apparatus 120 and / or the second substrate 122. For example, the oscillating magnetic field sources 72 may be similar to the quantization field control circuits disclosed in U.S. Application No. 63 / 525,300, filed July 6, 2023, the content of which is incorporated herein by reference in its entirety.

[0062] In various embodiments, the quantum computer 110 comprises an optics collection system 80 configured to collect and / or detect photons (e.g., stimulated emission) generated by quantum objects (e.g., during reading procedures). The optics collection system 80 may comprise one or more optical elements (e.g., lenses, mirrors, waveguides, fiber optics cables, and / or the like) and one or more photodetectors. In various embodiments, the photodetectors may be photodiodes, photomultipliers, charge-coupled device (CCD) sensors, complementary metal oxide semiconductor (CMOS) sensors, Micro-Electro-Mechanical Systems (MEMS) sensors, and / or other photodetectors that are sensitive to light at an expected fluorescence wavelength of the qubits (e.g., quantum objects) of the quantum computer 110. In various embodiments, the detectors may be in electronic communication with the controller 30 via one or more A / D converters 425 (see Figure 4) and / or the like.

[0063] In various embodiments, a computing entity 10 is configured to allow a user to provide input to the quantum computer 110 (e.g., via a user interface of the computing entity 10) and receive, view, and / or the like output from the quantum computer 110. The computing entity 10 may be in communication with the controller 30 of the quantum computer 110 via one or more wired or wireless networks 20 and / or via direct wired and / or wireless communications. In an example embodiment, the computing entity 10 may translate, configure, format, and / or the like information / data, quantum computing algorithms (e.g., quantum circuits), and / or the like into a computing language, executable instructions, command sets, and / or the like that the controller 30 can understand, execute, and / or implement.

[0064] In various embodiments, the controller 30 is configured to control operation of the voltage sources 50, magnetic field generators 70, cryogenic system and / or vacuum system controlling the temperature and pressure within the cryogenic and / or vacuum chamber 40, manipulation sources 64, and / or other systems controlling various environmental conditions (e.g., temperature, pressure, and / or the like) within the cryogenic and / or vacuum chamber 40, configured to manipulate and / or cause a controlled evolution of quantum states of one ormore quantum objects within the confinement apparatus, and / or read and / or detect a quantum (e.g., qubit) state of one or more quantum objects confined by the confinement apparatus. For example, the controller 30 may cause a controlled evolution of quantum states of one or more quantum objects within the confinement apparatus to execute a quantum circuit and / or algorithm. For example, the controller 30 may perform one or more shelving and / or deshelving operations on one or more quantum objects confined by the confinement apparatus at one or more points during the execution of a quantum circuit. In various embodiments, the quantum objects confined by the confinement apparatus are used as qubits of the quantum computer 110.Example Shelving / Deshelving Operation

[0065] Figure 2 illustrates a portion of the energy space 200 of an example quantum object. The illustrated portion of the energy space 200 includes a first manifold 210, which in the illustrated example is the F = 1 manifold of a quantum object that is an ion with a nuclear spin of Vi. The illustrated portion of the energy space 200 also includes a second manifold 220, which in the illustrated example is the F = 2 manifold of the quantum object. For example, in the illustrated portion of the energy space 200, the first manifold 210 consists of the F = 1, m = -1; F = 1, m = 0; and F = 1, m = 1 states and the second manifold 220 consists of the F = 2, m = -2; F = 2, m = -1; F = 2, m = 0; F = 2, m = 1; and F = 2, m = 2 states.

[0066] A first sub-space 230 and a second sub-space 240 are defined within the energy space 200. In an example embodiment, the first sub-space 230 is a qubit space including qubit states. For example, the first and second state of the first sub-space 230 are a first qubit state 232 and a second qubit state 234, in an example embodiment. In various embodiments, the states of the first sub-space 230 are magnetic field insensitive states (e.g., clock states at a low quantization field). For example, the energy and / or frequencies of the states of the first sub-space 230 are, at least to first order, not dependent on the external magnetic field experienced by the quantum object.

[0067] The second sub-space 240 includes a first shelving state 242 and second shelving state 244. In various embodiments, the states of the second sub-space are sensitive to the magnetic fields. For example, the energy and / or frequency of the first shelving state 242 and the second shelving state 244 are dependent on the external magnetic field experienced by the quantum object, in an example embodiment.

[0068] In various embodiments, the shelving operation includes performing a shelving transition. For example, a shelving operation includes transitioning a quantum object from afirst quantum state to a second quantum state. In various embodiments, the first quantum state and the second quantum state are in different sub-spaces of the energy space of the quantum object.

[0069] As used herein, a shelving transition transitions and / or evolves the quantum state of a quantum object from a first quantum state in a first sub-space 230 to a second quantum state in a second sub-space 240. For example, a shelving transition includes causing a quantum object in a first qubit state 232 in a first sub-space 230 to transition to a first shelving state 242 in a second sub-space 240 via a first transition, in an example embodiment. In another example, a shelving transition includes causing a quantum object in a second qubit state 234 in a first sub-space 230 to transition to a second shelving state 244 in a second subspace 240 via a second transition, in an example embodiment. For example, the manipulation signal couples a particular state in the first sub-space to a particular state in the second subspace so as to cause a population inversion therebetween to perform a shelving operation.

[0070] In various embodiments, a deshelving operation includes performing a deshelving transition. As used herein, a deshelving transition transitions and / or evolves the quantum state of a quantum object from the second quantum state in the second sub-space 240 to the first quantum state in the first sub-space 230. For example, a deshelving transition includes causing a quantum object in a first shelving state 242 in a second sub-space 240 to transition to a first qubit state 232 in a first sub-space 230 via a first transition, in an example embodiment. In another example, a deshelving transition includes causing a quantum object in a second shelving state 244 in a second sub-space 240 to transition to a second qubit state 234 in a first sub-space 230 via a second transition, in an example embodiment.

[0071] As illustrated in Figure 2, a first transition frequency Afi corresponds to the first transition and a second transition frequency Afz corresponds to the second transition. The first transition and the second transition are degenerate, meaning that the first transition frequency Afi is approximately equal to the second transition frequency Afz. Therefore, applying a manipulation signal configured to drive a conventional shelving or deshelving operation (e.g., characterized by the transition frequency of the intended transition) drives both the first transition and the second transition. Since the Rabi frequencies of the first transition and the second transition are differ by an irrational number, it is impossible to drive both the first transition and the second transition with high fidelity (e.g., near 100% population transference between the respective first sub-space states and the respect second sub-space states). Various embodiments, however, provide a technical solution to this technical challenge.

[0072] In various embodiments, a dressing field 252 (e.g., 252A, 252B) is applied to the quantum object located at the target location 125. For example, the manipulation source 64D (e.g., the dressing field source) is operated to cause the dressing field 252 to be applied to the target location 125. In an example embodiment, the dressing field 252 is a microwave field polarized in a first direction. The dressing field 252 is characterized by a dressing field frequency fa and a dressing field amplitude Aa. In various embodiments, the dressing field frequency fa is detuned from the first transition frequency Afi and from the second transition frequency Afz by a detuning 5. In various embodiments, the detuning 5 is in a range of 50 - 800 kHz. In example embodiment, the detuning 5 is in a range of 80 - 120 kHz.

[0073] As result of the detuning of the dressing field frequency fa from the first transition frequency Afi and from the second transition frequency Afz, the dressing field 252 does not drive either the first transition or the second transition. Rather, the dressing field 252 interacts with the quantum object disposed at the target location 125 to cause the quantum states of the quantum object to be dressed and / or modified to a set of superposition states 250 referred to as dressed states.

