Active stabilization of coherent controllers using nearby qubits

Abstract

Aspects of the present disclosure describe techniques involving active stabilization of a coherent controller using nearby qubits. In one aspect, a quantum information processing (QIP) system for stabilizing qubit phase damping is described, which includes providing first and second qubit ions, measuring magnetic field fluctuations using the second qubit ion, and generating one or more magnetic fields based on the measured magnetic field fluctuations, where the one or more magnetic fields are applied near the first qubit ion to cancel the magnetic field fluctuations and stabilize the phase damping of the first qubit ion. Another such QIP system provides first and second qubit ions, locks a local oscillator to a frequency reference associated with the second qubit ion, and uses the local oscillator to track the frequency of the first qubit ion based on the frequency reference. Methods associated with these QIP systems are also described.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Patent Application No. 17 / 362,810, filed June 29, 2021, which also claims priority to and the benefit of U.S. Provisional Patent Application No. 63 / 046,559, filed June 30, 2020, both entitled "Active Stabilization of a Coherent Controller Using Nearby Qubits," the contents of which are incorporated herein by reference in their entireties.

[0002] [Government Licensing Rights] This invention was made with U.S. government support under Contract No. W911NF-18-1-0218 awarded by the Army Research Office (ARO) and Contract No. 3130638 awarded by the Intelligence Advanced Research Projects Activity (IARPA). The U.S. government has certain rights in this invention. [Background technology]

[0003] Aspects of the present disclosure relate generally to controlling mechanisms that can lead to qubit degradation, and more particularly to techniques involving active stabilization of coherent controllers using nearby qubits.

[0004] Atomic hyperfine qubits are unique compared to other solid-state qubits (e.g., superconducting qubits) in that qubit quality (e.g., qubit stability over time) can approach perfection as long as the qubits are perfectly isolated. Two mechanisms that describe qubit degradation—amplitude decay, measured by relaxation time T1, and phase decay, measured by relaxation time T2—are generally limited by various system parameters. The shorter the periods T1 and T2, the shorter the period during which the qubit is stable enough to be used to perform quantum computations.

[0005] Therefore, it is desirable to develop techniques to increase the periods T1 and T2 in order to improve the stability of qubits used in quantum computing. Summary of the Invention

[0006] The following presents a simplified summary of one or more aspects in order to provide a basic understanding of such aspects. This summary is not an exhaustive overview of all contemplated aspects, and is not intended to identify key or critical elements of all aspects or to delineate the scope of any or all aspects. Its sole purpose is to present some concepts of one or more aspects in a simplified form as a prelude to the more detailed description that is presented later.

[0007] In one aspect of the present disclosure, a method for stabilizing phase damping of a qubit is described, comprising providing a first qubit ion and a second qubit ion, measuring magnetic field fluctuations using the second qubit ion, and generating one or more magnetic fields based on the measured magnetic field fluctuations, wherein the one or more magnetic fields are applied in the vicinity of the first qubit ion to cancel the magnetic field fluctuations and stabilize the phase damping of the first qubit ion.

[0008] In another aspect of the present disclosure, a quantum information processing (QIP) system for trapped ions is described, including at least one ion trap having a first qubit ion and a second qubit ion, one or more coils, and a stabilizer for stabilizing qubit phase damping, the stabilizer configured to measure magnetic field fluctuations using the second qubit ion and generate one or more magnetic fields using the one or more coils based on the measured magnetic field fluctuations, the one or more magnetic fields being applied in proximity to the first qubit ion to cancel the magnetic field fluctuations and stabilize the phase damping of the first qubit ion.

[0009] In another aspect of the present disclosure, a method for stabilizing phase damping of a qubit is described, comprising providing a first qubit ion and a second qubit ion, locking a local oscillator to a frequency reference associated with the second qubit ion, and using the local oscillator to track the frequency of the first qubit ion based on the frequency reference.

[0010] In another aspect of the present disclosure, a QIP system for trapped ions is described, including at least one ion trap having a first qubit ion and a second qubit ion, and a local oscillator, the local oscillator locked to a frequency reference associated with the second qubit ion, and the local oscillator configured to track the frequency of the first qubit ion based on the frequency reference.

[0011] In yet another aspect of the present disclosure, a computer-readable storage medium storing code having processor-executable instructions for stabilizing phase decay of a qubit is described.

[0012] To the accomplishment of the foregoing and related ends, the one or more aspects comprise the features hereinafter fully described and particularly pointed out in the claims. The following description and the annexed drawings set forth in detail certain illustrative features of the one or more aspects. These features are indicative, however, of but a few of the various ways in which the principles of the various aspects may be employed, and the description is intended to include all such aspects and their equivalents.

[0013] The disclosed aspects are hereinafter described in connection with the accompanying drawings, which are provided to illustrate, but not to limit, the disclosed aspects, and in which like reference numerals refer to like elements. [Brief explanation of the drawings]

[0014] [Figure 1] FIG. 1 shows a diagram of atomic ions trapped within a linear crystal or chain according to an aspect of the present disclosure. [Figure 2] FIG. 2 illustrates example energy levels of an atomic hyperfine qubit according to an embodiment of the present disclosure. [Figure 3A] FIG. 10 illustrates an example of local magnetic field cancellation according to aspects of the present disclosure. [Figure 3B] FIG. 10 illustrates an example of local magnetic field cancellation according to aspects of the present disclosure. [Figure 3C] FIG. 10 illustrates an example of local magnetic field cancellation according to aspects of the present disclosure. [Figure 4A] FIG. 1 illustrates an example of using juxtaposed atomic hyperfine qubits as a frequency reference, according to aspects of the present disclosure. [Figure 4B] FIG. 1 illustrates an example of using juxtaposed atomic hyperfine qubits as a frequency reference, according to aspects of the present disclosure. [Figure 4C] FIG. 1 illustrates an example of using juxtaposed atomic hyperfine qubits as a frequency reference, according to aspects of the present disclosure. [Figure 5] FIG. 1 illustrates an example of a computing device according to aspects of the present disclosure. [Figure 6] FIG. 1 is a block diagram illustrating an example of a quantum information processing (QIP) system, according to an aspect of the present disclosure. [Figure 7] 1 is a flow diagram illustrating an example method for stabilizing phase decay of a qubit according to aspects of the present disclosure. [Figure 8] 1 is a flow diagram illustrating an example method for stabilizing phase decay of a qubit according to aspects of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0015] The detailed description set forth below in connection with the accompanying drawings is intended as a description of various configurations and is not intended to represent the only configurations in which the concepts described herein may be practiced. The detailed description sets forth specific details for the purpose of providing a thorough understanding of various concepts. However, it will be apparent to those skilled in the art that these concepts may be practiced without these specific details. In some instances, well-known components are shown in block diagram form to avoid obscuring such concepts.

