The discovery of the quantum factorization algorithm more than a decade ago triggered intense interest in exploring possible physical realizations of quantum computers. Among the many solid state proposals, electron and nuclear spins in Si and group IV related materials have long coherence times and the capability of state preparation, gating and read-out using electric, magnetic and optical fields. Proposals involving silicon seek to take advantage of an existing mature technology and the implicit promise of scalability from solid state materials. Nevertheless, building such quantum systems depends in many cases on the development of fabrication techniques with nearly atomic precision. Managing decoherence, initialization and read-out in any quantum computer remains a daunting task. In this review we summarize proposals and recent developments relevant to the possible realization of a quantum computer constructed out of Si (or group IV) materials.
The discovery of the quantum factorization algorithm more than a decade ago triggered intense interest in exploring possible physical realizations of quantum computers. Among the many solid state proposals, electron and nuclear spins in Si and group IV related materials have long coherence times and the capability of state preparation, gating and read-out using electric, magnetic and optical fields. Proposals involving silicon seek to take advantage of an existing mature technology and the implicit promise of scalability from solid state materials. Nevertheless, building such quantum systems depends in many cases on the development of fabrication techniques with nearly atomic precision. Managing decoherence, initialization and read-out in any quantum computer remains a daunting task. In this review we summarize proposals and recent developments relevant to the possible realization of a quantum computer constructed out of Si (or group IV) materials.
Schemes for the nuclear spin quantum memory are proposed based on a system composed of two electrons or one electron coupled to a single nuclear spin in isotopically purified group-IV elemental and II-VI compound semiconductors. The qubit consists of the singlet state and one of the triplet states of two electrons or simply of an electron spin. These systems are free from the decoherence due to the nuclear dipole-dipole interaction and are advantageous for the long memory time. In the case of two electrons, the protocol for the quantum state transfer between the electron-spin qubit and the nuclear spin qubit is based on the magnetic or electric field tuning of the singlet-triplet state crossing and on the hyperfine coupling supplemented with a well-defined scheme to initialize the nuclear spin. In the case of a single-electron qubit, the quantum state transfer is driven by the hyperfine interaction itself without the need of the nuclear spin initialization. Many practical systems are considered, e.g., two electrons loaded on a Si or ZnSe quantum dot, a single-electron charged state in a Si quantum dot doped with a P atom, a single-electron charged 28Si quantum dot doped with an isotope atom of 29Si, and a localized electron system of Si:P and ZnSe:F in the bulk crystal. General aspects of these systems are investigated and a comparison of merits and demerits is made between the two-electron qubit and the single-electron qubit.
Quantum computation offers the extraordinary promise of solving mathematical and physical problems which are simply beyond the reach of classical computers. However, the experimental realization of quantum computers is extremely challenging, because of the need to initialize, manipulate and measure the state of a set of coupled quantum systems while maintaining fragile quantum coherence. In this thesis work, we have taken significant steps towards the realization of a practical quantum computer: using nuclear spins and magnetic resonance techniques at room temperature, we provided proof of principle of quantum computing in a series of experiments which culminated in the implementation of the simplest instance of Shor’s quantum algorithm for prime factorization (15 = 3 × 5), using a seven-spin molecule. This algorithm achieves an exponential advantage over the best known classical factoring algorithms and its implementation represents a milestone in the experimental exploration of quantum computation. These remarkable successes have been made possible by the synthesis of suitable molecules and the development of many novel techniques for initialization, coherent control and readout of the state of multiple coupled nuclear spins. Furthermore, we devised and implemented a model to simulate both unitary and decoherence processes in these systems, in order to study and quantify the impact of various technological as well as fundamental sources of errors. In summary, this work has given us a much needed practical appreciation of what it takes to build a quantum computer. Furthermore, while liquid NMR quantum computing has well-understood scaling limitations, many of the techniques that originated from this research may find use in other, perhaps more scalable quantum computer implementations.