[0074] For example, when the quantum object is experiencing the quantization field of the low quantization field regime (e.g., a magnetic field in the particular magnetic field direction / quantization direction with a magnetic field strength greater than 0 and less than 100 Gauss), the energy space of the quantum object includes an initial set of quantum states of the energy space 200. When the quantum object experiences the dressing field 252, the quantum states of the quantum object are dressed and / or modified to from the set of superposition states 250 (which may include additional dressed states in addition to those illustrated in Figure 2).

[0075] Each dressed state of the set of superposition states 250 is a superposition of two or more states of the initial set of quantum states of the quantum object. For example, a first pair of dressed states 260 of the set of superposition states 250 are superpositions of the first qubit state 232 and the first shelving state 242 and a second pair of dressed states 270 of the set of superposition states 250 are superpositions of the second qubit state 234 and the second shelving state 244. For example, the first dressed state 262 of the first pair of dressed states 260, is the superposition state ajfirst qubit state 232> + b jfirst shelving state 242> and the second dressed state 264 of the first pair of dressed states 260 is the superposition state ajfirst shelving state 242> - b jfirst qubit state 232>, where a and b are constants that are determined based at least in part on the intensity of the dressing field 252 and the detuning 5. The firstdressed state 272 of the second pair of dressed states 270 is the superposition state c- (second qubit state 234> + d- (second shelving state 244> and the second dressed state 274 of the second pair of dressed states 270 is the superposition state c- (second shelving state 244> - d- (second qubit state 234>, where c and d are constants that are determined based at least in part on the intensity of the dressing field 252 and the detuning 5.

[0076] The frequency difference between the first pair of dressed states 260 is a first dressed frequency Afai and the frequency difference between the second pair of dressed states 270 is a second dressed frequency Afd2. The first dressed frequency Afai is a function of the Rabi frequency of the first transition (e.g., between the first qubit state 232 to the first shelving state 242). For example, in various embodiments, the first dressed frequency Afai is substantially equal to the square root of the sum of the Rabi frequency of the first transition i squared and the detuning 5 squared (e.g., Afai « ( i2+ 82)1 / 2). The second dressed frequency Afa2 is a function of the Rabi frequency of the second transition (e.g., between the second qubit state 234 to the second shelving state 244). For example, in various embodiments, the second dressed frequency Afa2 is substantially equal to the square root of the sum of the Rabi frequency of the second transition 2 squared and the detuning 5 squared (e.g., Afd2 « ( 22+ 52)1 / 2). As the Rabi frequency of the first transition i does not equal the Rabi frequency of the second transition 2 (e.g., i = 2), the first dressed frequency Afai is not equal to the second dressed frequency Afa2 (Afai Afd2).

[0077] In various embodiments, while the quantum object is experiencing the dressing field 252, an oscillating magnetic field is applied to the quantum object disposed at the target location 125. For example, the oscillating magnetic field source 72 may be operated to cause an oscillating magnetic field to be applied to the target location 125.

[0078] In various embodiments, the oscillating magnetic field at the target location 125 is in the particular magnetic field direction / quantization direction. For example, one or more magnetic field generators 70A, 70B are configured to generate a uniform magnetic field in the quantization direction at various target locations 125 of the confinement apparatus 120. The oscillating magnetic field source 72 may generate an oscillating magnetic field at the target location 125 that is also in the quantization direction. In an example embodiment, the quantization direction is normal to a surface of the confinement apparatus 120. In other embodiments, the quantization direction is parallel to a plane defined by the surface of the confinement apparatus 120 and / or transverse (but not necessarily normal) to the surface ofthe confinement apparatus 120. In various embodiments, the quantization field is orthogonal to the first direction.

[0079] For example, in various embodiments, the dressing field is polarized in the first direction. The oscillating magnetic field is in a second direction (e.g., the quantization direction and / or the particular magnetic field direction corresponding to the uniform magnetic field of the system). The first direction is orthogonal to the second direction.

[0080] In various embodiments, the oscillating magnetic field is characterized by a magnetic field frequency co and a magnetic field envelope amplitude AB. The magnetic field amplitude AB is the amplitude of an envelope of the oscillating magnetic field. The envelope of an oscillating signal or field is a smooth curve outlining its extremes. For example, at a time t, the magnitude of the oscillating magnetic field is the product of the magnetic field envelope amplitude AB and a periodic function (e.g., cosine, sine, and / or the like) having a period of 1 / co (e.g., AB-cos(cot)).

[0081] In various embodiments, when it is desired to drive the first transition (e.g., a transition between the first qubit state 232 and the first shelving state 242), the magnetic field frequency co is set and / or selected to be substantially equal to the first dressed frequency Afai. For example, the oscillating magnetic field with the magnetic field frequency co is set and / or selected to be substantially equal to the first dressed frequency Afai drives a transition between the first dressed state 262 of the first pair of dressed states 260 and the second dressed state 264 of the first pair of dressed states 260.

[0082] When it is desired to drive the second transition (e.g., a transition between the second qubit state 234 and the second shelving state 244), the magnetic field frequency co is set and / or selected to be substantially equal to the second dressed frequency Afn. For example, the oscillating magnetic field with the magnetic field frequency co is set and / or selected to be substantially equal to the second dressed frequency Afd2 drives a transition between the first dressed state 272 of the second pair of dressed states 270 and the second dressed state 274 of the second pair of dressed states 270.

[0083] As the first dressed frequency Afai is not equal to the second dressed frequency Afd2, when the magnetic field frequency co is set and / or selected to be substantially equal to the first dressed frequency Afai, the transition between the first dressed state 272 of the second pair of dressed states 270 and the second dressed state 274 of the second pair of dressed states 270 is not driven by the oscillating magnetic field. Similarly, when the magnetic field frequency co is set and / or selected to be substantially equal to the second dressed frequency Afn, the transition between the first dressed state 262 of the first pair ofdressed states 260 and the second dressed state 264 of the first pair of dressed states 260 is not driven by the oscillating magnetic field. For example, selection of the magnetic field frequency co effectively selects which of the first transition or the second transition is performed.

[0084] After the quantum object disposed at the target location 125 has experienced the oscillating magnetic field (and the dressing field) for a population transfer time (e.g., a sufficient amount of time for the transfer of the population between a respective state of the first sub-space and a respective state of the second sub-space and / or between respective states of a pair of dressed states), the quantum object is caused to stop experiencing the oscillating magnetic field (and the dressing field). For example, the quantum object may be transported out of the target location 125 to cause the quantum object to stop experiencing the oscillating magnetic field (and the dressing field). In another example, the oscillating magnetic field source 72 is caused to stop generating the oscillating magnetic field and the manipulation source 64D (e.g., the dressing field source) is caused to stop generating the dressing field. When the quantum object stops experiencing the dressing, the set of superposition states 250 is undressed and / or modified to return to the initial set of states of the energy space 200.

[0085] In an example, at an initial time immediately before and / or at the start of the performance of a shelving operation is performed on a quantum object disposed at the target location 125, the wavefunction of the quantum object is a|first qubit state 232> + P|second qubit state 234>. When a shelving operation is performed where the magnetic field frequency is selected to be the first dressed frequency co = Afai, at a final time (immediately) after completion of the shelving operation, the wavefunction of the quantum object is a|first shelving state 242> + P|second qubit state 234>. When a shelving operation is performed where the magnetic field frequency is selected to be the second dressed frequency co = Afd2, at a final time (immediately) after completion of the shelving operation, the wavefunction of the quantum object is a|first qubit state 232> + P|second shelving state 244>.

