A full-scale quantum computer would work like the standard desktop computer, in that it would have a place to store data, a place where a program manipulates the data, and interconnections to move the data from one to the other. In the computer you are using now, bits of data - stored as quantity of charge or its absence - are transferred from memory to a processor in the form of levels of voltage. At the processor the computer's program determines which logic operations the bits will be subjected to. Once the logic operations are completed, the bits are converted to amounts of charge and stored in memory again. Similarly, in an ion-trap computer, stored qubits would be called from a storage trap to a logic trap, the kind we've been building so far. The two traps would be connected by a long trap that acts like an interconnect or a data bus. It sounds simple, but such a structure would have to be repeated and connected many dozens of times on the same chip to handle the number of ions we'd need. Therefore, a quantum computer equivalent of very-large-scale integration would be required to handle the control circuitry just to move the ions around. The small-scale quantum algorithms that scientists are running today and plan to run in the near future will almost certainly lead to insights that could make full-scale quantum computing, if not easy, at least more tractable.
As discussed in Part I of this book, a qubit can in principle be encoded using two energy levels in an atom or ion. These levels are frequently referred to as | g ⧽ and | e ⧽, suggesting the ground state and some excited state, but the actual choice of levels is made so as to optimize the behavior of the system, and it is common to use two hyperfine sublevels of the ground state. As usual, we will simply call the levels |0⧽ and |1⧽. A quantum computer must, of course, have more than one qubit, and this is achieved by using more than one atom or ion, with one qubit encoded on each physical object. In order to make this approach practical, however, it is essential to trap the atoms or ions so that they can be held in a well-controlled environment where they can easily be manipulated. This can be achieved using electric and magnetic fields. The use of trapped ions was one of the first proposals for building quantum computers, and is still one of the best developed. Proposals involving trapped atoms are slightly more recent, and have both substantial advantages and disadvantages in comparison with trapped ions. These differences can ultimately be traced back to the fact that ions interact strongly with their environment and have long-range interactions with one another, while atoms interact more weakly and over shorter ranges. Comparing and contrasting the two approaches provides a useful general introduction to the problems underlying many other proposals. Ion traps It is relatively easy to trap an ion as it will interact strongly with an electric field through the Coulomb interaction.
Today's computers work on bits that exist as either 0 or 1. Quantum computers aren't limited to two states; they encode information as quantum bits, or qubits, which can exist in superposition. Qubits represent atoms, ions, photons or electrons and their respective control devices that are working together to act as computer memory and a processor. Because a quantum computer can contain these multiple states simultaneously, it has the potential to be millions of times more powerful than today's most powerful supercomputers. A processor that can use registers of qubits will be able to perform calculations using all the possible values of the input registers simultaneously. This superposition causes a phenomenon called quantum parallelism, and is the motivating force behind the research being carried out in quantum computing. Due to technical obstacles, till date, a quantum computer has not yet been realized. But the concepts and ideas of quantum computing has been demonstrated using various methods like NMR, Ion Trap, Quantum Dot, Optical Methods, etc. A quantum computer manipulates qubits by executing a series of quantum gates, each a unitary transformation acting on a single qubit or pair of qubits. In applying these gates in succession, a quantum computer can perform a complicated unitary transformation to a set of qubits in some initial state. The qubits can then be measured, with this measurement serving as the final computational result. Research must devise a way to maintain decoherence and other potential sources of error at an acceptable level. Probably the most important idea in this field is the application of error correction in phase coherence as a means to extract information and reduce error in a quantum system without actually measuring that system. Thereby, quantum computers will emerge as the superior computational devices and perhaps one day make today's modern computer obsolete.
This paper reports on a promising technology for constructing an ultrapowerful quantum computer, called the ion trap. Researchers have found a way to build ion traps from semiconductors in much the same way as computer chips. By linking several of these ion trap chips, researchers are able to manipulate much larger numbers of ions and demonstrate rudimentary components of a quantum computer over the next few years. A major benefit of chip-based ion traps is that they could be combined into large arrays. The goal is to create a big switchyard in which hundreds or thousands of ions are constantly being shuttled around in small groups, controlled by conventional electronics.