[0016] The detailed description includes a technique that can be used to eliminate phase errors in an ensemble of atomic qubits by sacrificing one or more qubits as an atomic clock for a local oscillator that can be used to track the phase of all other qubits. This eliminates nearly all idle decoherence in a particular qubit within the ensemble. Atomic qubits may generally refer to atom-based qubits, including, for example, atomic-ion qubits. As noted above, atomic hyperfine qubits are unique compared to other solid-state qubits in that qubit quality can approach perfection, as long as the qubits are perfectly isolated. To improve the stability of qubits used in quantum computing, two mechanisms that describe qubit degradation—amplitude decay, measured by T1, and phase decay, measured by T2—can be made arbitrarily long.

[0017] In general, a quantum bit (qubit) can be expressed by the following formula:

number

[0018] The decay of the relative amplitude (θ) arises from the tendency of the system to move from a higher energy population to a lower energy population. The decay of such a two-level system is characterized in nuclear magnetic resonance (NMR) by the relaxation time T, which is a measure of the amplitude decay. Apart from the relative amplitude, this two-level system also has an energy difference and therefore a unique frequency-time dependence, where the frequency is the qubit frequency ω. q Therefore, if the energy difference of this system is stable, and there is no movement or fluctuation, ωt is predictable and can be ignored, because knowledge of the qubit frequency allows precise knowledge of the behavior of the qubit at any time. Therefore, referring to the relative phase φ, the equation e when ωt can be ignored, since the qubit frequency is known and all movements are predictable, is i(ωt+φ) will be referred to.

[0019] However, in a real qubit system, the energy difference of the two-level system can fluctuate. This fluctuation can be reflected in the qubit frequency, and because we do not know exactly how the qubit frequency will fluctuate, making its behavior unpredictable, phase uncertainty can accumulate over time. This can eliminate the source of relative phase for the qubit. For example, a local clock or local oscillator can be used to count the oscillations (e.g., frequency) of the qubit, and the local clock typically operates at a predetermined frequency based on an atomic source or atomic reference. If the qubit runs off this local clock and there is no knowledge of the qubit's energy fluctuations, uncertainty can accumulate, and this uncertainty can cause a phase shift between the local clock (or local oscillator) and the qubit. That is, if the qubit's phase shifts without knowledge of the phase shift, a phase shift occurs between the local clock (or local oscillator) and the qubit. In NMR, this dephasing is characterized by the relaxation time T2, which is a measure of phase decay. Thus, T2 is a measure of the time interval over which coherence is maintained, i.e., the time before the phase of the qubit becomes untrackable as a result of a phase shift between the local clock and the qubit.

[0020] Superconducting qubits can typically maintain this coherence for about 1 nanosecond (ns), with recent results achieving high coherence of 50 microseconds (μs). However, because these types of qubits are constructed in circuits, they are inherently coupled to their environment. If these types of qubits become coupled to nearby electric fields, or if even a single atom moves, it becomes very difficult to know the fluctuations in the qubit frequency and the amount of uncertainty accumulated in the phase.

[0021] In contrast to the way superconducting qubits are structured, atomic hyperfine qubits use two ground states of atoms (or atomic ions) separated by hyperfine interactions. The hyperfine splitting is caused by the interaction of nuclear spins, which are all in the ground state and very well isolated from their environment. In these types of qubits, the intrinsic T1 times are measured over thousands of years (e.g., up to 10,000 years), significantly longer than those achievable with superconducting qubits. The extremely long T1 intervals in atomic hyperfine qubits make spontaneous decay highly unlikely for most quantum operations. For all practical purposes, spontaneous decay is unlikely in atomic hyperfine qubits, as it is in superconducting qubits.

[0022] In practice, however, the length of T1 may be limited by collisions with residual gas molecules in the vacuum chamber. These gases may collide with the qubit and flip its nuclear spin, affecting the qubit. Achieving a vacuum deep enough to avoid collisions for 10,000 years without decaying to T1 may be difficult. However, it is possible to achieve a vacuum deep enough to allow one collision every 30 minutes to an hour, and even to extend the collision rate to once a day or more. It is clear that the longer the time scales over which these collisions occur, the better the vacuum, and in this case, T1 is unlikely to be a factor for atomic hyperfine qubits.

[0023] On the other hand, T2 is determined by the ability to track the time-dependent relative oscillations that the two qubit states experience with respect to each other and by the energy difference between the two qubit levels. Therefore, T2 can be more difficult to improve because the energy difference can be affected by background noise such as electrical or magnetic hum (e.g., 50 Hz, 60 Hz, 100 Hz, or 120 Hz, depending on the local power line frequency). For atomic hyperfine qubits, T2 can be approximately 1 second, and the value of T2 is related to the energy or phase of the qubit relative to a local clock.

[0024] In current standard metrology, the local clock used in quantum computing can be based on the cesium (Cs) atomic clock used to define a second (e.g., to define a unit of time). Cesium atoms have a similar hyperfine structure (e.g., similar physical properties) to the structure of atoms used in hyperfine qubits (e.g., ytterbium atoms). That is, in cesium atoms, the electron spin and nuclear spin couple to form a hyperfine splitting. Two states within the cesium atom can then be used to define a second based on the hyperfine interaction between the two states. The choice of cesium can be arbitrary, and can be a rubidium (Rb) atom, or 171 Yb + , 133 Ba + , or 43 Ca + Other atomic species with similar hyperfine ground states, such as atomic ions, may be suitable as standards for defining the second (or frequency). In a typically used example, a local clock or oscillator is coupled to a Rb atomic clock and locks to the Rb transition to produce a frequency of approximately 6.3 GHz.