[0086] In another example, at an initial time immediately before and / or at the start of the performance of a deshelving operation is performed on a quantum object disposed at the target location 125, the wavefunction of the quantum object is a|first shelving state 242> + Plsecond shelving state 244>. When a deshelving operation is performed where the magnetic field frequency is selected to be the first dressed frequency co = Afai, at a final time (immediately) after completion of the deshelving operation, the wavefunction of the quantum object is a|first qubit state 232> + P|second shelving state 244>. When a deshelving operation is performed where the magnetic field frequency is selected to be the second dressedfrequency co = Afd2, at a final time (immediately) after completion of the deshelving operation, the wavefunction of the quantum object is a|first shelving state 242> + P|second qubit state 234>.

[0087] In various embodiments, the dressing field amplitude Ad and / or the magnetic field envelop amplitude AB evolve with time during performance of a shelving or deshelving operation. Figure 3 provides a plot 300 illustrating the time evolution of the dressing field amplitude Ad and the magnetic field envelope amplitude AB during performance of a shelving (or deshelving) operation, according to an example embodiment. The shelving (or deshelving) operation begins at an initial time to. At the initial time, the dressing field amplitude Ad is equal to a minimum dressing field amplitude Ad, min and the magnetic field envelope amplitude AB is equal to a minimum magnetic field envelope amplitude AB min. In various embodiments, the minimum dressing field amplitude Ad, min and / or minimum magnetic field envelope amplitude AB min is approximately equal to zero.

[0088] At a first time ti (ti > to), the dressing field amplitude Ad is a maximum dressing field amplitude Ad, max and the magnetic field envelope amplitude AB is still equal to a minimum magnetic field envelope amplitude AB, min. Between the initial time to and the first time ti, the dressing field amplitude Ad increases from the minimum dressing field amplitude Ad min to the maximum dressing field amplitude Ad, max as shown by the solid line 320 of plot 300. In various embodiments, the increase in the dressing field amplitude Ad between the initial time to and the first time ti is smooth and continuous. In various embodiments, the increase in the dressing field amplitude Ad is linear and / or of another functional form with respect to time (over the respective time period). In another example, the dressing field amplitude Ad increases as a monotonic portion of a cosine, sine, cosine squared, or sine squared function between the initial time to and the first time ti. For example, the increase in the dressing field amplitude Ad may be configured to have a time derivative substantially equal to zero at the initial time to and / or at the first time ti.

[0089] In various embodiments, the dressing field is turned on adiabatically. For example, the dressing field amplitude Ad is increased slowly such that the respective energy structures of the quantum object are dressed and / or modified from the set of initial states to the set of superposition states adiabatically. As used herein “slowly” relates to a field (e.g., the dressing field) being turned on or off at a time scale that is slow compared to the first dressed frequency Afdi, the second dressed frequency Afd2, and / or the detuning 5. For example, the time period that elapses between the initial time to and the first time ti (e.g., ti -to) is longer than the reciprocal of at least one of first dressed frequency Afai, the second dressed frequency Afd2, or the detuning 5.

[0090] At a second time t2 (t2 > ti), the dressing field amplitude A is being maintained at the maximum dressing field amplitude A ,max and the magnetic field envelope amplitude AB begins to increase from the minimum magnetic field envelope amplitude AB, min.

[0091] At a third time t3 (t3 > t ), the dressing field amplitude Aa is being maintained at the maximum dressing field amplitude Aa,max and the magnetic field envelope amplitude AB is equal to a maximum magnetic field envelope amplitude AB, max. Between the second time t2 and the third time t3, the magnetic field envelope amplitude AB increases from the minimum magnetic field envelope amplitude AB, min to the maximum magnetic field envelope amplitude AB max as shown by the dashed line 330 of plot 300.

[0092] In an example embodiment, the magnetic field envelope amplitude AB increases as a step function and / or square wave (e.g., t3 « t2). In various embodiments, the increase in the magnetic field envelope amplitude AB between the second time t2 and the third time t3 is smooth and continuous. In various embodiments, the increase in the magnetic field envelope amplitude AB is linear and / or of another functional form with respect to time (over the respective time period). In another example, the magnetic field envelope amplitude AB increases as a monotonic portion of a cosine, sine, cosine squared, or sine squared function between the second time t2 and the third time t3. For example, the increase in the magnetic field envelope amplitude AB may be configured to have a time derivative substantially equal to zero at the second time t2 and / or at the third time t3.

[0093] In various embodiments, the oscillating magnetic field is turned on adiabatically. For example, the magnetic field envelope amplitude AB is increased slowly. For example, the time period over which the magnetic field envelope amplitude AB increases from the minimum magnetic field envelope amplitude AB, min to the maximum magnetic field envelope amplitude AB, max is longer than the reciprocal of at least one of first dressed frequency Afai, the second dressed frequency Afd2, or the detuning 5. For example, in an example embodiment, the time period that elapses between the second time t2 and the third time t3 (e.g., t3 - 12) is longer than the reciprocal of at least one of first dressed frequency Afai, the second dressed frequency Af 2, or the detuning 5.

[0094] Between the third time t3 and the fourth time t4 ( > ti) application of the dressing field to the target location 125 is maintained such that the dressing field magnitude A is maintained at the maximum dressing field amplitude A ,max and application of the oscillating magnetic field to the target location 125 is maintained such that the magnetic field envelopemagnitude AB is maintained at the maximum magnetic field envelope amplitude AR ma . Starting at the fourth time the oscillating magnetic field begins to be turned off.

[0095] In various embodiments, the third time t3 and the fourth time are selected such that the quantum object experiences the oscillating magnetic field with the magnetic field envelope magnitude AB maintained at the maximum magnetic field envelope amplitude AB, max for at least a population transfer time tpt (e.g., t4 -t3 > tpt). In various embodiments, the population transfer time is equal to the inverse of the Rabi frequency of the transition between selected pair of dressed states as driven by the oscillating magnetic field.

[0096] At a fifth time ts (ts > ), the dressing field amplitude Aa is being maintained at the maximum dressing field amplitude Aa,max and the magnetic field envelope amplitude AB has been decreased to a minimum magnetic field envelope amplitude ARmin. In an example embodiment, the minimum magnetic field envelope amplitude ARmin is approximately equal to zero. Between the fourth time and the fifth time ts, the magnetic field envelope amplitude AB decreases from the maximum magnetic field envelope amplitude AB, max to the minimum magnetic field envelope amplitude AB,min as shown by the dashed line 330 of plot 300.

[0097] In an example embodiment, the magnetic field envelope amplitude AB decreases as a step function and / or square wave (e.g., « ts). In various embodiments, the decrease in the magnetic field envelope amplitude AB between the fourth time t4 and the fifth time ts is smooth and continuous. In various embodiments, the decrease in the magnetic field envelope amplitude AB is linear and / or of another functional form with respect to time (over the respective time period). In another example, the magnetic field envelope amplitude AB decreases as a monotonic portion of a cosine, sine, cosine squared, or sine squared function between the fourth time t4 and the fifth time ts. For example, the decrease in the magnetic field envelope amplitude AB may be configured to have a time derivative substantially equal to zero at the fourth time t4 and / or at the fifth time ts.