The power of quantum computation derives from algorithmic methods that exploit the availability of quantum superposition and entanglement to perform computations that are intractable with classical devices. The race is on to develop hardware that will unleash the promise of quantum algorithms. A handful of different types of hardware are currently being developed with the greatest efforts directed at superconducting, quantum-dot, trapped-ion, photonic, and neutral-atom approaches [1]. While all approaches have strengths and weaknesses, and are at different stages of development, the challenge of creating a practical design that can be scaled to a million or more qubits has not yet been met with any of the existing platforms. One may wonder if we really need a million qubits for a useful quantum computer. The answer depends on our ambition level. On the one hand it is widely believed that a quantum computer with less than 100 reliable qubits will be able to demonstrate a quantum advantage for a well defined computational problem [2]. Demonstration of a quantum computational advantage will generate great excitement in the halls of academia, but will have little broader import. A problem of great practical interest such as ab initio design of chemicals for increasing the yield of fertilizers for crop production, to name but one example, may also require just a few hundred qubits, provided computational sequences with circuit depth of 1010 or more operations can be reliably performed [3]. However, given the current performance of qubit hardware, which has demonstrated error rates not less than ∼10−3, computations with depth 1010 will only produce random outcomes of negligible value. The solution lies in the construction of error-correction circuitry operating on logical qubits, each composed of many physical qubits, which will enable logical error rates many orders of magnitude smaller than physical error rates. Although error correction is remarkably efficient for classical computing devices—Hamming codes detect and correct errors while only requiring roughly 10% overhead in the number of physical bits—quantum error correction is notoriously expensive. New approaches to error correction are the subject of intensive research with one promising direction being the development of codes that are optimized to suppress the dominant error mechanism in a particular physical platform [4,5]. Nevertheless, with physical error rates of 10−4, a plausible target for current qubit systems, the overhead required to reach logical error rates of 10−10 may be measured in thousands of physical qubits for each logical qubit. Thus a quantum computer able to perform deep calculations on a few hundred logical qubits could require a million physical qubits. A consequence of the cost of quantum error correction is that any viable approach to large-scale quantum computing needs to combine high-fidelity quantum logic operations with a capability for integrating large numbers of physical qubits. From this perspective neutral-atom qubits appear particularly promising [6] as they have already demonstrated control of more qubits than any other platform with recent experiments in 1D [7], 2D [8,9], and 3D [10] geometries showing control of up to 50 atomic qubits. Large qubit arrays can potentially be prepared in 1D, 2D, or 3D geometries. The number of proximal qubits increases with the dimensionality, which is advantageous for implementation of error correction code words, and points towards a preference for 2D or 3D arrays. On the other hand, the added overhead of compensating crosstalk incurred when targeting atoms inside a 3D volume makes parallel operations on multiple qubits challenging. A 2D geometry, as shown schematically in Fig. 1, may be an optimal choice since qubit control and measurement can be performed with lasers propagating normal to the plane of the array so that individual qubit sites can be addressed independently. With demonstrated array periods of a few micrometers we require a footprint of less than 1 mm2 for 104 qubits. Conceptual picture of a 2D neutral-atom qubit array. a) High-numerical-aperture lenses project several different wavelengths of light for control and measurement of the qubits. Specific choices of optical wavelengths depend on the atomic species. Not shown are optics for initial laser cooling, transport to the array, beam scanning, and imaging for qubit measurement. b) Averaged fluorescence image of 49 atomic qubits on a 2D grid with |
3.8μm| spacing [8]. From a fundamental perspective the prospects for scaling neutral-atom systems are particularly promising due to the exceptionally large ratio between coherent and incoherent coupling rates. Neutral-atom qubits are encoded in hyperfine ground states for which coherence times of the order of 10 s have been demonstrated [10]. This implies a dephasing rate |
γ∼0.1s−1|. The coherent coupling that enables quantum logic operations is switched on by exciting atoms to high-lying Rydberg states with principal quantum number close to 100 [11,12]. Rydberg excited atoms at spacings of a few micrometers in an optical lattice interact coherently with rates |
g>109s−1|. The ratio between desired coherent coupling and residual incoherent dephasing of g/γ ∼ 1010 establishes a figure of merit that is enabling for scalability. To our knowledge only trapped ions can claim a similar g/γ ratio [13], but without a correspondingly direct path towards controlling thousands of qubits in a single processing unit. Although the g/γ ratio is exceptionally favorable for neutral-atom qubits a complete set of universal gate operations has not yet been demonstrated with high fidelity. Single-qubit gates in large 2D and 3D arrays have reached fidelity |
F∼0.999| [8,10]. However, the highest demonstrated fidelity for two-qubit entanglement mediated by Rydberg-state interactions is |
F<0.8| [6,14,15], a value that is well short of the theoretical limit of |
F>0.9999| [16,17]. There is healthy optimism within the research community working with neutral-atom qubits that combining improved laser sources with reduced noise, better cooling to reduce motional dephasing, and control of stray electric fields that perturb Rydberg atoms will lead to substantially improved gate fidelity in the near future. Recent results with better filtering of laser phase noise have already demonstrated remarkable improvement in ground–Rydberg entanglement [18]. The outlook for the next few years appears very promising. We anticipate that with advances in lasers, optical lattices for atom trapping, deterministic rearrangement and loading of atoms in multi-dimensional arrays [19,20], and optics for fast beam scanning it will be possible to increase the number of physical qubits in a single neutral-atom module to at least 104. A challenging yet plausible path to a million-qubit processor can then be contemplated by connecting 100 such modules with atom–photon entanglement channels [21]. Beyond the potential for advancing the state of the art in computation, development of techniques for single-atom control inside large multi-atom arrays will enable other applications of quantum science including metrology and time-keeping. Rydberg interactions that are at the heart of a neutral-atom quantum computer may lead to multi-atom entanglement and Heisenberg scaling of atomic-clock precision [22]. This work was supported by the NSF and ARL CDQI.
Abstract The first generation of quantum computers are on the horizon, fabricated from quantum hardware platforms that may soon be able to tackle certain tasks that cannot be performed or modelled with conventional computers. These quantum devices will not likely be universal or fully programmable, but special-purpose processors whose hardware will be tightly co-designed with particular target applications. Trapped atomic ions are a leading platform for first-generation quantum computers, but they are also fundamentally scalable to more powerful general purpose devices in future generations. This is because trapped ion qubits are atomic clock standards that can be made identical to a part in 1015, and their quantum circuit connectivity can be reconfigured through the use of external fields, without modifying the arrangement or architecture of the qubits themselves. In this forward-looking overview, we show how a modular quantum computer with thousands or more qubits can be engineered from ion crystals, and how the linkage between ion trap qubits might be tailored to a variety of applications and quantum-computing protocols.