CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 62/837,655, filed April 23, 2019, entitled “QUANTUM COMPUTING STRUCTURES AND RESONATORS THEREOF,” which is hereby incorporated by reference herein in its entirety and for all purposes.

STATEMENT REGARDING FEDERALLY SPONSORED R&D

[0002] This invention was funded, in part, by government support under DOE Grant No. DE-SC0018773. The government has certain rights in the invention.

BACKGROUND

Field

[0003] The present disclosure relates to quantum computing structures, in particular to use of ion traps in quantum computing.

SUMMARY

[0004] Quantum computers (QC) rely on quantum bits (or qubits), which is a very fragile two-level quantum system. Qubits enable the use of quantum superposition and multi state entanglement in QC calculations. This allows for a QC to simultaneously calculate millions of computations at once. Entanglement lets a QC change the state of multiple qubits simultaneously via adjusting the state stored in a single bit, enabling computational power scalability unachievable with traditional computers.

[0005] However, a qubit state degrades rapidly due to the interaction with environmental degrees of freedom and added control channels. Described herein are resonators that can reduce the rate and/or degree of degradation of the qubit states. In some embodiments, Josephson junctions can be used, which may be located inside such a resonator. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Certain embodiments of the present disclosure will now be described, by way of example only, with reference to the accompanying drawings. From figure to figure, the same or similar reference numerals are used to designate similar components of an illustrated embodiment.

[0007] Figure 1 shows an example system for obtaining quantum calculations using an ion trap, according to some embodiments.

[0008] Figure 2 shows another example system for obtaining quantum calculations using trapped ions, according to some embodiments.

[0009] Figure 3 shows an example method for obtaining quantum computations using an ion trap, according to some embodiments.

[0010] Figure 4 shows an example mathematical model for ion traps.

[0011] Figure 5 shows qualitative relationships of various aspects of qubits.

[0012] Figure 6 shows an example orbit of an ion in a storage ring.

[0013] Figure 7 shows qualitative and quantitative interactions of a laser with moving ions.

DET AIDED DESCRIPTION

[0014] Quantum computing is a developing field of technology for storing and reading information. Quantum bits, unlike classical or traditional bits, do not necessarily need to be binary (on or off) but may exhibit information representing a wide range of information. The information stored as qubits, or quantum bits, can be useful, but currently there exist challenges related to the readability of the information from the qubits amid the noise associated with quantum phenomena.

[0015] Unlike classical computers, quantum computers are not limited to two states,“0” and“1”. They encode information as quantum bits, or qubits, which can exist in superposition. This superposition of qubits is what gives quantum computers their inherent parallelism. The parallelism allows a quantum computer to work on a million computations at once, while your desktop PC works on one. However, when the state of the qubit is measured directly, it becomes defined to a single value“0” or“1”, thus losing the advantage of parallelism. [0016] To make a practical quantum computer, the measurements have to be done indirectly to preserve the system's integrity. This is provided by the entanglement effect: when an outside force is applied to two atoms, it can cause them to become entangled, and the second atom can take on the properties of the first atom. This permits knowledge of a qubits’ value without direct measurements. In general, a quantum computer with N qubits can be in an arbitrary superposition of up to 2N different states simultaneously. This is a tremendous increase in capability compared to a normal computer that can only be in one of these 2N states at any one time.

[0017] One of the promising directions in Quantum Computing is based on using ion traps. Line of N ions stored in a combination of magnetic and RF fields gets irradiated with 2xN laser beams. Every ion has two stable or metastable states, which usually are two Zeeman sublevels of the ground state, separated by the effect of external magnetic field. Each ion serves as a single qubit except for the last one in the line, which operates as a“I/O” sensing vibrational motions of the whole line of ions.

[0018] The ions are cooled below the limit given by vibrational frequency in the trap (Lamb Dicke regime), which is accomplished using Doppler and Sideband cooling. Usually Paul traps are used instead of the Penning type taking advantage of reliable RF techniques versus these with using high magnetic fields. In 2018 the Quantum Computer succeeded storing 20 ions in entangled state.

[0019] There are two classes of frequencies of EM field induced by the ions stored and cooled in the trap. One frequency is optical corresponding emission of photons by the ions, excited by an external laser. These photons are detected by a photomultiplier to read the state of qubits. Another frequency is in the phonon range and is used for control of interaction between the ions in the trap.