[0098] In various embodiments, the oscillating magnetic field is turned off adiabatically. For example, the magnetic field envelope amplitude AB is decreased slowly. For example, the time period over which the magnetic field envelope amplitude AB decreases from the maximum magnetic field envelope amplitude AB, max to the minimum magnetic field envelope amplitude AB,min is longer than the reciprocal of at least one of first dressed frequency Afai, the second dressed frequency Afd2, or the detuning 5. For example, in an example embodiment, the time period that elapses between the fourth time t4 and the fifth time ts (e.g.,ts - ) is longer than the reciprocal of at least one of first dressed frequency Afai, the second dressed frequency Afd2, or the detuning 5.

[0099] At a sixth time te (te > ts), the dressing field amplitude Aa begins to decrease from the maximum dressing field amplitude Aa,max and the magnetic field envelope amplitude AB is maintained at the minimum magnetic field envelope amplitude AB, min.

[0100] At a final time t? (t? > te), the dressing field amplitude Aa is a minimum dressing field amplitude Ad min and the magnetic field envelope amplitude AB is still equal to a minimum magnetic field envelope amplitude AB, min. Between the sixth time te and the final time t?, the dressing field amplitude Aa decreases from the maximum dressing field amplitude Aa,max to the minimum dressing field amplitude Aa,min as shown by the solid line 320 of plot 300. In various embodiments, the decrease in the dressing field amplitude Aa between the sixth time te and the final time t? is smooth and continuous. In various embodiments, the decrease in the dressing field amplitude Aa is linear and / or of another functional form with respect to time (over the respective time period). In another example, the dressing field amplitude Aa decreases as a monotonic portion of a cosine, sine, cosine squared, or sine squared function between the sixth time te and the final time t?. For example, the decrease in the dressing field amplitude Aa may be configured to have a time derivative substantially equal to zero at the sixth time te and / or at the final time t?.

[0101] In various embodiments, the dressing field is turned off adiabatically. For example, the dressing field amplitude Aa is decreased slowly such that the respective energy structures of the quantum object are undressed and / or modified from the set of superposition states to the set of initial states adiabatically. For example, the time period over which the dressing field amplitude Aa decreases from the maximum dressing field amplitude Aa,max to the minimum dressing field amplitude Aa, min is longer than the reciprocal of at least one of first dressed frequency Afai, the second dressed frequency Afd2, or the detuning 5. For example, in an example embodiment, the time period that elapses between the sixth time te and the final time t7 (e.g., t? - te) is longer than the reciprocal of at least one of first dressed frequency Afai, the second dressed frequency Afd2, or the detuning 5.

[0102] In various embodiments, adiabatically turning on and / or off the dressing field and / or the oscillating magnetic field enables the shelving (or deshelving) transition(s) to be driven with a high likelihood of success (e.g., with a near 100% probability) while (coherently) maintaining the quantum information stored by the quantum object. Moreover, the shelving (or deshelving) transition(s) may be performed with a frequency selection toenable performance of just one of the first transition or the second transition, or performance of both the first transition and the second transition with high fidelity.Example Controller

[0103] In various embodiments, a confinement apparatus 120 is incorporated into a quantum computer 110 or other atomic system. In various embodiments, a quantum computer 110 or other atomic system further comprises a controller 30 configured to control various elements of the quantum computer 110 or other atomic system. For example, the controller 30 may be configured to control the voltage sources 50, a cryogenic system and / or vacuum system controlling the temperature and pressure within the cryogenic and / or vacuum chamber 40, manipulation sources 64 (e.g., 64A, 64B, 64C, 64D, 64E), magnetic field generators 70 (e.g., 70A, 70B), 72 active components of beam path systems 66, and / or other systems controlling the environmental conditions (e.g., temperature, humidity, pressure, and / or the like) within the cryogenic and / or vacuum chamber 40, configured to manipulate and / or cause a controlled evolution of quantum states of one or more quantum objects confined by the confinement apparatus 120, and / or read and / or detect a quantum state of one or more quantum objects within the confinement apparatus 120. For example, the controller 30 may be configured to control operation of the confinement apparatus 120 (e.g., via controlling one or more voltage sources 50 configured to provide voltage signals to various potential generating elements / electrodes of the confinement apparatus, in an example embodiment).

[0104] As shown in Figure 4, in various embodiments, the controller 30 may comprise various controller elements including processing device 405, memory 410, driver controller elements 415, a communication interface 420, analog-digital converter elements 425, and / or the like. For example, the processing device 405 may comprise processing elements, programmable logic devices (CPLDs), microprocessors, coprocessing entities, application-specific instruction-set processors (ASIPs), integrated circuits, application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), programmable logic arrays (PLAs), hardware accelerators, other processing devices and / or circuitry, and / or the like, and / or controllers. The term circuitry may refer to an entirely hardware embodiment or a combination of hardware and computer program products. In an example embodiment, the processing device 405 of the controller 30 comprises a clock and / or is in communication with a clock.

[0105] For example, the memory 410 may comprise non-transitory memory such as volatile and / or non-volatile memory storage such as one or more of as hard disks, ROM,PROM, EPROM, EEPROM, flash memory, MMCs, SD memory cards, Memory Sticks, 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, and / or the like. In various embodiments, the memory 410 may store qubit records corresponding the qubits of quantum computer (e.g., in a qubit record data store, qubit record database, qubit record table, and / or the like), a calibration table, an executable queue, computer program code (e.g., in a one or more computer languages, specialized controller language(s), and / or the like), and / or the like. In an example embodiment, execution of at least a portion of the computer program code stored in the memory 410 (e.g., by a processing device 405) causes the controller 30 to perform one or more steps, operations, processes, procedures and / or the like described herein for controlling one or more components of the quantum computer 110 or other atomic system (e.g., voltages sources 50, manipulation sources 64, magnetic field generators 70, and / or the like) to cause a controlled evolution of quantum states of one or more quantum objects, detect and / or read the quantum state of one or more quantum objects, and / or the like.

[0106] In various embodiments, the driver controller elements 415 may include one or more drivers and / or controller elements each configured to control one or more drivers. In various embodiments, the driver controller elements 415 may comprise drivers and / or driver controllers. For example, the driver controllers may be configured to cause one or more corresponding drivers to be operated in accordance with executable instructions, commands, and / or the like scheduled and executed by the controller 30 (e.g., by the processing device 405). In various embodiments, the driver controller elements 415 may enable the controller 30 to operate a manipulation source 64. In various embodiments, the drivers may be laser drivers; vacuum component drivers; drivers for controlling the flow of current and / or voltage applied to longitudinal, RF, and / or other electrodes used for maintaining and / or controlling the confinement potential of the confinement apparatus (and / or other driver for providing driver action sequences and / or control signals to potential generating elements of the confinement apparatus); cryogenic and / or vacuum system component drivers; and / or the like. For example, the drivers may control and / or comprise control and / or RF voltage drivers and / or voltage sources that provide voltages and / or electrical signals to the potential generators (e.g., control electrodes and / or RF electrodes). In various embodiments, the controller 30 comprises means for communicating and / or receiving signals from one or more detectors such as optical receiver components (e.g., cameras, MEMs cameras, CCD cameras, photodiodes, photomultiplier tubes, and / or the like). For example, the controller 30 maycomprise one or more analog-digital converter elements 425 configured to receive signals from one or more detectors, optical receiver components, calibration sensors, photodetectors of an optics collection system 80, and / or the like.

