Semiconductor quantum computation

National Science Review 6: 32–54, 2019 doi: 10.1093/nsr/nwy153 Advance access publication 22 December 2018 REVIEW PHYSICS Special Topic: Quantum Computing Semiconductor quantum computation ABSTRACT 1 Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei 230026, China and 2 Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China ∗ Corresponding authors. E-mails: ; Received 30 July 2018; Revised 5 November 2018; Accepted 18 December 2018 Semiconductors, a significant type of material in the information era, are becoming more and more powerful in the field of quantum information. In recent decades, semiconductor quantum computation was investigated thoroughly across the world and developed with a dramatically fast speed. The research varied from initialization, control and readout of qubits, to the architecture of fault-tolerant quantum computing. Here, we first introduce the basic ideas for quantum computing, and then discuss the developments of single- and two-qubit gate control in semiconductors. Up to now, the qubit initialization, control and readout can be realized with relatively high fidelity and a programmable two-qubit quantum processor has even been demonstrated. However, to further improve the qubit quality and scale it up, there are still some challenges to resolve such as the improvement of the readout method, material development and scalable designs. We discuss these issues and introduce the forefronts of progress. Finally, considering the positive trend of the research on semiconductor quantum devices and recent theoretical work on the applications of quantum computation, we anticipate that semiconductor quantum computation may develop fast and will have a huge impact on our lives in the near future. Keywords: semiconductor quantum dot, qubit, quantum computation, spin manipulation INTRODUCTION Recently, the tremendous advances in quantum computation have attracted global attention, putting this subject again in the spotlight since it was first proposed by Richard Feynman [1] in 1982. In the race to build a quantum computer, several competitors have emerged, such as superconducting circuits [2,3], trapped ions [4,5], semiconductors [6,7], nitrogen-vacancy centers [8,9], nuclear magnetic resonance [10], etc. Among these, semiconductors are a powerful contender for their significant role in the field of classical computing. They have not only changed our lives with the personal computer, smartphone, Internet and artificial intelligence but also boosted economics worldwide, such as the birth of Silicon Valley in the USA. With the aim of promoting another technological revolution in the quantum field, in the last decade, several significant breakthroughs in quantum information processing have been made based on semiconductors. These advances in turn confirm the faith of researchers trying to build a quantum computer out of semiconductors. Similar to the classical counterpart that is built upon classical bits, a quantum computer is made of quantum bits, which are also called ‘qubits’. A qubit is a two-level system that exhibits quantum properties: superposition and entanglement. Superposition refers to the ability that a qubit has to not only reside in the state |0 or |1 like a classical bit, but also in the state |ψ = cos(θ/2)|0 + e i ϕ (sin θ )/2|1. Here θ and ϕ are real numbers that define a point on a unit 3D sphere. Thus an arbitrary qubit state can be described as a point on the surface of a sphere, as depicted in Fig. 1a, which is termed a Bloch sphere. The basis states |0 and |1 are the north and south poles of the sphere,√ respectively, while the two √ superposition states 1/ 2(|0 + |1) and 1/ 2(|0 − |1) are on the equator.  C The Author(s) 2018. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. All rights reserved. For permissions, please e-mail: (1) Xin Zhang1,2 , Hai-Ou Li1,2,∗ , Gang Cao1,2 , Ming Xiao1,2 , Guang-Can Guo1,2 and Guo-Ping Guo1,2,∗ REVIEW Zhang et al. 33 The property of entanglement describes the correlation of different qubits √ during processing, i.e. a two-qubit state can be 1/ 2(|01 + |10), in which one qubit state depends on the other: if the first qubit were in state |0, the other qubit would be in state |1, and vice versa. By taking advantage of these two significant properties, many quantum algorithms have been proposed to give a nearly exponential speed-up compared to classical computing for a variety of problems, such as prime Figure 1. Single- and two-qubit gate control and devices for semiconductor qubits. (a) Bloch-sphere representation of a qubit. A superposition state |ψ can be represented by a point on the sphere (left). An arbitrary rotation from the initial state |ψi  to the target state |ψt  can be decomposed by successive rotations about the z and y axes for φ z and φ y , respectively (right). (b) The spin-up probability of the spin-up state for the right qubit P ↑R (blue) and the left qubit P ↑L (red) as a function of interaction time τp for input states |↓↑ and |↓↓. The vertical dashed line at τp = 130 ns corresponds to a CNOT gate. (Adapted from [17].) (c) and (d) are a false-color SEM image and a schematic cross-section of a Si/SiGe DQD, respectively. The DQD with two electrons confined in the potential created by gates L, M and R is used to form two spin-1/2 qubits and a SET under the DQD is used to work as a charge sensor. A slanting Zeeman field was created by a micro-magnet (not shown) for qubit control. (Adapted from [17].) (e), (f) and (g) are images and schematics for the device fabricated by STM hydrogen lithography. (Adapted from [30].) (e) Large-scale STM image of the device; red areas are P-doped to form a SET, source and drain leads, and electrostatic gates. A donor molecule (2P) and single donor (1P) are shown by two circles. (f) False-color composite SEM and STM image showing the buried donor structures (red) and the aluminum antenna (blue). (g) Vertical cross-section of the donor device, showing the thicknesses (not to scale) and relative positions of the silicon, phosphorus, oxide and aluminum layers. (h) and (i) are a SEM image and schematic oblique view of a device fabricated by ion implantation, highlighting the position of the P donor, the MW antenna and the readout SET. (Adapted from [31] and [51].) 34 Natl Sci Rev, 2019, Vol. 6, No. 1 namical decoupling pulses can be utilized and the resulting decay time is the intrinsic T2 . In some experiments when these two parameters cannot be obtained, the decay times of other coherent oscillations are also used to estimate the qubit coherence, such as the decay time of Rabi oscillations (TRabi ). Usually, the Rabi decay time TRabi is longer than T2 since the concatenation of its oscillations plays a similar role to dynamical decoupling (...truncated)