[0025] As described in more detail below, instead of using a Cs or Rb atomic clock as an absolute frequency reference (e.g., atomic source or atomic reference) for a local clock, an atomic hyperfine qubit can be used as an absolute atomic clock for quantum computation. That is, the local clock can be used as a frequency reference that defines time for one structure of atomic hyperfine qubits, rather than a commercially available atomic clock. In such a case, instead of tying time to the Cs or Rb atoms, time can be tied to the ytterbium atoms within the atomic hyperfine qubit. When this is done, T2 will be phase-continuous because any changes to the ytterbium-based hyperfine qubit being tracked will be experienced identically by the atomic hyperfine qubit used as the frequency reference.

[0026] As mentioned above, for atomic hyperfine qubits, where T2 can typically be around 1 second, coupling time to the atomic hyperfine qubit instead of a Cs or Rb atomic clock can make the local clock very accurate and improve T2. On the other hand, for superconducting qubits, where T2 is on the order of 50 μs, the accuracy of the local clock is not as important. When T2 is on the order of 1 second or tens of seconds, the local clock can be 10 μs. -11 For example, the Rb atomic clock currently requires an accuracy of 10 -12 By linking time to atomic hyperfine qubits, the accuracy of local clocks can be increased by 10 -18 This means that we can achieve precision six orders of magnitude higher than what is typically achievable today. For atomic hyperfine qubits, this also means that T2 can be extended from 1 second to 1 million seconds. However, deviations from the provided reference frequency can be attributed to how well time is tying to the reference atomic hyperfine qubit. The looser this tying, the more prone it is to phase drift and the more likely it is to develop phase misalignment. This makes it important to properly tying time to the reference atomic hyperfine qubit to take advantage of the benefits of using atomic hyperfine qubits as atomic references for local clocks.

[0027] As noted above, there may be other mechanisms that affect T2 by causing fluctuations in the energy difference of atomic hyperfine qubits, such as the presence of 60 Hz noise (or other noise frequencies) from power lines. For example, better isolation, such as shielding to prevent 60 Hz magnetic fields from coupling to the qubits, can extend T2 (e.g., from 1 second to over 1000 seconds). This can be achieved simply by implementing better magnetic field shielding, without considering the additional benefit of better coupling of the local clock (e.g., a radio frequency (RF) oscillator) to the Rb-atom-based atomic clock, and without considering the potential improvements that might result from coupling the local clock to the atomic hyperfine qubits instead of a Cs-atom-based or Rb-atom-based atomic clock. In other words, the combination of good coupling techniques, better shielding, and the use of atomic hyperfine qubits as frequency references can provide the necessary improvement in T2, whether implemented individually or in combination.

[0028] Qubits based on superconducting structures cannot achieve the kinds of improvements to T1 and T2 that are possible with atomic hyperfine qubits, and at least some of these improvements are based on various techniques described in this disclosure. For example, improvements to T1 for atomic hyperfine qubits are primarily related to providing a better vacuum to reduce the collision rate and bring the time interval closer to 10,000 years. T2 is limited by the degree of coupling between the RF oscillator and the atomic clock (e.g., a Rb atom-based clock, a Cs atom-based clock) and environmental fluctuations (e.g., 60 Hz magnetic field noise) that can couple to the qubit energy (e.g., the energy difference between energy levels). As described above, the solution needed to improve the T2 time interval is to ensure as much as possible that the classical RF oscillator is locked to the atomic reference, which is a system implementation issue, and to provide good shielding to avoid fluctuations due to environmental influences. These may be implemented independently or in combination. Also, as described herein, the T2 time interval can be improved by coupling the classical RF oscillator to the atomic hyperfine qubit reference.

[0029] This disclosure details methods for improving the stability of atomic standards by using one or more qubits in a chain of qubits (e.g., a chain of atomic hyperfine qubits) to measure local environmental conditions (e.g., local magnetic fields) in the vicinity of the remaining qubits in the chain so that the effects of the local environmental conditions can be canceled out across the entire system. For example, if the qubits in the chain are ytterbium-based qubits, one or more ytterbium-based qubits can be used to measure local magnetic fields (e.g., fluctuations or changes in the local magnetic field). Qubits in a chain are typically spaced about 5 microns apart, making the entire chain about 200 microns in a 32-qubit implementation. By placing qubits in the chain or nearby chains relatively close together, any one qubit can be used to accurately read the local magnetic field affecting all qubits, especially since the wavelength of 60 Hz noise is much longer than the chain and its effect on the qubits is likely to be nearly identical. The one or more qubits used to probe or measure the local magnetic field need not be ytterbium-based qubits but could be qubits based on other atoms or species.

[0030] As noted above, atomic hyperfine qubits use two levels for the qubit states |0> and |1>. However, these levels tend to be largely insensitive to magnetic fields. Other levels in the hyperfine structure are more sensitive to magnetic fields and can be used to measure local magnetic fields. These other levels are 10,000 times more sensitive to magnetic fields than the levels used for the qubit states |0> and |1>. Using these other levels to measure magnetic fields can implement a form of feedback control to stabilize the magnetic field by nulling the effect of the local magnetic field. This can further reduce the sensitivity of energy levels that are largely insensitive to magnetic fields (e.g., qubit states |0> and |1>). For example, if the magnetic field-zeroing process reduces the local magnetic field by a factor of 10,000, the sensitivity of energy levels that are largely insensitive to magnetic fields (e.g., qubit states |0> and |1>) can be reduced by an additional three or four orders of magnitude.

[0031] Thus, as proposed in this disclosure, one or more qubits in a chain, which may be the same qubit type as used for quantum computing or a different qubit type (e.g., a spectator qubit in the chain), can be used to probe the local environment (e.g., probe or measure the local magnetic field) and use the results of the probe to provide a very stable environment as seen by the qubits in the chain. This accomplishes two things: it provides good magnetic field shielding to avoid fluctuations caused by environmental effects, and it uses nearby qubits to probe and stabilize the local environment. One or more qubits in the chain then become less susceptible to local magnetic fields as a result of the shielding and stabilization provided by the local probing.