Technological growth in the electronics industry has historically been measured by the number of transistors that can be crammed onto a single microchip. Unfortunately, all good things must come to an end; spectacular growth in the number of transistors on a chip requires spectacular reduction of the transistor size. For electrons in semiconductors, the laws of quantum mechanics take over at the nanometre scale, and the conventional wisdom for progress (transistor cramming) must be abandoned. This realization has stimulated extensive research on ways to exploit the spin (in addition to the orbital) degree of freedom of the electron, giving birth to the field of spintronics . Perhaps the most ambitious goal of spintronics is to realize complete control over the quantum mechanical nature of the relevant spins. This prospect has motivated a race to design and build a spintronic device capable of complete control over its quantum mechanical state, and ultimately, performing computations: a quantum computer. In this tutorial we summarize past and very recent developments which point the way to spin-based quantum computing in the solid state. After introducing a set of basic requirements for any quantum computer proposal, we offer a brief summary of some of the many theoretical proposals for solid-state quantum computers. We then focus on the Loss–DiVincenzo proposal for quantum computing with the spins of electrons confined to quantum dots. There are many obstacles to building such a quantum device. We address these, and survey recent theoretical, and then experimental progress in the field. To conclude the tutorial, we list some as-yet unrealized experiments, which would be crucial for the development of a quantum dot quantum computer.
Any physical implementation of quantum information processing is known to be extremely demanding. One should be able to perform long coherent quantum manipulations (gating), precise quantum-state synthesis, and detection as well. Ever since the very beginning it has been recognized that the major obstacle arises from the unavoidable open character of any realistic quantum system. The coupling with external (i.e. non-computational) degrees of freedom spoils the unitary structure of quantum evolution, which is the crucial ingredient in quantum computation (QC). The only existing experimental realizations of quantum processors are based on quantum optics and atomic/molecular systems. It is however generally believed that future applications of quantum information may hardly be realized in terms of such systems, which do not permit the large-scale integration of existing microelectronics technology. In contrast, in spite of the serious difficulties related to the fast decoherence times, a solid-state implementation of QC seems to be the only way to benefit synergistically from the recent progress in ultrafast optoelectronics as well as in nanostructure fabrication and characterization. Following this spirit, we shall propose and discuss potential implementations of quantum computation/information based on semiconductor nanostructures. More specifically, as originally envisioned Zanardi and Rossi, 1 we shall present an all-optical implementation of QC based on semiconductor macroatoms. 2 In this context we shall discuss a number of excitonic encoding schemes based on charge and/or spin degrees of freedom. In particular, we shall review a novel implementation scheme 3 which merges ideas from both the fields of spintronics and optoelectronics and sets the stage for an all optical semiconducting spin based quantum information processing.
An architecture for a quantum computer is presented in which spins associated with donors in silicon function as qubits. Quantum operations on the spins are performed using a combination of voltages applied to gates adjacent to the spins and radio frequency magnetic fields applied resonant with spin transitions. Initialization and measurement of electron spins is made by electrostatic probing of a two electron system, whose orbital configuration must depend on the spin states of the electrons because of the Pauli Principle. Specific devices will be discussed which perform all the necessary operations for quantum computing, with an emphasis placed on a qualitative presentation of the principles underlying their operation. The likely impediments to achieving large-scale quantum computation using this architecture will be addressed: the computer must operate at extremely low temperature, must be fabricated from devices built with near atomic precision, and will require extremely accurate gating operations in order to perform quantum logic. Refinements to the computer architecture will be presented which could remedy each of these deficiencies. I will conclude by discussing a possible specific realization of the computer using Si/SixGe1–x heterostructures into which donors are deposited using a low energy focused ion beam.
Over the past several decades, quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer is yes, and many research groups around the world are working towards the highly ambitious technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for quantum computation. However, it remains unclear which technology, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain the major challenges for the future. This review outlines the principles of operation of quantum computers and their elements. The theory of ideal computers that do not interact with the environment and are immune to quantum decohering processes is presented. Decohering processes in quantum computers are investigated. The review considers methods for correcting quantum computing errors arising from the decoherence of the state of the quantum computer, as well as possible methods for the suppression of the decohering processes. A brief enumeration of proposed quantum computer realizations concludes the review.