Read about ion trap quantum computers in one article
This September marks the centenary of the birth of Hans Georg Dehmelt, one of the inventors of ion trap technology and Nobel laureate in physics, who invented it back in the 1950s when it was used to improve the accuracy of spectroscopic measurements. Today, ion traps are the primary physical system for implementing quantum computing. In honor of this pioneer of ion trap technology, this article will describe how ion traps can be useful in the field of quantum computing.
The principle of ion traps themselves is simple: the interaction forces created between the charge and the magnetic field are used to confine the charged particles, allowing their behavior to be controlled. The two most common types of ion traps are the Penning trap, proposed by Dehmelt, which creates a potential through a combination of electric and magnetic fields, and the Paul trap, proposed by Wolfgang Paul (who shared the 1989 Nobel Prize in Physics with Dehmelt), which creates a potential through a combination of static and oscillating electric fields.
Unlike routes such as superconductivity and optical quantum, ion-trap quantum computers require the integration of technologies from many different fields: vacuum, laser and optical systems, RF and microwave technologies, and coherent electronic control.
Specifically, ion trap quantum computers have several advantages.
1) Longer coherence time. In January 2021, Qi Huan Jin's research group at the Institute of Cross-Information, Tsinghua University set a new coherence time record: for the first time, a single quantum bit coherence time of more than one hour was achieved in an ion trap system.
(2) Single quantum bit gate and double quantum bit gate have high fidelity. Among them, the fidelity of single quantum bit rotation is up to 99.9999%; in double quantum bit entanglement, the fidelity of ultra-fine quantum bit is up to 99.9%, and only the performance of superconducting quantum bit can be compared with it.
3) More direct state preparation and readout. The initialization and readout fidelity data are better than any other quantum bit technique: the use of laser measurements leads to readout fidelity of over 99.99% detection time in 200 μs and 99.93% in 11 μs [1]. This year Quantinuum's ion trap system uses barium ion quantum bits to increase SPAM fidelity to 99.9904% - the highest of all quantum technologies to date.
4) High repeatability of quantum bits. All ions of a particular species and isotope are essentially the same, so the microwave or laser frequency required to process each ion in the system is the same, and each ion has the same coherence time. This improves the reproducibility of the quantum bits and limits the number of calibration steps needed at the beginning of the calculation compared to other techniques.
Until 2018, the only representative of the ion trap camp is IonQ, which is weak compared to the superconducting quantum bits represented by IBM, Google, and Rigetti. But starting in 2020, Honeywell's ion trap quantum computers lead the world in the metric of quantum volume (QV). Today, Quantinuum (a Honeywell subsidiary), IonQ, and AQT, all three ion trap companies, have achieved at least 20 quantum bits.
01Trapping ion traps
How can ions be trapped and how can they be controlled? Ions are single charged atoms, and by controlling the charge to control the electric and magnetic fields, hot ions plus laser, and laser cooling, the velocity of ions can become very low, and finally measured again with light.
1) Types of ion traps
Usually ions are kept in space using Penning or Paul traps. in a Penning trap, a static electric field provides confinement in one axial dimension and a parallel static magnetic field allows confinement in two perpendicular radial directions. in a Paul trap, an oscillating electric field sets up a qualitatively dynamic confining pseudopotential in two or three dimensions ( ponderomotive confining pseudopotential) in two or three dimensions. The RF trap depends on the time variation of the potential, and the stability of the ion in this trap potential depends on the RF potential and on the parameters of the ion itself: the charge-to-mass ratio of the ion, the RF frequency, the RF amplitude and the curvature of the potential, etc.