[0032] As mentioned above, another improvement is to lock a local clock or local oscillator to one or more atomic hyperfine qubits, so that with better magnetic field shielding and / or qubit stabilization, the reference qubit can become a more stable qubit to use as a frequency reference. This qubit will be three or four orders of magnitude smaller than before due to better shielding and magnetic field stabilization by nulling the local magnetic field, but it may still fluctuate slightly. Once the local oscillator is locked to one or more stable qubits, even if it still fluctuates slightly, both the qubits and the local oscillator move together so that no fluctuations occur (e.g., no phase shift occurs). Therefore, by coupling the local oscillator to the qubit itself or to a nearby qubit (sometimes called a spectator qubit that is nearby but does not participate in the quantum computation), fluctuations in the qubit may not cause a phase shift because the local oscillator sees the same fluctuations. That is, the device used to count oscillations (e.g., the local clock or local oscillator) and the entity being counted (e.g., the qubit) are locked to each other. This allows the coherence of the system and therefore the T2 time interval to be significantly increased.

[0033] Thus, atomic hyperfine qubits offer several unique advantages over other solid-state qubits (e.g., superconducting qubits) in that qubit quality can approach perfection as long as the qubits are perfectly isolated. Using various techniques described in this disclosure, two mechanisms that describe qubit degradation—amplitude decay, measured by T1, and phase decay, measured by T2—can be significantly improved. While improved vacuum quality is beneficial, currently achievable vacuums may be good enough not to limit qubit T1 for most applications. As quantum computers or quantum information processing systems grow in size (e.g., more qubits) and computations become longer, it may be necessary to continue improving collision rates. The primary limitations of current qubits are (1) residual magnetic field fluctuations, primarily due to 60 Hz noise from power lines, and (2) the ability to stabilize / lock the frequency of a (classical) experimental clock (e.g., a local clock or local oscillator) to match the qubit frequency.

[0034] In the following, various aspects associated with the solution to the above problem will be described in more detail with reference to FIGS.

[0035] FIG. 1 is a diagram 100 showing a plurality of atomic ions 105 (e.g., used as atomic hyperfine qubits) trapped in a linear crystal or chain 110 using a linear RF Paul trap, simply referred to as an ion trap, typically located in a vacuum chamber. These atomic ions 105 can then be used as quantum bits (e.g., qubits 105) for quantum computing. In the example shown in FIG. 1 , the vacuum chamber of the quantum system contains a plurality (e.g., N>1, where N is a number equal to or greater than 100, and in some implementations N=32) of atomic ytterbium ions (e.g., ytterbium ions) confined in chain 110 and laser-cooled to near quiescence. 171 Yb + The number of trapped atomic ions is configurable, and more or fewer atomic ions may be trapped. 171 Yb+ The chain 110 is illuminated with laser (optical) radiation tuned to the resonance of the atomic ions, and the fluorescence of the atomic ions is imaged on a camera. In this example, the atomic ions are separated from each other by a distance 115 of approximately 5 microns (μm), as indicated by the fluorescence. The distance 115 can be, for example, in the range of approximately 3 μm to 6 μm. The separation of the atomic ions is determined by the balance between the external confinement force and the Coulomb repulsion force. The chain 110 contains an alkaline earth metal (Be + , Mg + , Ca + , Sr + , Ba + ) and certain transition metals (Zn + , Hg + , Cd + and Yb + Simple atomic ions with isolated outer electrons, such as |, can be used. Within these atomic ions, qubits can be represented by two stable electronic levels, often characterized by two qubit states |↑) and |↓), or effective spins with equivalent |1〉 and |0〉.

[0036] The polarization of the Raman beam required to drive the qubit transitions depends on the atomic structure of the qubit levels and their coupling to excited states. As an example, the present disclosure describes a system in which coherent stimulated Raman transitions, such as those shown in energy level diagram 200 of FIG. 2, are labeled |0〉 and |1〉 and have frequencies ω q (For example, ω q / 2π=12.6 GHz), and the σ + / σ + or σ _ / σ _ The Raman process is driven by a 355 nm laser field with either polarization (e.g., any Raman process can be performed with polarization σ + or σ _ Coupling the two qubit states (driven by both beams) 171 Yb +Consider a system (e.g., an atomic hyperfine system). In addition to the |0〉 and |1〉 energy levels of the two qubit states, diagram 200 also shows other energy levels, some of which may be more sensitive to magnetic fields or other environmental conditions than the energy levels used for the qubit states. As noted above, 171 Yb + Other systems having similar ultrastructure to the system may be used in connection with the various techniques described in this disclosure.

[0037] 3A-3C are diagrams 300a-300c illustrating various examples of local magnetic field cancellation or nulling according to embodiments of the present disclosure. Generally, to stabilize the effects of the magnetic field, a magnetic shield is first constructed around the qubit using a highly permeable material (e.g., mu-metal, highly conductive copper, or a superconducting material at cryogenic temperatures). The magnetic field can be further stabilized by using another atom co-trapped with the qubit ion (or in a nearby trap) to measure the qubit's local magnetic field using atomic energy levels that are highly sensitive to magnetic fields (as opposed to the qubit state, which is not very sensitive to magnetic fields). A feedback loop can then be implemented to add a canceling magnetic field to stabilize the local magnetic field environment.

[0038] Diagram 300a illustrates an implementation of a stabilization technique that improves the overall T2 time interval of one or more qubits 105 in a chain 110 by reducing the amount of magnetic field in the vicinity of the qubits 105.

[0039] One aspect of the stabilization technique is to use magnetic field shields 340 to reduce the amount of magnetic field (e.g., magnetic field fluctuations) experienced by the qubits 105 in the chain 110. The magnetic field shields 340 (also simply referred to as magnetic shields) may be used to shield the qubits 105 from static or low-frequency magnetic fields. The magnetic field shields 340 may be formed of materials with high magnetic permeability, including one or more of mu-metal, highly conductive copper, or superconducting materials at cryogenic temperatures. Mu-metal may be composed of a nickel-iron soft ferromagnetic alloy with very high magnetic permeability.