[0020] One of the serious issues of Quantum Computers is decoherence. Quantum Error correction techniques include developing redundant chains of qubits with correcting codes or employing Quantum Zeno effect. Time of decoherence sets a limit for the length of working cycle of the computers.

[0021] Scalable Quantum Computers based on interacting traps are proposed for storing multiple set of qubits and exchanging information between them. Quantum charge- coupled device (QCCD), has been tested and serves as a proof of principle for“multi-chip” Quantum Computer.

[0022] A method of obtaining quantum computations can include using an ion trap. The method may include trapping a plurality of ions using, for example, a synchrotron beamline. Other accelerators, such as looped or circular accelerators, may also be used. These accelerators may provide a storage ring or other device that contains ions in a recirculating orbit. The method can include cooling the plurality of ions by irradiating each of the plurality of ions with coherent light. The one or more of the plurality of ions can be excited using a coherent light source. A field response can be detected by an electromagnetic detector, such as a photomultiplier. The field response of the one or more ions can be obtained from excitation from the coherent light source.

[0023] In some embodiments, the method includes forming the ions into a multi dimensional pattern within the storage ring. The multi-dimensional pattern can include a three-dimensional crystalline pattern. The method can include applying an alternating gradient using, for example, the storage ring.

[0024] There are several conditions for storing“crystallized” beams of ions in an alternating gradient synchrotron or other type of circular accelerator. One condition comes from the requirement of having horizontal tune larger than the scaled energy. Another constraint is that the energy of the ions should be less than transition energy of the machine.

[0025] The type of the crystal is determined by a combination of the density of ions and the strength of transverse focusing. As the density increases, ions form, first, a 1-D chain, then 2-D zig-zag and, then, 3-D crystal. Ions in a crystal interact with phonons transversely while the motion is“frozen” in azimuthal direction.

[0026] Doppler laser cooling is realized by two counterpropagating UV beams. Scanning the light frequency one can either probe or cool the ion beam while recording fluorescence with a photomultiplier in a photon counting mode.

[0027] The techniques developed in experiments with crystalline beams enable injection, storage, acceleration, cooling and control over hundreds of ions in a storage ring.

[0028] The high degree of control of ion beams in crystalline accelerators is often sufficient to expand this concept towards building a first Quantum Computer with many hundreds of qubits. In comparison with conventional ion traps there appears multiple advantages of using crystalline beams in storage rings as the medium for qubits . Some of them are presented below:

• Choice of the ions’ kind and the matching laser frequency can be simplified by adjusting the energy of ions and using the Doppler shift to exact match of resonance condition.

• The circumference of crystalline storage rings reaches several meters, opening a possibility of storing many hundreds or thousands of ions separated by tens of microns. This translates in having more qubits, which, in turn, means more redundancy in the QC calculations.

• In particular, many more ions are now stored in the crystalline ring enabling more efficient Quantum Error corrections as a single qubit can be stored in many ions and there are more candidates for the checkbits.

• Quantum error correction can also be realized using‘watchdog’ or quantum Zeno effect.

• Due to the macroscopic size of the ring, the ions moving through interaction regions with laser beams permit for time domain analysis in addition to the frequency domain in collecting information from the phonon excitation bus. This is a clear advantage to the conventional ion traps, where the timing methods would need to exhibit tough resolution requirements.

• Crystalline beams could be cooled down to ground state. One might expect that the recoil, being macroscopic, can be measured with existing RF techniques.

• One could consider scalable Quantum Computers based by having several rings of ions in a storage ring rotating on different orbits.

[0029] The methods described herein can include (1) attaining a short chain of ions, (2) cooling them down to, for example, the ground state, (3) using a diagnostics system to detect, for example, fluorescence, (4) using a laser beam to initiate a predefined distribution of the qubit states, and/or (5) using an RF sensing system, reading time- dependent RF signal induced by interaction of ions in the chain.