Geometric illustration of the RF Paul trap. (a) Basic concept of an RF trap, i.e., a set of (parabolic) electrodes generating a quadrupole field oscillating at RF frequencies. (b) Basic RF trap with cylindrical symmetry, specifically the "ring and end cap" point trap geometry. (c) Translational symmetric basic RF trap, which can be used to create a linear trap. (d) and (e) are topologically equivalent deformations of the geometry shown in (b). (f) is a topologically equivalent deformation of the geometry in (c) with the addition of additional end-cap electrodes to form a four-bar linear trap. (g) is a deformation of the four-bar trap in (f), so that all electrodes lie in one plane, forming a linear "surface electrode trap". (h) A subset of the electrodes in the linear trap can be split to allow for multiple areas of trapping along the axial direction.
(2) Loading ions into the trap
All ion trapping experiments start with loading one/multiple ions into the trap: the ions collected in the trap are held in orbit within the trap by a combination of DC, RF voltages.
Due to the relatively deep depth of the ion trap (0.1-1 eV) and the long trapping lifetime, many experiments can be performed after the ions are successfully loaded into the trap. Recently, the "Resonance enhanced multiphoton ionization" (REMPI) technique allows for a high probability of excitation of the desired isotope to the ionized state using the frequency change of the isotope. Due to the relatively large ionization energy of the atoms used as trapped ion quantum bits, excitation is typically performed in two steps: the first step uses photons of different energies, at least one of which resonates with a strong binding-binding optical transition in the UV part/near UV part of the spectrum (exceptions are Be+ and Mg+, which are typically formed by single-wavelength, two-step photoionization). At this moderate first-step laser intensity, the probability of detuned excitation of other isotopes is greatly reduced.
The second step must be performed before the atoms spontaneously decay or leave the trapping trap, and it does not require resonance because the atoms are either excited to the free electron continuum or, as in the case of Sr, to the self-ionized state. The second step is often driven with higher laser intensities to achieve high photoionization rates.
Compared to the above mentioned ion capture techniques and alternative methods using laser cooling of neutral atoms, lowering the temperature of the atomic vapor compresses the "Boltzmann velocity distribution": thus it is possible to capture more of the incident flux and achieve high loading rates with significantly less deposition.
02Ion trap quantum bits
Schematic diagram of the quantum bit energy level. (a) The basic electronic structure of the ions used for QC. All ions have S and P levels, with lower D levels (e.g. Ca+, etc.) and F levels (e.g. Yb+) requiring quadrupole or octupole transitions from the ground state, respectively; (b) structure of a zero-nuclear spin (I = 0, usually an even isotope) ion in a magnetic field. Zeeman, optical and fine structure quantum bits are depicted in Fig. (c) Structure of a non-zero nuclear spin (I≠0, odd isotopes) ion in a magnetic field. A structure with I=1/2 level is depicted (levels D and F are omitted for clarity). Typical (order of magnitude) energy level splits for various types of quantum bits are: Zeeman quantum bits, 1-10 MHz; optical quantum bits, 100-1000 THz; fine-structure quantum bits, 1-10 THz; hyperfine quantum bits, 1-10 GHz. level numbers are labeled using spectroscopic notation, where s is the total spin quantum number (in the case of univalent electrons ), L refers to the orbital momentum quantum number, written as S, P, D, F, ... , j is the total angular momentum quantum number.
1) Zeeman quantum bits
Zeeman quantum bits consist of a pair of states at the same electron orbital and hyperfine energy level, separated by a small magnetic field at MHz frequency, providing an essentially infinite quantum bit lifetime.
Single- and double-bit logic operations are typically performed using two-photon stimulated Zeeman transitions, where the two beams of light from the double photon come from the same laser that is tuned to resonate near the P level in the ion.Zeeman quantum bits are typically highly sensitive to changes in the magnetic field. Magnetic field fluctuations can lead to the accumulation of different phases in the quantum bits, so great care must be taken to protect the ions from magnetic field variations to achieve long coherence times. Currently, coherence times of 300 ms (and 2.1 s dynamic decoupling pulses) have been achieved; in the future, new materials with better temperature control, and better magnetic properties will be needed.