[0107] In various embodiments, the controller 30 may comprise a communication interface 420 for interfacing and / or communicating with a computing entity 10. For example, the controller 30 may comprise a communication interface 420 for receiving executable instructions, command sets, and / or the like from the computing entity 10 and providing output received from the quantum computer 110 (e.g., from an optics collection system 80 comprising one or more photodetectors) and / or the result of a processing the output to the computing entity 10. In various embodiments, the computing entity 10 and the controller 30 may communicate via a direct wired and / or wireless connection and / or one or more wired and / or wireless networks 20.Example Method of Performing a Shelving (or Deshelving) Operation

[0108] Figure 5 provides a flowchart illustrating various processes, procedures, and / or the like performed by a controller 30 of a quantum computer 110 and / or atomic system for performing a shelving operation, in accordance with various embodiments. In various embodiments, the shelving operation is performed as part of and / or in preparation of performing a magnetic field sensitive operation (e.g., a quantum logic gate mediated by a magnetic field gradient), a quantum state reading operation, and / or the like.

[0109] Starting at step 502, the controller 30 causes one or more quantum objects on which the shelving operation is to be performed to be located and / or confined at respective target locations 125. For example, one or more quantum objects on which the shelving operation is to be performed may be disposed at one or more target locations 125. When it is determined (e.g., based on a quantum object or qubit record stored in memory 410 of the controller 30) that a quantum object on which a shelving operation is to be performed is not located at a respective target location 125, the controller 30 causes the confinement apparatus 120 to transport the quantum object to the target location 125. For example, the controller 30 controls operation of the voltage sources 50 to cause transportation of the quantum object to the target location 125.

[0110] At step 504, the controller 30 controls operation of one or more dressing field sources (e.g., one or more manipulation sources 64D) to cause generation of the dressing field such that the dressing field is applied and / or provided to the target location 125 with the dressing field characterized by a dressing field amplitude and a dressing field frequency. Invarious embodiments, the dressing field frequency is detuned from the first transition frequency Afi and the second transition frequency Afz by a detuning 5.

[0111] In various embodiments, the initial amplitude of the dressing field (the dressing field amplitude at an initial time to) is a minimum dressing field amplitude Ad, min. In an example embodiment, the minimum dressing field amplitude Ad min is approximately equal to zero. In various embodiments, controlling operation of the one or more dressing field sources to cause generation of the dressing field includes causing the dressing field source(s) to increase the dressing field amplitude Ad from the minimum dressing field amplitude Ad min to a maximum dressing field amplitude Ad, max smoothly, continuously, and / or adiabatically.

[0112] In various embodiments, the controller 30 controls operation of one or more dressing field sources (e.g., manipulation sources 64D) via execution of executable instructions by the processing device 405 and / or driver controller elements 415 configured to control operation of the respective manipulation source(s) and / or one or more voltage and / or current sources 50. For example, the controller 30 may control operation of one or more voltage and / or current sources 50 (e.g., via execution of executable instructions by the processing device 405 and / or driver controller elements 415) to provide voltage and / or current signals to the dressing field source (e.g., an integrated circuit formed on the confinement apparatus 120 and / or second substrate 122) to cause the dressing field source to generate the dressing field. In various embodiments, the dressing field is generated such that, at the target location 125, the dressing field is polarized in a first direction.

[0113] At step 506, the controller 30 controls operation of one or more oscillating magnetic field sources 72 to cause generation of the oscillating magnetic field such that the oscillating magnetic field is applied and / or provided to the target location 125 with the oscillating magnetic field characterized by a magnetic field envelope amplitude and a magnetic field frequency. In various embodiments, the magnetic field frequency co is selected to be one of the first dressed frequency Afi or the second dressed frequency Afz.

[0114] In various embodiments, the initial amplitude of the envelope of the oscillating magnetic field is a minimum magnetic field envelope amplitude AB, min. In an example embodiment, the minimum magnetic field envelope amplitude AB, min is approximately equal to zero. In various embodiments, controlling operation of the one or more oscillating magnetic field sources 72 to cause generation of the oscillating magnetic field includes causing the magnetic field source(s) to increase the magnetic field envelope amplitude AB from the minimum magnetic field envelope amplitude AB, min to a maximum magnetic field envelope amplitude AB, max smoothly, continuously, and / or adiabatically.

[0115] In various embodiments, the controller 30 controls operation of one or more oscillating magnetic field sources 72 via execution of executable instructions by the processing device 405 and / or driver controller elements 415 configured to control operation of respective voltage and / or current sources 50. For example, the controller 30 may control operation of one or more voltage and / or current sources 50 (e.g., via execution of executable instructions by the processing device 405 and / or driver controller elements 415) to provide voltage and / or current signals to the oscillating magnetic field source 72 (e.g., an integrated circuit formed on the confinement apparatus 120 and / or second substrate 122) to cause the oscillating magnetic field source 72 to generate the oscillating magnetic field.

[0116] In various embodiments, the oscillating magnetic field is characterized by a second direction. In various embodiments, the second direction is parallel to the quantization direction and / or the particular magnetic field direction of the uniform quantization field (e.g., generated and / or provided by the magnetic field generators 70A and / or 70B) that is spatially uniform and temporally stable across the confinement apparatus 120 during operation of the quantum computer 110. In various embodiments, the first direction (e.g., the direction of the polarization of the dressing field) and the second direction are orthogonal.

[0117] The controller 30 may control operation of the dressing field source(s) and the oscillating magnetic field source(s) 72 to continue applying the dressing field at the target location 125 with the maximum dressing field amplitude and to continue applying the oscillating magnetic field at the target location 125 with the maximum magnetic field envelope amplitude for a population transfer time. In various embodiments, the population transfer time is equal to the inverse of the Rabi frequency of the transition between selected pair of dressed states as driven by the oscillating magnetic field.

[0118] At step 508, the controller 30 controls operation of one or more oscillating magnetic field sources 72 to cause generation of the oscillating magnetic field to stop such that the oscillating magnetic field is no longer applied and / or provided to the target location 125.

[0119] In various embodiments, the amplitude of the envelope of the oscillating magnetic field at the beginning of performance of step 508 is a maximum magnetic field envelope amplitude AB, max and the amplitude of the envelope of the oscillating magnetic field at the end of performance of step 508 is a minimum magnetic field envelope amplitude AB, min. In an example embodiment, the minimum magnetic field envelope amplitude AB, min is approximately equal to zero. In various embodiments, controlling operation of the one or more oscillating magnetic field sources 72 to cause generation of the oscillating magneticfield includes causing the magnetic field source(s) to decrease the magnetic field envelope amplitude AB from the maximum magnetic field envelope amplitude AB, max to a minimum magnetic field envelope amplitude AB, min smoothly, continuously, and / or adiabatically.

[0120] In various embodiments, the controller 30 controls operation of one or more oscillating magnetic field sources 72 via execution of executable instructions by the processing device 405 and / or driver controller elements 415 configured to control operation of respective voltage and / or current sources 50. For example, the controller 30 may control operation of one or more voltage and / or current sources 50 (e.g., via execution of executable instructions by the processing device 405 and / or driver controller elements 415) to provide voltage and / or current signals to the oscillating magnetic field source 72 (e.g., an integrated circuit formed on the confinement apparatus 120 and / or second substrate 122) to cause the oscillating magnetic field source 72 to stop generating the oscillating magnetic field (e.g., the amplitude of the voltage and / or current sources 50 may be reduced to approximately zero).

[0121] At step 510, the controller 30 controls operation of one or more dressing field sources (e.g., one or more manipulation sources 64D) to cause generation of the dressing field to stop such that, at a final time, the dressing field is no longer applied and / or provided to the target location 125.