[0040] In this example, qubit 105a, which may be an atomic hyperfine qubit, may be used for quantum computation. Improving the stability of qubit 105a (e.g., a better T2, assuming the provided vacuum is sufficient to avoid the T1 limit) can improve the overall performance of the quantum system performing the quantum computation. Qubit 105b may be another hyperfine qubit adjacent or nearby to qubit 105a so as to experience the same local environmental conditions as qubit 105a. Qubits 105a and 105b may also be referred to as juxtaposed qubits. Qubit 105b may be referred to as a probing qubit (e.g., probing qubit 105b). While shown next to qubit 105a, probing qubit 105b need not be directly adjacent to qubit 105a, as long as it is close enough to experience the same environmental conditions. Probing qubit 105b does not participate in the quantum computation of qubit 105a and may instead be considered a spectator qubit. Probing qubit 105b may thereby be used to measure or probe the local magnetic field 315 affecting qubit 105a. As noted above, fluctuations in local magnetic field 315 are lower than would otherwise be the case due to the use of magnetic field shield 340. Furthermore, probing qubit 105b may be based on a different atom or ion than qubit 105a, in terms of atomic species or isotopes.

[0041] The stabilizer 305 may be used to provide a feedback mechanism for canceling or nulling the local magnetic field 315. The stabilizer 305 may include a local magnetic field measurement component 310 configured to measure or probe the local magnetic field 315 using magnetic-field-sensitive energy levels in the qubit 105b. While not shown, the local magnetic field measurement component 310 may include and / or control various light sources and / or elements to perform the measurements. The stabilizer 305 may also include a cancellation magnetic field generation component 320 configured to receive information from the measurements made by the local magnetic field measurement component 310 and use that information to generate signals to apply to one or more coils 330 to generate one or more magnetic fields to cancel or null (or at least significantly reduce) the local magnetic field 315. In one implementation, one or more coils 330 may be present in a quantum computer or quantum information processing system to counter other magnetic fields, such as the Earth's magnetic field, and may be used to stabilize the qubit 105 as described above. In another implementation, one or more coils 330 may be uniquely configured to be used to stabilize the qubit 105, and a separate set of coils may be used to address other magnetic fields.

[0042] Diagrams 300b and 300c illustrate other implementations for stabilizing the T2 time interval of one or more qubits 105 in a chain 110. In these examples, qubit 105a is in a first chain 110a implemented in a first ion trap, and probing qubit 105b is in a second chain 110b implemented in a second ion trap adjacent or nearby to the first ion trap, such that probing qubit 105b experiences the same environmental conditions (e.g., the same local magnetic field 315) as qubit 105a. Alternatively, the first chain 110a and second chain 110b in Diagrams 300b and 300c may be implemented in different regions of the same ion trap.

[0043] It should be understood that the local magnetic field 315 may cover multiple qubits 105a and the stabilization mechanisms described in connection with Figures 300a-c may be used to stabilize the multiple qubits 105a. Similarly, multiple probing qubits 105b may be probed to generate the information necessary to generate a canceling or zero magnetic field.

[0044] 4A-4C are diagrams 400a-400c illustrating various examples of using a collocated atomic hyperfine qubit as a frequency reference, according to embodiments of the present disclosure. Currently, for the local oscillator in a local clock, a stable oscillator is locked to a commercially available atomic source (such as Rb) to track the qubit frequency. Current qubit coherence times are limited by the relative stability between the Rb atomic reference and the qubit state. Another approach is to lock the local oscillator using one or more nearby qubits (which experience the same environment, such as a magnetic field) as a frequency reference, thereby eliminating any differential energy level shifts resulting from the qubit and atomic reference (Rb in the current setup). Essentially, by using the qubit itself as a frequency reference, coherence can be maintained indefinitely, with the precision required to lock the local oscillator to the qubit's atomic reference.

[0045] Diagram 400a illustrates a typical implementation that uses an atomic reference (e.g., a Cs atomic clock or an Rb atomic clock) where a local RF oscillator (LO) 420 in a local clock 410 locks to a reference frequency provided by the atomic reference 430. How well these two are coupled can affect the overall performance of the system.

[0046] Local clock 410 can then be used to track (e.g., track the frequency of) the oscillations of qubits 105a (e.g., atomic hyperfine qubits) in chain 110. As noted above, changes in the energy difference of qubits 105a due to environmental conditions can cause qubits 105a and local clock 410 to shift out of phase.

[0047] Diagram 400b illustrates an implementation of a stabilization technique that reduces or eliminates phase shifts by improving the coherence and overall T2 time interval of one or more qubits 105 in chain 110. In this example, instead of being tied to a commercially available atomic standard (e.g., a Cs atomic clock or an Rb atomic clock), local clock 410 and local RF oscillator 420 are tied to qubit 105c (also referred to as reference qubit 105c) in chain 110. In such an implementation, any fluctuations in qubit 105a caused by environmental conditions are experienced by reference qubit 105c, making phase shifts less likely to occur.

[0048] Diagram 400c shows an alternative implementation, similar to diagram 400b, in which qubit 105a is in a first chain 110a implemented in a first ion trap, and reference qubit 105c is in a second chain 110b implemented in a second ion trap adjacent or nearby to the first ion trap so that it experiences the same environmental conditions as qubit 105a. Additionally, any fluctuations in qubit 105a caused by environmental conditions are also experienced by reference qubit 105c, making it less likely to become out of phase. Alternatively, the first chain 110a and second chain 110b in diagram 400c may be implemented in different regions of the same ion trap.

[0049] 3A-3C and 4A-4C may be combined, such that probing qubit 106b can be used to measure or probe local environmental conditions and cancel or null their effects, and reference qubit 105c can be used as an atomic frequency reference for a local clock or local oscillator. Probing qubit 105b and reference qubit 105c may be different qubits or the same qubit with respect to atomic species or isotopes.

[0050] Referring to FIG. 5, an example of a computing device 500 is shown. The computing device 500 can represent, for example, a single computing device, multiple computing devices, or a distributed computing system. The computing device 500 may be configured as a quantum computer (e.g., a quantum information processing (QIP) system), a classical computer, or a combination of quantum and classical computing capabilities. For example, the computing device 500 may be used to process information using quantum algorithms based on trapped ion technology and thus may implement methods or techniques for actively stabilizing a coherent controller using nearby qubits (e.g., improving the T2 time interval). The computing device 500 may also implement techniques for improving the T1 time interval, such as better vacuum technology. A general example of a computing device 500 as a QIP system capable of implementing various techniques described herein is shown in the example illustrated in FIG. 6.