2) Hyperfine Quantum Bits
Hyperfine quantum bits consist of a pair of states in the ground state hyperfine manifold, which can provide the long lifetime that Zeeman quantum bits have, along with a high degree of magnetic field-volatility insensitivity. Because there is a significant quantum bit energy level splitting, its state detection is more straightforward than Zeeman quantum bits; however, the energy level structure is more complex and requires more laser frequency components to handle all electronic energy levels for state preparation, measurement.
3) Optical Quantum Bits
Optical quantum bits, consist of one state in the ground state manifold and one state in the metastable D level. However, the laser used to control the optical quantum bit must be narrowed to approximately 1 Hz to take full advantage of the second energy level lifetime; furthermore, since the laser is essentially a local oscillator of the optical quantum bit, its phase fluctuations can cause the quantum bit to decoherence. Despite these limitations, optical quantum bits facilitate system scaling.
Currently, coherence times of up to 0.2 s have been achieved in zero-core spin ions by controlling the laser linewidth and the vibration of the optical elements.
4) Fine structured quantum bits
Using a pair of states in the D manifold, a quantum bit with energy splitting in the THz range can be formed from both the D3/2 and D5/2 energy level splitting levels - a fine structure quantum bit.
By integrating photonics techniques, fine-structured quantum bits are more easily scalable than the blue and UV lasers required for Raman conversion of Zeeman, ultrafine quantum bits; because this transfer is done by laser, higher detection efficiency can be obtained for fine-structured quantum bits with the same technology.
03Control of trapped ions
Precise control is required in any way to initialize the system quantum states, perform gate operations, and read out the final state.
Schematic diagram of the trapped ion hardware. A linear ion chain is trapped near a surface electrode trap (trap not shown). A laser (not shown) illuminates all ions during cooling, initialization, and detection, and the fluorescence of each ion is imaged through a lens (detection optics) and directed to the individual photomultiplier channels. Two linearly polarized Raman beams are aimed at each quantum bit ion, a globally addressed beam coupled to all quantum bits (red) and a separately addressed beam focused on each ion (blue). An acousto-optic modulator (AOM) modulates the frequency and amplitude of these beams to generate single quantum bit rotations and logic gates between any pair of quantum bit ions.
1) State Preparation
Before loading the trap for quantum operation, the ion register must be prepared to the desired initial state; unlike trap loading, high-fidelity initial state preparation must be repeated after each experimental realization. Therefore, it is necessary to optically pump the ions to the desired initial state, or some intermediate state that can be coupled to the initial state with high fidelity. Optical pumping schemes come in many different forms, but typically utilize a selection rule for photon absorption and emission, with a high probability of sequestering the quantum state amplitude in a single state after repeated absorption and emission.
In addition to internal state preparation, it is often necessary to control the motion states of the ion register as well. Laser-based Doppler cooling is useful for rapidly reducing the effective ion temperature, which can be effectively used to reduce the kinematic state occupancy of the ion register when processing a small number of ions or controlling a small number of kinematic modes; however, because the technique can only cool a single mode at a time and requires repeated resonance processing of weak transitions, the process can be for large ion chains with many kinematic modes The process can be very slow for large ion chains with many modes of motion.
Alternatively, cooling can be achieved by changing the light absorption profile of the ion register through the "electromagnetic induction" (EIT) technique. By selecting the laser frequency and polarization, photon scattering can be suppressed, thereby reducing the occupancy of the kinematic state. This technique was first applied to single ions, but has recently been extended to ion chains consisting of different atomic ion species, and to handle multiple modes of motion simultaneously.
2) Quantum logic gates
Quantum logic gates input quantum bits and convert their states to outputs in a deterministic, reversible manner. Ion well quantum computers need to perform gate operations on arbitrarily large quantum bit registers in order to perform calculations. The following table gives a comparison of the advanced gate performance of different schemes.
There are three different types of single-quantum-bit logic gates: Raman, optical and microwave.
1) Hyperfine quantum bits use two hyperfine internal states of an ion, usually separated at GHz frequencies, as |0⟩ and |1⟩ states, whose single quantum bit gates are realized by microwave or Raman transitions. As shown in the figure below.