[0030] Turning now to the Figures, Figure 1 shows an example system 100 for obtaining quantum calculations using an ion trap, according to some embodiments. The system 100 includes a beamline 104 from a particle accelerator (e.g., synchrotron, cyclotron, etc.). The system 100 includes a light source 108 such as a laser or other coherent light source. Although not shown in Figure 1, the system 100 can include a plurality of light sources. Each of the plurality of light sources can be configured (e.g., tuned) to emit light at different wavelengths to perform various actions on trapped ions, such as ion cooling, ion excitation, etc. The laser may be tuned to a wavelength that is configured to cool trapped ions. The plurality of ions 112 that are trapped in the beamline 104 can be cooled by the light source 108. The plurality of ions 112 can be trapped in a two-dimensional (2D) and/or three- dimensional (3D) pattern, such as a crystalline pattern. The plurality of ions 112 can include 2, 3, 5, 10, 15, 20, 25, 50, 75, 85, 100, 125, 150, 200, 300, 500, 700, 1000, or any other smaller number of ions, or the number of ions may fall within a range having endpoints therein.

[0031] The system 100 can use a light source, such as the light source 108, to select one or more target ions 116. The target ions 116 can be excited in such a way as to emit an electromagnetic field response, such as fluorescence. The system 100 can further include one or more detectors such as a detector 120. The detector 120 can be configured to detect the electromagnetic field response. The detector 120 (or another detector) can be configured to detect phonon signals.

[0032] Figure 2 shows another example system 150 for obtaining quantum calculations using trapped ions, according to some embodiments. The system 150 includes an ion injector 152, a storage ring 154, a first cooling laser 158, a second cooling laser 160, a gate laser 164, and a radiofrequency (RF) pick-up 168. The ion injector 152 provides ions into the storage ring 154. The system 150 drives the plurality of ions 162 around the plurality of ions 162 at a velocity substantially below the speed of light. The first cooling laser 158 and second cooling laser 160 are configured to work together to cool the plurality of ions 162 to below a threshold temperature. The threshold temperature is a temperature at which quantum computing effects become possible. For example, quantum computing effects may not become possible until the plurality of ions 162 are able to be in a superposition and/or entangled. Below the threshold temperature, the plurality of ions 162 may maintain the lattice structure primarily based on Coulomb forces. The plurality of ions 162 may revolve around the storage ring 154 in a lattice structure or other multi-dimensional structure described herein.

[0033] The first cooling laser 158 and second cooling laser 160 can irradiate the plurality of ions 162 at a frequency of light that is resonant with the vibrational and/or motional energy of the ions. Thus, the lasers 158, 160 can reduce the temperature of the plurality of ions 162, such as below the threshold temperature. The threshold temperature may be about 100 mK, about 50 mK, about 10 mK, about 1 mK, about 750 microK (mK), about 600 mK, about 500 mK, about 300 mK, about 250 mK, about 200 mK, about 100 mK, about 80 mK, about 60 mK, about 50 mK, about 35 mK, about 20 mK, about 10 mK, about 5 mK, about 3 mK, about 1 mK, any value therein, or fall within any range having endpoints therein, depending on the type of application needed (e.g., the ions used, the types of lasers, etc.)· The lasers 158, 160 may use one or more cooling techniques described herein, such as Doppler cooling or Sideband cooling. By allowing the formation of ions to be in motion (e.g., not static or stationary), the embodiments herein can allow for more ions to obtain stable qubit properties and participate in providing quantum computing readouts. The number ions may be greater than 100, greater than 500, greater than 750, greater than 1000, greater than 1500, greater than 2000, greater than 3000, greater than 5000, greater than 10000, greater than 50000, and/or greater than 100000.

[0034] The gate laser 164 ensures that the parameters achieved for quantum effects are maintained. The gate laser can program the state of the ions. For example, the gate laser pulse acts on an ion in the crystalline beam, setting it into particular quantum state needed for quantum computation. The RF pick-up 168 reads the RF signal corresponding to a phonon mode from the plurality of ions (e.g., in a crystalline beam) traversing it. For example, the RF pick-up 168 can read out a final state of one or more of the plurality of ions 162.

[0035] Figure 3 shows an example method 200 for obtaining quantum computations using an ion trap, according to some embodiments. The method 200 may be performed by any system disclosed herein, such as the system 100. The system may at block 204 trap a plurality of ions using a synchrotron beamline. At block 208, the system may cool the plurality of ions by irradiating each of the plurality of ions with coherent light. At block 212 the system may excite one or more of the plurality of ions using a coherent light source. At block 216, the system may detect an electromagnetic field response of the one or more ions from the coherent light source.