[0051] The computing device 500 may include a processor 510 for performing processing functions associated with one or more of the features described herein. The processor 510 may include a single or multiple sets of processors or multi-core processors. Furthermore, the processor 510 may be implemented as an integrated and / or distributed processing system. The processor 510 may include a central processing unit (CPU), a quantum processing unit (QPU), a graphics processing unit (GPU), or a combination of these types of processors. If quantum operations are supported, the processor 510 may include at least trapped ions to perform the quantum operations. In one aspect, the processor 510 may refer to the general processor of the computing device 500, which may also include additional processors 510 to perform more specific functions, such as functions for actively stabilizing a coherent controller using nearby qubits, canceling or nulling one or both of the qubit's local environmental conditions, or using a qubit as an atomic frequency reference instead of a commercially available atomic clock.

[0052] In one example, computing device 500 may include memory 520 that stores instructions executable by processor 510 to perform functions described herein. In one implementation, for example, memory 520 may correspond to a computer-readable storage medium that stores code or instructions for performing one or more functions or operations described herein. In one example, memory 520 may include instructions for performing aspects of method 700 and method 800, described below in connection with FIGS. 7 and 8, respectively. Like processor 510, memory 520 may refer to the general memory of computing device 6500, which may include additional memory 520 to store instructions and / or data for more specific functions, such as instructions and / or data for actively stabilizing a coherent controller that uses nearby qubits.

[0053] Additionally, computing device 500 may include a communications component 530 that provides for establishing and maintaining communications with one or more parties using hardware, software, and services as described herein. Communications component 530 may facilitate communications between components on computing device 500 and between computing device 500 and external devices, such as devices located over a communications network and / or devices serially or locally connected to computing device 500. For example, communications component 530 may include one or more buses and may further include transmit chain and receive chain components associated with transmitters and receivers, respectively, operable to interface with external devices.

[0054] Additionally, computing device 500 may include data store 540, which may be any suitable combination of hardware and / or software that provides mass storage of information, databases, and programs used in connection with the implementations described herein. For example, data store 540 may be a data repository for operating system 560 (e.g., a classical OS or a quantum OS). In one implementation, data store 540 may include memory 520.

[0055] Computing device 500 may also include a user interface component 550 operable to receive input from a user of computing device 500 and further operable to generate output for presentation to the user or to provide (directly or indirectly) to a different system. User interface component 550 may include one or more input devices, including, but not limited to, a keyboard, a number pad, a mouse, a touch-sensitive display, a digitizer, navigation keys, function keys, a microphone, a voice recognition component, any other mechanism capable of receiving input from a user, or any combination thereof. Additionally, user interface component 550 may include one or more output devices, including, but not limited to, a display, a speaker, a haptic feedback mechanism, a printer, any other mechanism capable of presenting output to a user, or any combination thereof.

[0056] In one implementation, the user interface component 550 may send and / or receive messages corresponding to the operation of the operating system 560. The processor 510 may also execute, and the memory 520 or the data store 540 may store, the operating system 560 and / or applications or programs.

[0057] When computing device 500 is implemented as part of a cloud-based infrastructure solution, user interface component 550 may be used to enable users of the cloud-based infrastructure solution to interact with computing device 500 remotely.

[0058] FIG. 6 is a block diagram illustrating an example of a QIP system 600 according to an embodiment of the present disclosure. QIP system 600 may also be referred to as a quantum computing system, a computer device, etc. In one embodiment, QIP system 600 may correspond to part of a quantum computer implementation of computer device 500 of FIG. 5. Furthermore, embodiments of FIGS. 300a, 300b, 300c, 400a, 400b, and 400c may be included in QIP system 600. For example, embodiments of these figures may be implemented in or in association with chamber 650 of QIP system 600.

[0059] QIP system 600 may include a source 660 that provides atomic species (e.g., a flux of neutral atoms) to chamber 650 (e.g., a vacuum chamber associated with chain 110 in FIG. 1 ), which has an ion trap 670 that traps the atomic species once ionized (e.g., photoionized) by optical controller 620. Light source 630 within optical controller 620 may include one or more laser sources (e.g., optical or laser beam sources) that can be used to ionize atomic species, control atomic ions, fluorescence of atomic ions that can be monitored and tracked by image processing algorithms operating in imaging system 640 within optical controller 620, and / or perform tracking, probing, and / or measurement functions described herein. In one aspect, light source 630 may be implemented separately from optical controller 620.

[0060] Imaging system 640 may include a high-resolution imager (e.g., a CCD camera) for monitoring the atomic ions while they are being provided to the ion trap or after they have been delivered to ion trap 670. In one aspect, imaging system 640 may be implemented separately from optical controller 620, although the use of fluorescence to detect, identify, and label atomic ions using image processing algorithms may need to be coordinated with optical controller 620.

[0061] QIP system 600 may also include an algorithm component 610 that may operate in conjunction with other portions of QIP system 600 (not shown) to perform quantum algorithms or operations, including a stack or sequence of combinatorial single-qubit and / or multi-qubit operations (e.g., two-qubit operations) and extended quantum computation. As such, algorithm component 610 may provide instructions to various components of QIP system 600 (e.g., optical controller 620) to enable implementation of quantum algorithms or operations, such that various techniques described herein can be implemented to improve qubit quality.

[0062] 6, parts of QIP system 600 include stabilizer 305, local clock 410, and coil 330. Stabilizer 305 and local clock 410 may operate in conjunction with other components or subcomponents of QIP system 600, including, for example, optical controller 620 and the chain of ions formed in ion trap 670. Coil 330 may be located in different locations within QIP system 600, and in some implementations may be a coil located external and / or internal to chamber 650.

[0063] 7, a method 700 for stabilizing phase decay in a qubit (e.g., improving the T2 time interval of the qubit) is described. In one aspect, method 700 may be performed in a computer system such as computing device 500 described above, which may perform the functions of method 700 using processor 510, memory 520, data store 540, and / or operating system 560, etc. Similarly, the functions of method 700 may be performed by one or more components of a QIP system, such as QIP system 600 and its components (e.g., stabilizer 305, optical controller 620). Accordingly, each aspect described herein with respect to method 700 may be implemented in computing device 500 and QIP system 600, alone or in combination with other aspects.