Schematic diagram of the level structure used in the stimulated Raman transition. The |0⟩ and |1⟩ states are coupled by two lasers with frequencies separated by the quantum bit energy level splitting Δ. For sufficiently large Rabi frequencies Ω1,2 and Raman detuning Δ, the quantum bit transitions can be efficiently driven with a negligible number of large losses and short-lived states |e⟩.
2) Optical quantum bits use a metastable excited state as |0⟩ with a transition frequency in the optical range (>100 THz). For these quantum bits, a single quantum bit gate can be done with a resonant laser.
Multiple quantum bit gates entangle the internal and kinematic states of the trapped ions through Coulomb interactions. The first gate on entanglement between two ions, the CZ gate, was proposed by Cirac and Zoller; all multi-quantum bit gates so far have the basic features of the CZ gate: the shared motion pattern of the ions is used as a bus to transfer quantum information between them.
Schematic diagram of the Cirac-Zoller gate. (a) The red sideband π pulse on the capture ion shifts the amplitude from the |1⟩c state to the ground state |n=1⟩ of the first excited state |0⟩c. (b) For the population of |n=1⟩ kinematic states in the first step, a red sideband 2π pulse is applied to the target ion by the auxiliary excited state |e⟩c|n=0⟩. (c) The last red sideband π pulse on the control ion returns it to the initial state. The dashed line indicates that the transition to the non-existent kinematic state is forbidden.
The requirement that ions start and end in the kinematic ground state is an important restriction on the CZ gate. This is because, even if the ions have been cooled to the kinematic ground state, they are subsequently heated by the electric field noise.
In 1999, Mølmer and Sørensen introduced another type of controlled phase gate, the MS gate, which can be implemented without the need to be in the kinematic ground state. It can be used for ions that are not cooled to the kinematic ground state, and multiple inter-ion entanglement can be generated using only a globally controlled laser (i.e., no laser is required to focus on each ion independently). Currently, the highest fidelity of both optical (99.6%) and hyperfine double quantum bit gates is achieved using MS gates.
A third type of double quantum bit gate for ions is Leibfried's geometric phase gate. This gate uses a pair of detuned laser beams to generate a state-dependent force that traces a closed path in phase space: the
Phase space trajectories of double ion states between geometric phase gates. Space-independent forces drive specific ion states (|10⟩ and |01⟩) along a closed path in phase space, giving the closed region a set geometric phase Φ. The |00⟩ and |11⟩ states are not coupled to the control field and therefore do not accumulate geometric phases.
Although this gate also uses the co-movement of ions to produce coupling and, is insensitive to the initial ion motion state; it differs from the MS gate in that it does not involve a transition between |1⟩ and |0⟩ quantum bit states. Geometric phase gates are the first gates to achieve high fidelity: such gates have been shown to have 97% fidelity in 9Be+ ions with a gate time of 250 μs.
04Ion state readout
The determination of ion states needs to be accurate, fast, and ideally scalable to many ions.
Currently, it relies mainly on fluorescence detection. During the measurement, the trapped ions show a "Bright state" - scattering many photons when irradiated by the laser - or a "Dark state" - scattering few photons. state) - scattering few photons. The scattered photons can be collected with a high-NA lens and detected with a high-efficiency detector, and the ion state can be inferred by analyzing the number of photons produced.
Capture ion state readout. (a) Schematic of the fluorescence detection of captured ions. The ions scatter a number of photons from the resonant laser beam, which are collected by an NA lens. The collected photons are imaged on the detector, which records the photon counts with its own efficiency ηd. (b) Simulated photon collection histogram of the captured ion state detection. The bright (dark) state photon counts are taken from a Poisson distribution, showing a high accuracy determination of the ion state.
05Quantum algorithm implementation
A quantum algorithm is a program (usually written as a set of gates and measurement operations on a quantum bit register) to solve a number of problems.