[0122] In various embodiments, the final amplitude of the dressing field (the dressing field amplitude at a final time t?) is a minimum dressing field amplitude Ad, min. In an example embodiment, the minimum dressing field amplitude Ad min is approximately equal to zero. In various embodiments, controlling operation of the one or more dressing field sources to cause generation of the dressing field to stop includes causing the dressing field source(s) to decrease the dressing field amplitude Ad from the maximum dressing field amplitude Ad, max to a minimum dressing field amplitude Ad, min smoothly, continuously, and / or adiabatically.

[0123] In various embodiments, the controller 30 controls operation of one or more dressing field sources (e.g., manipulation sources 64D) via execution of executable instructions by the processing device 405 and / or driver controller elements 415 configured to control operation of the respective manipulation source(s) and / or one or more voltage and / or current sources 50. For example, the controller 30 may control operation of one or more voltage and / or current sources 50 (e.g., via execution of executable instructions by the processing device 405 and / or driver controller elements 415) to provide voltage and / or current signals to the dressing field source (e.g., an integrated circuit formed on the confinement apparatus 120 and / or second substrate 122) to cause the dressing field source tostop generating the dressing field (e.g., the amplitude of the voltage and / or current sources 50 may be reduced to approximately zero).

[0124] In an example, at an initial time immediately before and / or at the start of the performance of a shelving operation is performed on a quantum object disposed at the target location 125, the wavefunction of the quantum object is a|first qubit state 232> + P|second qubit state 234>. When a shelving operation is performed where the magnetic field frequency is selected to be the first dressed frequency co = Afai, at a final time (immediately) after completion of the shelving operation, the wavefunction of the quantum object is a|first shelving state 242> + P|second qubit state 234>. When a shelving operation is performed where the magnetic field frequency is selected to be the second dressed frequency co = Afd2, at a final time (immediately) after completion of the shelving operation, the wavefunction of the quantum object is a|first qubit state 232> + P|second shelving state 244>.

[0125] At step 512, the controller 30 controls various components of the atomic system and / or quantum computer to cause one or more operations to be performed while the one or more quantum objects are shelved. For example, the controller 30 may cause a magnetic field sensitive quantum logic operation (e.g., a single qubit, two-qubit, and / or multi-qubit quantum logic gate that is mediated by a magnetic field gradient) while the one or more quantum objects confined at the target location are shelved. In another example, the controller 30 may perform a quantum state reading operation to determine the quantum state (e.g., encoding the quantum information stored by the quantum object) while the quantum objects confined at the target location are shelved. Various operations may be performed while the one or more quantum objects are shelved, in various embodiments, as appropriate for the application.

[0126] At step 514, the quantum objects confined at the target location 125 are deshelved. For example, the controller 30 controls operation of the one or more dressing field sources 68 and one or more oscillating magnetic field sources 72 to perform a deshelving operation of one or more quantum objects confined at respective target locations 125. In various embodiments, a deshelving operation is similar to a shelving operation. For example, performing a deshelving operation, in an example embodiment, includes performing steps 504-510. For example, the controller 30 controls operation of the one or more dressing field sources (e.g., manipulation sources 64D) to cause a dressing field to be provided to the target location 125 that is a microwave field polarized in a first direction and detuned from the first transition and the second transition by a detuning 6. The controller 30 may further control operation of one or more oscillating magnetic field sources 72 to cause an oscillatingmagnetic field to be provided to the target location 125 that is direction in a second direction and that oscillates with a magnetic field frequency that is substantially equal to one of a first dressed frequency or a second dressed frequency. The first direction is orthogonal to the second direction. In various embodiments, controlling operation of the one or more dressing field sources to cause generation of the dressing field to begin and / or stop includes causing the dressing field source(s) to increase / decrease the dressing field amplitude Ad smoothly, continuously, and / or adiabatically. In various embodiments, controlling operation of the one or more magnetic field sources to cause generation of the oscillating magnetic field to begin and / or stop includes causing the magnetic field source(s) to increase / decrease the magnetic field envelope amplitude AB smoothly, continuously, and / or adiabatically.

[0127] In various embodiments, the shelving operation (and / or deshelving operation) are performed as part of a quantum circuit and / or quantum program. In various embodiments, after completing the shelving operation and / or after completing the deshelving operation, the controller 30 may control various components of the atomic system and / or quantum computer to continue execution and / or performance of a quantum circuit and / or quantum program.Technical Advantages

[0128] In various scenarios, the energy space of a quantum object includes a first subspace of quantum states and a second sub-space of quantum states where multiple transitions between respective first sub-space of states and respective second sub-space states are degenerate. For example, a first transition between a first state of the first sub-space of states (also referred to as a first qubit state herein) and a first state of the second sub-space of states (also referred to as a first shelving state herein) may be degenerate with (e.g., correspond to substantially the same energy change and / or transition frequency as) a second transition between a second state of the first sub-space of states (also referred to as a second qubit state herein) and a second state of the second sub-space of states (also referred to as a second shelving state herein). Conventional shelving / deshelving techniques include applying a laser beam to a quantum object to shelve or deshelve the quantum object using, for example, a Rabi flop. The frequency of the laser beam is used to control which transition of the quantum object is driven. However, since the first transition and the second transition are degenerate (e.g., correspond to substantially the same transition frequency), attempting to perform the first transition to shelve quantum objects from the first qubit state to the first shelving state will also drive the second transition, which may not be desired. Moreover, since the Rabifrequencies of the first transition and the second transition are different, the first transition and second transition cannot be driven simultaneously with high fidelity.

[0129] For example, an example quantum object has a first sub-space including qubit states F = 1, m = 0 and F = 2, m = 0, and a second sub-space including states F = 2, m = 1 and F = 1, m = 1. It may be desired to shelve the F = 1, m = 0 qubit state to the F = 2, m = 1 shelving state and the F = 2, m = 0 qubit state to the F = 1, m = 1 shelving state. However, the frequency difference between the F = 1, m = 0 qubit state and the F = 2, m = 1 shelving state is sufficiently similar to the frequency difference between the F = 2, m = 0 qubit state and the F = 1, m = 1 shelving state that both of the transitions are simultaneously driven with a single laser or microwave tone. The length of time for which the single laser or microwave tone is applied to cause a near 100% population inversion via the Rabi flop is the inverse of the Rabi frequency of the transition. However, the Rabi frequencies of the two transitions are different by a factor of an irrational number. Therefore, the shelving transitions cannot be performed with near 100% probability for both pairs of states. Thus, the probability of performing a complete shelving of both qubit states is not high enough for the performance of high-fidelity quantum logic gate, for example. Moreover, it may be desired to drive only one of the first transition or the second transition, but due to the degeneracy of the two transitions, attempting to drive the first transition results in the driving of the second transition, and vice versa. As such, technical problems exist regarding the shelving and deshelving of quantum objects.

[0130] Various embodiments provide technical solutions to these technical problems. For example, a dressing field is applied to a quantum object to be shelved. The dressing field is characterized by a dressing field frequency that is detuned from the first transition frequency corresponding to a transition from the first qubit state to the first shelving state (or vice versa) and from the second transition frequency corresponding to a transition from the second qubit state to the second shelving state (or vice versa). Notably the first transition frequency and the second transition frequency are approximately equal. The application of the dressing field to the quantum object causes formation of a first pair dressed states, which are dressed states that are superpositions of the first qubit state and the first shelving state, and a second pair dressed states, which are dressed states that are superpositions of the second qubit state and the second shelving state.