[0036] In some embodiments, the system may apply an alternating gradient using the synchrotron beamline. In some embodiments, the system may cool one or more ions to a ground state of the ion(s). The one or more trapped ions may be trapped in a 2D or 3D pattern, such as a crystalline pattern, such as disclosed herein. The method may include detecting a phonon signal from the plurality of ions. In some embodiments, the electromagnetic field response includes a fluorescence of the plurality of ions. [0037] Figure 4 shows an example mathematical model for ion traps. N ions in a harmonic potential, to le) 729 nm (qubit ~10 ¹⁵ Hz), Ig, 0) to Ig, 1)

phonon ~10 ⁶ Hz.

[0038] Figure 5 shows qualitative relationships of various aspects of qubits.

[0039] Figure 6 shows an example orbit of an ion in a storage ring. Moving ions sample a range of fields along their orbit. These lead to decoherence of qubit quantum state due to interaction of ion and the fields. Path dependent quantum phase shifts due to Zeeman effect. Ions travel along somewhat different paths. At orbit misaligned by 100 mm— > magnetic field is 200 Gs. This corresponds to the energy level shift of 30 MHz. Compare with phonon frequency of ~1 MHz. Big effect. May be beneficial to maintain orbit of ions in macroscopic ring. It raises a question of whether diagnostics of ion crystal’s orbit around the ring are needed. Looking at PALLAS: 3.6 m in circumference. Some systematic errors may arise: Reproducibility of orbit / focusing. Random errors: RF noise. HT: dispersion and focusing in storage rings effects impacting ions temperature in a storage ring lattice with dispersion coupling between x coordinate and momentum spread. Affects formation of large crystals with apparent temperature at PALLAS.

Focusing ions may oscillate transversely with the period of focusing structure. Apparent temperature at PALLAS.

Periodicity and tune separate function, for example, in ASTRID:

PALLAS: lower Ts are attainable in an RFQ lattice than in the separate

function lattice. Storage Rings can offer comparable focusing (w _c ) to that in ion traps.

Consider qubits on the transverse (x, y) degrees of freedom.

[0040] Moving ions in QC traps may be desired. Longitudinal Temperature in QC on ion trap, assume that ion absorbs a visible light (1 is wavelength) photon, the ion gains velocity of 4 cm/s after absorption of a photon. For multiple ions this change in momentum is spread over the whole crystal. To witness this change in momentum, corresponding T of z-motion should be <5 mK.

Laser cooling techniques include Doppler rings with Doppler, Sideband, Sisyphus, and/or trapping technologies.

[0041] Quantum Computers require stable phonon frequencies and ability to form strings with a given number of ions. Storage Ring: revolving cloud of 10 ⁵ ... 10 ⁶ ions with longitudinally constrained by the Coulomb force of crystal. Introduction of longitudinal potential well may be desired. The number of phonon modes grows with number of ions (3xN modes). Resolving modes with 1000s of ions is a challenging problem.

[0042] Figure 7 shows qualitative and quantitative interactions of a laser with moving ions. A model for Quantum Gate includes moving ion crystal in a Storage Ring at 2.8 km/s, ions absorb a laser photon to drive it through the transition. Laser waist is half of separation of ions

1 eV ion (PALLAS) moves through the 10 mm wide laser waist in 5 ns = laser pulse length low power laser (mW), frequency bandwidth of 10s GHz. Addressing every ion moving around in the ring is a challenge. For example, acousto-optical modulators and electro-optical modulators, and cross-talk of laser tails between neighboring ions, fast ions— > interval for ion-laser interaction is limited by time of flight.

[0043] In the quantum regime, ion Tz may need to be small enough to maintain noise level below quantum of motion state

[0044] Lamb-Dicke parameter and corresponding regime quantifies the coupling strength between internal states and motional states of an ion and quantum of vibrational motion is much larger than the recoil energy and transitions changing the motional

state of the ion are negligible

Minimum T achievable in storage rings may be higher than these in ion traps. Recent advances in building QCs on“warm” ions. Molmer-Sorensen gate operates outside Lamb- Dicke regime.

^* esti mates

[0045] One advantage of embodiments disclosed herein is large qubit capacity with an ability to develop algorithms to combat errors due to decoherence. This may enable solving more complex problems on a shorter timeframe. Alternative solutions seem better suited to the QC applications requiring high ion capacity. Toroidal Trap, Trap on microchips, Shuttling ions between multiple traps. Embodiments disclosed have many advantages, such as they can include low noise and high degree of reproducibility of parameters in a macroscopic storage ring, storage of low energy ions, sensing techniques, photon counting and RF pickup of low intensity signals, conditions for storing low temperature crystals, alternative cooling techniques, QC on“warm” ions, longitudinal confinement of many ions and detection of phonon modes, stable potential well, transverse phonon modes.