The first quantum algorithm to be implemented in an ion trap system was the Deutsch-Jozsa algorithm. Although of little practical value, it is worth noting that while a classical computer requires multiple queries to the "black box" to determine whether the output is a constant or an equilibrium, a quantum computer with N+1 quantum bits can determine the answer with a single query: in 2003, using only one trapped ion, the experiment demonstrated that N=1 in the Deutsch-Jozsa algorithm, a milestone in quantum computing with captured ions.
In 2005, the semi-classical quantum Fourier transform was demonstrated in a linear chain of three Be+ trapped ion quantum bits: not only did this calculation use multiple ions, but the quantum Fourier transform itself was a key element in the final step of Shor's algorithm to perform an efficient task. at the end of 2005, the first fully quantum algorithm using entanglement of multiple trapped ion quantum bits was successfully demonstrated. A demonstration of the Grover search algorithm in a two-ion system successfully "searched" for tagged elements with a probability of 60%, exceeding the maximum probability of 50% for classical systems.
In 2011, the first capture ion algorithm for universal, digital quantum simulations was used to simulate two-dimensional Ising interactions in chains of up to six ions: with up to 100 gate operations, the experiment still represents a significant advance in the number of bits and complexity of capture ion quantum algorithms. 2016, Shor's algorithm was used to factorize the number 15 in a five-ion system with a success rate of 99%, which is the most famous demonstration of the quantum algorithm.
Quantum chemical calculations of the ground state energies of H2 and LiH molecules have also been performed in a few ion systems by the Variational Quantum Computing (VQE) algorithm, and similar calculations for H2O have recently been performed using up to 11 ions. Even without error correction, the overall success rate of these algorithms is as high as 90-95%.
The five-quantum-bit ion trap quantum computer has also been compared with IBM's five-superconducting quantum-bit computer: running the Bernstein-Vazirani algorithm, Hidden Shift algorithm, the overall success rate of the ion trap simulator is between 85% and 90%, higher than the success probability in the superconducting circuit device, but the overall algorithm execution time of the superconducting device is faster [2]. The higher success probability of the trapped ion system is partly due to the fact that this system is fully connected: it is possible to operate a direct gate between any, any two ions.
In addition to this, quantum simulation is a different approach to quantum computation of trapped ions. Instead of using a generic gate set, the trapped ion system for the simulator is designed with a Hamiltonian for the ion system and maps it to other many-body systems. In the near future, trapped ion systems may be able to simulate other quantum systems with 50-100 quantum bits.
06Ion trap integration techniques
In order to build practical quantum computers based on trapped ions, hardware techniques for controlling and measuring large numbers of ions and low error rates need to be developed. So, which hardware will improve the scalability of trapped ions?
1) Chip-level ion traps
Surface electrode ion trap technology is needed because of the need to increase the number of ion trap electrodes and increase the complexity of electrode configurations. A typical surface electrode ion trap consists of a substrate or chip composed of materials such as sapphire, quartz/silicon with a metallic electrode pattern on its surface (on which ions are trapped). These electrodes are typically formed by deposition of metal a few microns thick, followed by optical lithography and chemical etching to define the electrode pattern; electroplating techniques are also often used; the design allows for arbitrary electrode shapes, patterns, and multiple metal layers (separated by an insulating layer) useful for electrode wiring and electrical signal routing.
Surface electrode ion trap chip. 1 cm square trap (gray) is mounted in a ceramic needle mesh array (gold and black) and the trap consists of a sapphire substrate on which a 1 µm thick layer of aluminum metal is deposited and patterned by optical lithography to define the trap electrodes. This special trap confines the ions to a linear array 50 µm above the chip surface.
Wafer-scale fabrication on 1200 mm diameter wafers is now possible, so that in principle, extremely large arrays of traps can be realized on a single substrate.
2) Integrated photonics for optical transport
In order to control and measure trapped ions, lasers with different wavelengths are required. The laser needs to be sent to each location where the ions are located or where quantum manipulation is to be performed. Therefore, as the array size increases, the number of laser beams sent to the precise location in the ion trap array increases.