[0064] At 702, method 700 includes providing a first qubit ion and a second qubit ion (see, eg, qubits 105a and 105b in FIGS. 3A-3C).

[0065] At 704, method 700 includes measuring magnetic field fluctuations using the second qubit ions (see, eg, stabilizer 305 and local magnetic field measurement component 310 of FIGS. 3A-3C).

[0066] At 706, the method 700 includes generating, based on the measured magnetic field fluctuations, one or more magnetic fields that are applied in the vicinity of the first qubit ion to cancel the magnetic field fluctuations and stabilize the phase decay of the first qubit ion (see, e.g., stabilizer 305, cancellation magnetic field generating component 320, and coil 330 in Figures 3A-3C).

[0067] Method 700 is described with respect to one first qubit ion and one second qubit ion. However, it should be understood that method 700 need not be so limited and may be performed with one or more first qubit ions and one or more second qubit ions. For example, method 700 may be performed with at least one first qubit ion and one second qubit ion, one first qubit ion and at least one second qubit ion, or at least one first qubit ion and at least one second qubit ion.

[0068] In one aspect of method 700, the first qubit ion and the second qubit ion are atomic hyperfine qubits.

[0069] In one aspect of method 700, the first qubit ion and the second qubit ion are of the same atomic ion or same atomic species (eg, they are both ytterbium atom-based qubits).

[0070] In one aspect of method 700, the first qubit ion and the second qubit ion are of different atomic ions or different atomic species.

[0071] In one aspect of method 700, the first qubit ion and the second qubit ion are atomic hyperfine qubits, the first qubit ion being addressable with light at a first wavelength and the second qubit ion being addressable with light at a second wavelength different from the first wavelength. In one example, the first qubit ion is: 171 Yb + and the second qubit ion is 133 Ba + It consists of:

[0072] In one aspect of method 700, the first qubit and the second qubit are co-trapped in the same ion trap (see, eg, FIG. 3A).

[0073] In one aspect of method 700, a first qubit is trapped in a first ion trap and a second qubit is trapped in a second ion trap adjacent to the first ion trap (see, eg, FIGS. 3B and 3C).

[0074] In one aspect of method 700, the second qubit ion has an energy level that is sensitive to a magnetic field, and measuring the magnetic field fluctuation using the second qubit ion includes measuring the magnetic field fluctuation using the magnetic field-sensitive energy level of the second qubit ion. The second qubit ion may have other energy levels that are not sensitive to a magnetic field. The magnetic field-sensitive energy levels may include, for example, Zeeman levels. Further, measuring the magnetic field fluctuation using the second qubit ion includes optically probing the magnetic field-sensitive energy levels of the second qubit ion (e.g., by performing optical probing using optical controller 620) to detect characteristics of the magnetic field fluctuation.

[0075] In one aspect of the method 700, the magnetic field fluctuations include 60 Hz noise. In other examples, the noise may be 50 Hz, 100 Hz, and / or 120 Hz noise.

[0076] In one aspect of method 700, method 700 may further include providing a magnetic shield (e.g., magnetic field shield 340) configured to reduce magnetic field fluctuations in the vicinity of the first qubit ions and the second qubit ions, the magnetic shield being formed of a material having high magnetic permeability, including one or more of mu-metal, highly conductive copper, or a superconducting material at cryogenic temperatures.

[0077] In one aspect of method 700, a sequence including measuring magnetic field variations and generating one or more magnetic fields that cancel the magnetic field variations is repeated as part of a feedback loop. In some implementations, the feedback loop may have a bandwidth of at least 1 KHz.

[0078] In one aspect of method 700, the first qubit ion is configured to participate in the quantum computation and the second qubit ion is a spectator qubit configured not to participate in the quantum computation.

[0079] In one aspect of method 700, method 700 further includes providing one or more additional qubit ions (e.g., in addition to the first qubit ion and the second qubit ion), where one or more magnetic fields are applied in proximity to the first qubit ion and the one or more additional qubit ions to cancel magnetic field fluctuations and stabilize phase damping of the first qubit ion and the one or more additional qubit ions. The one or more additional qubit ions may be in the same ion trap as the first qubit ion or in a nearby ion trap.

[0080] In connection with method 700, a QIP system may be used to perform such method. The QIP system may be an implementation of QIP system 600 including at least one ion trap (e.g., one or more ion traps 670) having first and second qubit ions, one or more coils (e.g., one or more coils 330), and a stabilizer (e.g., stabilizer 305) that stabilizes the phase decay of the qubits. In this implementation, the stabilizer is configured to measure magnetic field fluctuations using the second qubit ions (e.g., by local magnetic field measurement component 310 in stabilizer 305) and generate, using one or more coils, one or more magnetic fields based on the measured magnetic field fluctuations (e.g., by cancellation magnetic field generation component 320 in stabilizer 305), which are applied in the vicinity of the first qubit ions (e.g., by coils 330) to cancel the magnetic field fluctuations and stabilize the phase decay of the first qubit ions.

[0081] Method 700 for stabilizing the phase decay of a quantum bit may also be implemented by a computer-readable storage medium (e.g., memory 520 and / or data store 540) storing code having instructions executable by a processor (e.g., processor 510).

[0082] 8, a method 800 for stabilizing phase decay in a qubit (e.g., improving the time interval of T2) is described. In one aspect, method 800 may be performed in a computer system such as computing device 500 described above, which may perform the functions of method 700 using processor 510, memory 520, data store 540, and / or operating system 560, etc. Similarly, the functions of method 800 may be performed by one or more components of a QIP system, such as QIP system 600 and its components (e.g., stabilizer 305, optical controller 620). Accordingly, each aspect described herein with respect to method 800 may be implemented in computing device 500 and QIP system 600, alone or in combination with other aspects.

[0083] At 802, method 800 includes providing a first qubit ion and a second qubit ion (see, eg, qubits 105a and 105c in FIGS. 4B and 4C).

[0084] At 804, method 800 includes locking a local oscillator to a frequency reference associated with the second qubit ion (see, for example, local RF oscillator 420 in local clock 410 locked to the atomic reference provided by qubit 105c in Figures 4B and 4C).