[0131] The first pair of dressed state corresponds to a first dressed frequency and the second pair of dressed state corresponds to a second dressed frequency. For example, in various embodiments, the first dressed frequency is parameterized by and / or a function of theRabi frequency of the transition between the first qubit state and the first shelving state. In various embodiments, the second dressed frequency is parameterized by and / or a function of the Rabi frequency of the transition between the second qubit state and the second shelving state. As the Rabi frequency of the transition between the first qubit state and the first shelving state is not equal to the Rabi frequency of the transition between the second qubit state and the second shelving state, the first dressed frequency is not equal to the second dressed frequency.

[0132] A magnetic field is applied to the quantum object that oscillates at a magnetic field frequency. When it is desired to drive the first transition between the first qubit state and the first shelving state, the magnetic field frequency is set and / or selected to be substantially equal to the first dressed frequency. When it is desired to drive the second transition between the second qubit state and the second shelving state, the magnetic field frequency is set and / or selected to be substantially equal to the second dressed frequency.

[0133] After a period of time, the oscillating magnetic field may be turned off and the dressing field may be turned off such that they are no longer applied to the quantum object. When the quantum object is no longer experiencing the dressing field, the dressed states return to their constituent states. However, when the magnetic field frequency is substantially equal to the first dressed frequency, when the quantum object is no longer experiencing the dressing field, the initial population of the first qubit state has been transferred to the first shelving state and the initial population of the first shelving state has been transferred to the first qubit state. When the magnetic field frequency is substantially equal to the second dressed frequency, when the quantum object is no longer experiencing the dressing field, the initial population of the second qubit state has been transferred to the second shelving state and the initial population of the second shelving state has been transferred to the second qubit state.

[0134] Therefore, various embodiments enable frequency-selected shelving and / or deshelving in a situation in which conventional shelving techniques would drive multiple transitions. Thus, embodiments provide technical improvements and technical advantages to the fields of quantum object shelving (and / or deshelving) and atomic systems and / or quantum computers that use shelving (and / or deshelving) operations.Example Computing Entity

[0135] Figure 6 provides an illustrative schematic representative of an example computing entity 10 that can be used in conjunction with embodiments of the presentinvention. In various embodiments, a computing entity 10 is configured to allow a user to provide input to the quantum computer 110 (e.g., via a user interface of the computing entity 10) and receive, display, analyze, and / or the like output from the quantum computer 110.

[0136] As shown in Figure 6, a computing entity 10 can include an antenna 612, a transmitter 604 (e.g., radio), a receiver 606 (e.g., radio), and a processing device 608 that provides signals to and receives signals from the transmitter 604 and receiver 606, respectively. The signals provided to and received from the transmitter 604 and the receiver 606, respectively, may include signaling information / data in accordance with an air interface standard of applicable wireless systems to communicate with various entities, such as a controller 30, other computing entities 10, and / or the like. In this regard, the computing entity 10 may be capable of operating with one or more air interface standards, communication protocols, modulation types, and access types. For example, the computing entity 10 may be configured to receive and / or provide communications using a wired data transmission protocol, such as fiber distributed data interface (FDDI), digital subscriber line (DSL), Ethernet, asynchronous transfer mode (ATM), frame relay, data over cable service interface specification (DOCSIS), or any other wired transmission protocol. Similarly, the computing entity 10 may be configured to communicate via wireless external communication networks 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 IX (IxRTT), 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), Wi-Fi Direct, 802.16 (WiMAX), ultra-wideband (UWB), infrared (IR) protocols, near field communication (NFC) protocols, Wibree, Bluetooth protocols, wireless universal serial bus (USB) protocols, and / or any other wireless protocol. The computing entity 10 may use such protocols and standards to communicate using 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 / S ecure, Internet Message Access Protocol (IMAP), Network Time Protocol (NTP), Simple Mail Transfer Protocol (SMTP), 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), and / or the like.

[0137] Via these communication standards and protocols, the computing entity 10 can communicate with various other entities using concepts such as Unstructured Supplementary Service information / data (USSD), Short Message Service (SMS), Multimedia Messaging Service (MMS), Dual-Tone Multi-Frequency Signaling (DTMF), and / or Subscriber Identity Module Dialer (SIM dialer). The computing entity 10 can also download changes, add-ons, and updates, for instance, to its firmware, software (e.g., including executable instructions, applications, program modules), and operating system. In various embodiments, the computing entity 10 comprises a network interface 620 configured to communicate via one or more wired and / or wireless networks 20.

[0138] In various embodiments, the processing device 608 may comprise processing elements, programmable logic devices (CPLDs), microprocessors, coprocessing entities, application-specific instruction-set processors (ASIPs), integrated circuits, application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), programmable logic arrays (PLAs), hardware accelerators, other processing devices and / or circuitry, and / or the like. The term circuitry may refer to an entirely hardware embodiment or a combination of hardware and computer program products.

[0139] The computing entity 10 may also comprise a user interface device comprising one or more user input / output interfaces (e.g., a display 616 and / or speaker / speaker driver coupled to a processing device 608 and a touch screen, keyboard, mouse, and / or microphone coupled to a processing device 608). For instance, the user output interface may be configured to provide an application, browser, user interface, interface, dashboard, screen, webpage, page, and / or similar words used herein interchangeably executing on and / or accessible via the computing entity 10 to cause display or audible presentation of information / data and for interaction therewith via one or more user input interfaces. The user input interface can comprise any of a number of devices allowing the computing entity 10 to receive data, such as a keypad 618 (hard or soft), a touch display, voice / speech or motion interfaces, scanners, readers, or other input device. In embodiments including a keypad 618, the keypad 618 can include (or cause display of) the conventional numeric (0-9) and related keys (#, *), and other keys used for operating the computing entity 10 and may include a full set of alphabetic keys or set of keys that may be activated to provide a full set of alphanumeric keys. In addition to providing input, the user input interface can be used, for example, to activate or deactivate certain functions, such as screen savers and / or sleep modes.Through such inputs the computing entity 10 can collect information / data, user interaction / input, and / or the like.

[0140] The computing entity 10 can also include volatile storage or memory 622 and / or non-volatile storage or memory 624, which can be embedded and / or may be removable. For instance, the non-volatile memory may be ROM, PROM, EPROM, EEPROM, flash memory, MMCs, SD memory cards, Memory Sticks, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, and / or the like. The volatile memory may be RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, and / or the like. The volatile and non-volatile storage or memory can 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, and / or the like to implement the functions of the computing entity 10.Conclusion

[0141] Many modifications and other embodiments of the invention set forth herein will come to mind to one skilled in the art to which the invention pertains having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the invention is not to be limited to the specific embodiments disclosed and that 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.

Claims

CLAIMS1. A method of performing a shelving operation, the method performed by a controller of an atomic system or a quantum system, the method comprising: causing a dressing field source to start to provide a dressing field characterized by a dressing field frequency and a dressing field amplitude, wherein the dressing field frequency is detuned by a detuning from a transition frequency corresponding to both (a) a first transition between a first qubit state of a quantum object and a first shelving state of the quantum object and (b) a second transition between a second qubit state of the quantum object and a second shelving state of the quantum object, the dressing field is polarized in a first direction, and the dressing field is caused to be incident on the quantum object; causing a magnetic field source to start to provide an oscillating magnetic field in a second direction, the second direction being orthogonal to the first direction, and the oscillating magnetic field oscillating with a magnetic field frequency, wherein the magnetic field frequency corresponds to one of a first dressed frequency or a second dressed frequency; causing the magnetic field source to stop providing the oscillating magnetic field; and causing the dressing field source to stop providing the dressing field, wherein the dressing field being incident on the quantum object causes (a) the first qubit state and the first shelving state to form a first pair of dressed states and (b) the second qubit state and the second shelving state to form a second pair of dressed states, wherein the first dressed frequency corresponds to the first pair of dressed states and the second dressed state frequency corresponds to the second pair of dressed states, wherein when the magnetic field frequency corresponds to the first dressed frequency, at least one of a population of the first qubit state is transferred to the first shelving state or a population of the first shelving state is transferred to the first qubit state, and wherein when the magnetic frequency corresponds to the second dressed frequency, at least one of a population of the second qubit state is transferred to the second shelving state or a population of the second shelving state is transferred to the second qubit state.