Current methods of treating individual ions with lasers typically employ free-space optics such as lenses, acousto-optic modulators (AOMs), and lenses. AOMs are also used as high extinction and high-speed optical converters, as well as precise tuners of optical laser frequency and phase; these optics can be used to guide and switch the laser beam to treat small numbers of ions in linear arrays. The challenge of accurately delivering a large number of focused laser beams into a two-dimensional array of ions with low crosstalk can be addressed using integrated photonics; among the most critical integrated photonic elements are optical waveguides.
Integrated photonics for light transmission. (a) Illustration of an integrated photonic waveguide and grating coupler that delivers light to two locations above a surface electrode ion trap. The waveguide and grating consist of a patterned high optical index core (blue-grey) and a low index cladding (white). Square windows are cut into the trap metal (light gray) to allow light from the grating coupler (red) to reach the ions (blue circles). The inset shows an enlarged view of the grating coupler. (b) Cross-sectional view of the integrated photonics ion trap. The figure shows the layers including the chip substrate (dark gray), whose thickness is not to scale.
One challenge to the widespread use of integrated photonics is optical loss. Waveguide materials must be highly transmissive over the wide range of wavelengths required for complete ion trapping control and readout. Therefore, low-loss integrated photonic devices must be developed using materials that can be fabricated with low roughness. Devices made from materials that are transparent in the UV to visible wavelength range, such as SiN, gallium nitride (GaN), aluminum nitride (AlN), lithium niobate (LiNbO3), and aluminum oxide (Al2O3), are being explored. Meanwhile, the issue of scattered light scalability remains an open challenge.
3) Integrated optics, detectors for light collection and measurement
As the size of ion arrays grows, techniques need to be developed to collect, and detect, photons emitted by large numbers of individual ions. Optics integrated in surface electrode ion traps, and single photon detectors provide a potential means to achieve these rate increases.
In principle, we can imagine a detector under each ion to be measured. Since the integrated detectors would be located very close to the ion, they could have a compact form factor, but their effective area could still collect photons from a solid point of view. The inclusion of integrated optics between the ion and detector can further improve collection efficiency and provide spatial filtering to prevent stray light, or light from neighboring ions, from reaching the detector. Integrated collection optics can also be used to couple photons emitted by the ions into single-mode integrated photonic waveguides that can guide the photons as needed.
Future demonstrations will focus on the integration of detectors and collection optics to enable high-speed, high-fidelity measurements: not susceptible to stray light and offering advantages over traditional collection and detection techniques.
4) Integrated electronics
More research is focused on demonstrating the modularity of ion chains: there is a growing need for ion motion control. This control is achieved by varying the voltages across the trap electrodes, which are typically generated by a large number (approximately one per electrode) of digital-to-analog converters (DACs).
These DACs are typically placed on an electron rack away from the ion trap and the signal is passed to the electrodes through a large array of vacuum leads. While this approach works well for a few electrode traps, it becomes difficult to manage as the trap complexity increases. In addition, the long signal path is susceptible to noise due to the remote location of the DAC. However, the capture and transport of Ca+ ions has been demonstrated in this system.
Monolithic integrated electronics are highly promising. Already, ion traps have been fabricated in commercial CMOS foundries and have demonstrated loading and trapping of stable Sr+ ions, which opens the door to ion trap operation using CMOS electronics. Building on this result, recent work has demonstrated monolithic integration of 16 DAC channels into a surface electrode ion trap fabricated in a 180 nm CMOS foundry process, where Ca+ ions are trapped and stably transported.
While integrated electronics hold great promise, it remains to be demonstrated that they do not introduce harmful effects, for example, by demonstrating that on-chip power dissipation can be managed and that the current in the circuit does not generate fluctuating magnetic fields that cause the ion quantum bits to decoherence. In the meantime, demonstrations of functional CMOS DACs integrated into ion traps may pave the way for integrated electronics beyond DACs.