[0085] At 806, method 800 includes tracking the frequency of the first qubit ion based on a frequency reference using a local oscillator (see, e.g., tracking qubit 105a with local RF oscillator 420 in local clock 410).

[0086] Method 800 is described with respect to one first qubit ion and one second qubit ion. However, it should be understood that method 800 need not be so limited and may be performed with one or more first qubit ions and one or more second qubit ions. For example, method 800 may be performed with at least one first qubit ion and one second qubit ion, one first qubit ion and at least one second qubit ion, or at least one first qubit ion and at least one second qubit ion.

[0087] In one aspect of method 800, the first qubit ion and the second qubit ion have the same atomic hyperfine structure.

[0088] In one aspect of method 800, the first qubit ion and the second qubit ion are different ionic species.

[0089] In one aspect of method 800, the first qubit ion and the second qubit ion have atomic hyperfine structures and are addressable with different wavelengths of light.

[0090] In one aspect of method 800, the first qubit ion is 171 Yb + and the second qubit ion is 133 Ba + It consists of:

[0091] In one aspect of method 800, the first qubit ion and the second qubit ion are proximate to each other and experience substantially the same environmental variations. The first qubit ion and the second qubit ion are proximate to each other by being in the same ion trap or in separate adjacent ion traps.

[0092] In one aspect of method 800, method 800 further includes measuring magnetic field fluctuations using the second qubit ion (e.g., by local magnetic field measurement component 310 in stabilizer 305) and generating one or more magnetic fields based on the measured magnetic field fluctuations (e.g., by cancellation magnetic field generation component 320 in stabilizer 305), which are applied in the vicinity of the first qubit ion (e.g., by coil 330) to cancel the magnetic field fluctuations.

[0093] In connection with method 800, a QIP system may be used to perform such method. The QIP system may be an implementation of QIP system 600 that includes at least one ion trap (e.g., one or more ion traps 670) having first and second qubit ions, and a local oscillator (e.g., local RF oscillator 420). The local oscillator is locked to a frequency reference associated with the second qubit ions, and the local oscillator is configured to track the frequency of the first qubit ions based on the frequency reference.

[0094] Method 800 for stabilizing the phase decay of a quantum bit may also be implemented by a computer-readable storage medium (e.g., memory 520 and / or data store 540) storing code having instructions executable by a processor (e.g., processor 510).

[0095] The previous description of the disclosure is provided to enable any person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other variations without departing from the spirit or scope of the disclosure. Furthermore, although elements of the described aspects may be described or claimed in the singular, the plural is contemplated unless limitation to the singular is explicitly stated. Furthermore, unless otherwise stated, all or a portion of any aspect may be utilized with all or a portion of any other aspect. Thus, the disclosure is not intended to be limited to the examples and designs described herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. at least one ion trap having at least one first qubit ion and at least one second qubit ion; one or more coils; a stabilizer for stabilizing the phase decay of the qubit; a stabilizer configured to measure magnetic field fluctuations using the at least one second qubit ion and generate one or more magnetic fields using the one or more coils based on the measured magnetic field fluctuations, the one or more magnetic fields being applied in proximity to the at least one first qubit ion to cancel the magnetic field fluctuations and stabilize the phase damping of the at least one first qubit ion;

2. the at least one first qubit ion includes a plurality of first qubit ions; the at least one second qubit ion includes a plurality of second qubit ions; Alternatively, the at least one first qubit ion includes a plurality of first qubit ions, and the at least one second qubit ion includes a plurality of second qubit ions.

3. The QIP system of claim 1 , wherein the phase attenuation is characterized by a measurement of a parameter T2.

4. The QIP system of claim 1 , wherein the at least one first qubit ion and the at least one second qubit ion are atomic hyperfine qubits.

5. 5. The QIP system of claim 4, wherein the at least one first qubit ion is addressable with light at a first wavelength and the at least one second qubit ion is addressable with light at a second wavelength different from the light at the first wavelength.

6. 6. The QIP system of claim 5, wherein the at least one first qubit ion is a qubit composed of 171Yb+ and the at least one second qubit ion is a qubit composed of 133Ba+.

7. the at least one ion trap comprises a single ion trap; The QIP system of claim 1 , wherein the at least one first qubit ion and the at least one second qubit ion are co-trapped in the single ion trap.

8. the at least one ion trap includes a first ion trap and a second ion trap adjacent to the first ion trap; 2. The QIP system of claim 1, wherein the at least one first qubit ion is trapped in the first ion trap and the at least one second qubit ion is trapped in the second ion trap.

9. the at least one second qubit ion has an energy level that is sensitive to a magnetic field; 2. The QIP system of claim 1, wherein the stabilizer is configured to measure the magnetic field fluctuations using the magnetic field sensitive energy levels of the at least one second qubit ion.

10. 10. The QIP system of claim 9, wherein the at least one second qubit ion has another energy level that is not sensitive to a magnetic field.

11. The QIP system of claim 9 , wherein the magnetic field-sensitive energy levels include Zeeman levels.

12. The QIP system of claim 1 , wherein the magnetic field fluctuations include 60 Hz noise.

13. a magnetic shield configured to reduce the magnetic field fluctuations in a vicinity of the at least one first qubit ion and the at least one second qubit ion; 10. The QIP system of claim 1, wherein the magnetic shield is formed of a material having high magnetic permeability, including one or more of mu-metal, highly conductive copper, or a superconducting material at cryogenic temperatures.

14. The QIP system of claim 1 , wherein the stabilizer is configured to repeat a sequence including measuring the magnetic field fluctuations and generating the one or more magnetic fields to cancel the magnetic field fluctuations as part of a feedback loop.

15. 15. The QIP system of claim 14, wherein the feedback loop has a bandwidth of at least 1 KHz.

16. 2. The QIP system of claim 1, wherein the stabilizer is further configured to optically probe a magnetic field-sensitive energy level of the at least one second qubit ion to detect characteristics of the magnetic field fluctuations, thereby measuring the magnetic field fluctuations using the at least one second qubit ion.

17. the QIP system is configured to perform quantum computing; the at least one first qubit ion is configured to participate in the quantum computation; The QIP system of claim 1 , wherein the at least one second qubit ion is a spectator qubit configured not to participate in the quantum computation.

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