[0046] One of the promising benefits of the embodiments disclosed herein in Quantum Computers (QC) is based on using ion traps. In some embodiments, several tens of ions are collected in a small electromagnetic trap, with their motion cooled down to micro K temperature level, leading to entanglement of their quantum states, controlled by the laser and RF fields. These ions become qubits and are used to run quantum computations at unprecedented rate using specialized codes (one example is QuTip, Quantum Toolbox in Python).

[0047] Certain embodiments hold a potential to support much higher capacity of qubits as compared with the state-of-the-art devices on Paul traps. Crystalline beams of ions in a storage ring can be used as the medium for qubits. The crystalline beams can be used for cooling particles, which form a revolving crystalline-like structure. Comparing this concept with the QC on a conventional ion trap, embodiments herein can form a small storage ring with high qubit capacity. The latter is important for evolution of the QC capabilities, including the processing power and robustness against errors due to decoherence.

[0048] Doppler cooling may be used. Absorption of photon indicates (e.g., equals) the momentum of the photon, which counteracts momentum of ion’s thermal motion. If cooling in 3D then several lasers may be used. An ion can be brought to a temperature as low as 0.5 mK. This may be limited by linewidth of the excited state. Sideband cooling and staircasing of vibrational motion levels may be used. Laser tuned to red sideband transition Ig, n) to le, n - 1), spontaneous emission, alternative is Raman transition with 2 laser beams, minimum ion’s T achieved is 1 mK.

[0049] Another example type of cooling is known as Sisyphus cooling. Counter- propagating laser beams with orthogonal polarization— > standing wave + optical pumping. Ions may reach levels as low as about 0.1 mK. Figure 21 shows some relevant energy levels of 171Yb+ for Sisyphus cooling, under section (a). Section (b) shows an example of a single ion Sisyphus cooling event from optical pumping between shifted harmonic trapping potentials associated with two effective sub-levels of the 2S1/2IF=1) ground state. The shift in potentials is due to dipole forces from the ID polarization gradient shown, which is formed by counter-propagating, linearly polarized Sisyphus beams in a transverse magnetic field. Section (c) shows an example laser beam configuration. The configuration includes double-pass acousto-optic modulators (AOMs) that are used to control the power and frequency of the Sisyphus beams, which enter the vacuum chamber and trap from the north and south sides. Transverse (e.g., perpendicular) Raman beams entering from the east and south are used to probe ion motion in the axial trap direction; west and south beams are used for the transverse directions. Shown at right are the axial and transverse

Raman wavevector directions overlaid on the principal axes of the trap.

Example Embodiments

[0050] The following list of embodiments is provided as example only and does not exhaust the possible embodiments of systems or methods described herein.

[0051] In a 1st example, a method of obtaining quantum computations using an ion trap comprises: trapping a plurality of ions using a synchrotron beamline; cooling the plurality of ions by irradiating each of the plurality of ions with coherent light; exciting one or more of the plurality of ions using a coherent light source; and detecting an electromagnetic field response of the one or more ions from the coherent light source.

[0052] In a 2nd example, the method of example 1, further comprising forming the ions into a multi-dimensional pattern within the synchrotron beamline.

[0053] In a 3rd example, the method of example 2, wherein the multi-dimensional pattern comprises a three-dimensional crystalline pattern.

[0054] In a 4th example, the method of any of examples 1-3, wherein trapping the plurality of ions comprises applying an alternating gradient using the synchrotron beamline.

[0055] In a 5th example, the method of any of examples 1-4, wherein cooling the plurality of ions comprises cooling at least one ion to a ground state of the at least one ion.

[0056] In a 6th example, the method of any of examples 1-5, wherein the plurality of ions comprises at least 100 ions.

[0057] In a 7th example, the method of any of examples 1-6, further comprising detecting a phonon signal from the plurality of ions.

[0058] In an 8th example, the method of any of examples 1-7, wherein detecting an electromagnetic field response comprises detecting a fluorescence of the plurality of ions.