07Future Technology Development
1) Ion species selection
Basic trapping and control of nearly all alkaline earth and alkaline earth-like ions has been performed, however, there are potential benefits/drawbacks to using specific ions as the system scales up in size and capability; while many ion quantum bits and quantum logic gate types are available, there are still many technologies that need to be developed to create more scalable systems. There are different trade-offs in the choice of different ion types because they differ in mass, energy spectrum, coupling strength of spectral states to electromagnetic radiation, nuclear spin and specific isotopic abundance. The properties of a few of the most commonly used ion species in experiments are shown in the following table.
Common ion properties for quantum computing. The first-order field-independent (FOFI) transitions used are indicated in the last column by the desired magnetic field; "Clock" indicates the use of a nominally zero-field clock state. The symbol I is the nuclear spin, and λ1/2, λ3/2, and λD are the transition wavelengths from the ground state to the decay rates γD at the P1/2, P3/2, and (if present) D5/2 levels. Types of quantum bits commonly encoded: Z (Zeeman), H (hyperfine), F (fine structure) and O (optical); types of gates commonly used: R (Raman), O (optical), M (magnetic [AC or static gradient]). a) There is no good state discrimination for these isotopes; b) This isotope of barium is radioactive and has a half-life of 10.5 years; c) 532 nm (355 nm) light from a double (triple) YAG laser has been used to drive the Raman conversion of Ba+ (Yb+).
2) Selection of quantum bits and gate types
In the current experiments, the two most popular choices of quantum bit-gate pairs are hyperfine quantum bits manipulated using Raman gates, and optical quantum bits manipulated using quadrupole transitions (quadrupole transitions), both using laser excitation.
In the case of single and double quantum bit gates, direct optical gates can be done using only one laser beam, while Raman gates require two or three laser fields and their relative interferometric stability. Therefore, the single-quantum bit-gate operation with Raman gates is much less dependent on the motion of the cooling ion to the ground state of the trap potential than the optical transition (optical transition). Two-quantum bit gates, which are typically slower than single-quantum bit gates due to the need to excite ion (and not just electron) motion, can be compared in a similar way, and the power required will be greater.
The optical power required to drive the optical and Raman gates as a function of the gate time of the ion species. The power is the total power assumed to be equally distributed between the two Raman beams, and the optical gating is performed between the ground state and the D5/2 state. (a) Single quantum bit gates with errors within 10-4. (b) Double quantum bit gates with errors of 10-3 or less. In the optical case, reducing the spontaneous emission error requires a shorter gate time (by increasing the power), while in the Raman case, the scattering error can be reduced by increasing the detuning and power for the same gate time.
3) Choice of system temperature
While the kinetic energy of the atomic ions is reduced by Doppler cooling to a temperature of ≈1 mK, and subsequently cooled down to a temperature of 20 μK; the trap itself can be kept at (or even above) room temperature during operation: the internal electron quantum bits can be effectively isolated from the heat source.
However, for scalable systems, the effect of the trap-electrode temperature needs to be considered. For example, ion lifetimes require ultra-high pressures, and the use of cryogenic techniques to achieve low pressures has the added benefit of a wide choice of materials, since degassing at low temperatures is exponentially suppressed. On the other hand, since the cooling power of most materials is limited at low temperatures, this leads to challenges in power handling, e.g., dissipation of integrated optics and electronics.
4) Summary and outlook
The combination of the above considerations presents a special solution for the system scaling of trapped ions.
If the gate duration is about 10-5 seconds, there is no limit to the overall processor speed, and lower optical power requirements can be obtained using optical logic gates instead of excited Raman excitation. However, if faster gates are required (at or below the microsecond level for double quantum bit gate durations), less power is required through Raman gates. For potentially scalable architectures utilizing an integrated photonics approach, optical gates have the added advantage of operating at generally longer wavelengths in the red and infrared; Raman gates may need to provide high optical power at blue and UV wavelengths, where the loss in the optical waveguide is somewhat higher. Therefore, if the gate operation is done optically, the on-chip power dissipation is reduced.