2. The method of claim 1, wherein the first dressed frequency is not equal to the second dressed frequency or a harmonic thereof.

3. A method of performing a shelving operation, the method comprising: causing, at an initial time, a dressing field source to start to provide a dressing field characterized by a dressing field frequency and a dressing field amplitude, wherein the dressing field frequency is detuned by a detuning from a transition frequency corresponding to a transition between a qubit state of a quantum object and a shelving state of the quantum object, the dressing field is polarized in a first direction, and the dressing field is caused to be incident on the quantum object; causing a magnetic field source to start to provide an oscillating magnetic field in a second direction, the second direction being orthogonal to the first direction, and the oscillating magnetic field oscillating with a magnetic field frequency, wherein the magnetic field frequency corresponds to a dressed frequency; causing the magnetic field source to stop providing the oscillating magnetic field; and causing, at a final time, the dressing field source to stop providing the dressing field, wherein at the final time, at least one of a population of the qubit state at the initial time has been transferred to the shelving state or a population of the shelving state at the initial time has been transferred to the qubit state.

4. The method of any of claims 3, wherein at least one of starting to provide the dressing field or stopping providing the dressing field is done adiabatically.

5. The method of claim 4, wherein starting to provide the dressing field adiabatically comprises causing the dressing field amplitude to increase from a minimum dressing field amplitude to a maximum dressing field amplitude over a time period that is longer than at least one of (a) one divided by the detuning or (b) one divided by the first dressed state frequency, and stopping providing the dressing field adiabatically comprises causing the dressing field amplitude to decrease from the maximum dressing field amplitude to the minimum dressing field amplitude over a time period that is longer than at least one of (a) one divided by the detuning or (b) one divided by the first dressed state frequency.

6. The method of any of claims 3, wherein starting to provide the oscillating magnetic field comprises smoothly increasing a magnetic field envelope amplitude of an envelope of the oscillating magnetic field from a minimum magnetic field envelope amplitude to a maximum magnetic field envelop amplitude and stopping providing the oscillating magnetic field comprises smoothly decreasing the magnetic field envelope amplitude from themaximum magnetic field envelope amplitude to the minimum magnetic field envelope amplitude.

7. The method of claim 6, wherein the magnetic field envelope amplitude is increased from the minimum magnetic field envelope amplitude to the maximum magnetic field envelope amplitude adiabatically and the magnetic field envelope amplitude is decreased from the maximum magnetic field envelope amplitude to the minimum magnetic field envelope amplitude adiabatically.

8. The method of any of claims 3, wherein the quantum object is confined by a confinement apparatus and the confinement apparatus defines a plane, the first direction being parallel to the plane.

9. The method of any of claims 3, wherein the dressed frequency corresponds to a Rabi frequency of the transition.

10. The method of claim 9, wherein the dressed frequency is substantially equal to the square root of the sum of the Rabi frequency of the transition squared and the detuning squared.

11. The method of any of claims 3, wherein the second direction is a quantization direction used to define the first qubit state and the first shelving state.

12. The method of any of claims 3, further comprising: performing one or more shelved operations on at least one of the quantum object or another quantum object, wherein the quantum object and the other quantum object are both confined by a confinement apparatus, and performing a deshelving operation on the quantum object.

13. The method of claim 12, wherein performing the deshelving operation on the quantum object comprises: causing the dressing field source to start to provide the dressing field; causing the magnetic field source to start to provide the oscillating magnetic field in the second direction; causing the magnetic field source to stop providing the oscillating magnetic field; andcausing the dressing field source to stop providing the dressing field, such that at least one of (a) the population of the qubit state is transferred to the shelving state or (b) the population of the shelving state is transferred to the qubit state.

14. A system comprising: a confinement apparatus configured to confine one or more quantum objects at one or more target locations; a dressing field source configured to generate and provide a dressing field polarized in a first direction at a respective target location of the one or more target locations; a magnetic field source configured to generate and provide an oscillating magnetic field in a second direction at the respective target location, the first direction being orthogonal to the second direction; and a controller configured to control operation of the confinement apparatus, the dressing field source, and the magnetic field source, the controller configured to: cause, at an initial time, a dressing field source to start to provide a dressing field characterized by a dressing field frequency and a dressing field amplitude, wherein the dressing field frequency is detuned by a detuning from a transition frequency corresponding to a transition between a qubit state of a quantum object of the one or more quantum objects and a shelving state of the quantum object, the dressing field is polarized in a first direction, and the dressing field is caused to be incident on the quantum object; cause a magnetic field source to start to provide an oscillating magnetic field in a second direction, the second direction being orthogonal to the first direction, and the oscillating magnetic field oscillating with a magnetic field frequency, wherein the magnetic field frequency corresponds to a dressed frequency; cause the magnetic field source to stop providing the oscillating magnetic field; and cause, at a final time, the dressing field source to stop providing the dressing field, wherein at the final time, at least one of a population of the qubit state at the initial time has been transferred to the shelving state or a population of the shelving state at the initial time has been transferred to the qubit state.

15. The system of claim 14, wherein at least one of starting to provide the dressing field or stopping providing the dressing field is done adiabatically.

16. The system of claim 15, wherein starting to provide the dressing field adiabatically comprises causing the dressing field amplitude to increase from a minimum dressing field amplitude to a maximum dressing field amplitude over a time period that is longer than at least one of (a) one divided by the detuning or (b) one divided by the first dressed state frequency, and stopping providing the dressing field adiabatically comprises causing the dressing field amplitude to decrease from the maximum dressing field amplitude to the minimum dressing field amplitude over a time period that is longer than at least one of (a) one divided by the detuning or (b) one divided by the first dressed state frequency.

17. The system of any of claims 14, wherein starting to provide the oscillating magnetic field comprises smoothly increasing a magnetic field envelope amplitude of an envelope of the oscillating magnetic field from a minimum magnetic field envelope amplitude to a maximum magnetic field envelop amplitude and stopping providing the oscillating magnetic field comprises smoothly decreasing the magnetic field envelope amplitude from the maximum magnetic field envelope amplitude to the minimum magnetic field envelope amplitude.

18. The system of claim 17, wherein the magnetic field envelope amplitude is increased from the minimum magnetic field envelope amplitude to the maximum magnetic field envelope amplitude adiabatically and the magnetic field envelope amplitude is decreased from the maximum magnetic field envelope amplitude to the minimum magnetic field envelope amplitude adiabatically.

19. The system of any of claims 14, wherein the quantum object is confined by the confinement apparatus and the confinement apparatus defines a plane, the first direction being parallel to the plane.

20. The system of any of claims 14, wherein the dressing field being incident on the quantum object causes the qubit state and the shelving state to from a pair of dressed states and the dressing frequency is corresponds to a frequency difference between dressed states of the pair of dressed states.

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