In cases where low storage error, high-fidelity entanglement is required, hyperfine quantum bits are the best choice; Zeeman quantum bits are a potential second choice if the system requirements allow magnetic shielding. Optical and fine structured quantum bits are subject to metastable state lifetime limitations and are therefore less suitable for situations where long time error-free entanglement is required, such as NISQ quantum simulations.
The high ion mass of hyperfine quantum bits, on the other hand, leads to an increase in the power required for Raman gates and also requires higher voltages to be applied to the ion trap, which is another challenge for increasing scalability. Lighter ions allow higher trap frequencies and therefore may allow faster gate operation (if sufficient power is available), but their wavelengths are outside the UV range, which limits the applicability of standard integrated photonics techniques. Medium weight ions can be used for portable applications such as quantum sensors, which are feasible on the basis of electrical and optical power compromises.
If there were to be a "universal" ion, it would probably be Ca+. It has been used extensively in experiments: all types of quantum bits and gates have been demonstrated, with high-fidelity two-qubit gates, state preparation, measurements, and very long coherence times. It has also been used to demonstrate many quantum computing algorithms, as well as for quantum simulation studies. the wavelengths required for Ca+ are also relatively convenient: roughly across the visible spectrum, and fully functional ionic quantum bits with (43Ca+) or without (40Ca+) nuclear spin can be chosen, each with optically addressable levels for shelving or performing quantum operations. Thus, it is even possible to build a system around a single ion - Ca+ - especially in cases where flexible operations or eventual quantum computing-related applications are required.
Finally, since captured ion quantum bit technology has already played a key role in advancing the field of quantum computing and highlighting the realization of large-scale quantum information processing over the past two decades, although the previously listed experimental proposals to explore the long-term prospects of captured ion quantum computing are not exhaustive, we believe that in the coming years, captured ions may continue to be an exploration of quantum computing capabilities and quantum information technology as powerful tool for exploring quantum computing capabilities and quantum information technology in the years to come.
References：
[1]https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.220501
[2]https://aip.scitation.org/doi/10.1063/1.5088164
[3]https://ieeexplore.ieee.org/document/365700
[4]https://www.nature.com/articles/nature07125
[5]https://iopscience.iop.org/article/10.1088/1367-2630/15/12/123012
[6]https://www.nature.com/articles/nphys2900
[7]https://arxiv.org/abs/1902.04059
[8]https://journals.aps.org/prx/abstract/10.1103/PhysRevX.7.041061
[9]https://www.nature.com/articles/s41566-017-0007-1
[10]https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.021012
[11]https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.123603
[12]https://arxiv.org/abs/1902.08543[13]https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.090502
[14]https://www.science.org/doi/10.1126/sciadv.1601540
[15]https://iopscience.iop.org/article/10.1088/2058-9565/aae0fe
[16]https://www.science.org/doi/10.1126/science.aad9958
[17]https://www.pnas.org/doi/full/10.1073/pnas.1618020114
[18]https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.11.024010
[19]https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.040503
[20]https://iopscience.iop.org/article/10.1088/1367-2630/18/2/023047
[21]https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.023201
[22]https://iopscience.iop.org/article/10.1088/1367-2630/aa6918
[23]https://link.springer.com/article/10.1007/s00340-018-6903-3
[24]https://link.springer.com/article/10.1007/s00340-016-6527-4
[25]https://aip.scitation.org/doi/10.1063/1.5045326
[26]https://iopscience.iop.org/article/10.1088/2058-9565/ab0513
[27]https://journals.aps.org/pra/abstract/10.1103/PhysRevA.99.023405
[28]https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.063430
[29]https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.140501
[30]https://www.spiedigitallibrary.org/conference-proceedings-of-spie/10933/2507647/Towards-fast-and-scalable-trapped-ion-quantum-logic-with-integrated/10.1117/12.2507647.short?SSO=1
[31]https://journals.aps.org/pra/abstract/10.1103/PhysRevA.84.030303
