Experimental implementation of a concatenated quantum error-correcting code

Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information processing. We report the implementation of a concatenated quantum error-correcting code able to correct phase errors with a strong correlated component. The experiment was performed using liquid-state nuclear magnetic resonance techniques on a four spin subsystem of labeled crotonic acid. Our results show that concatenation between active and passive quantum error correction is a practical tool to handle realistic noise involving both independent and correlated errors.     

Experimental realization of an order-finding algorithm with an NMR quantum computer

We report the realization of a nuclear magnetic resonance quantum computer which combines the quantum Fourier transform with exponentiated permutations, demonstrating a quantum algorithm for order finding. This algorithm has the same structure as Shor's algorithm and its speed-up over classical algorithms scales exponentially. The implementation uses a particularly well-suited five quantum bit molecule and was made possible by a new state initialization procedure and several quantum control techniques.     

Magnetic resonance realization of decoherence-free quantum computation

We report the realization, using nuclear magnetic resonance techniques, of the first quantum computer that reliably executes a complete algorithm in the presence of strong decoherence. The computer is based on a quantum error avoidance code that protects against a class of multiple-qubit errors. The code stores two decoherence-free logical qubits in four noisy physical qubits. The computer successfully executes Grover's search algorithm in the presence of arbitrarily strong engineered decoherence. A control computer with no decoherence protection consistently fails under the same conditions.     

Benchmarking quantum computers: the five-qubit error correcting code.

The smallest quantum code that can correct all one-qubit errors is based on five qubits. We experimentally implemented the encoding, decoding, and error-correction quantum networks using nuclear magnetic resonance on a five spin subsystem of labeled crotonic acid. The ability to correct each error was verified by tomography of the process. The use of error correction for benchmarking quantum networks is discussed, and we infer that the fidelity achieved in our experiment is sufficient for preserving entanglement.     

Nuclear magnetic resonance: A quantum technology for computation and spectroscopy

In this article we consider nuclear magnetic resonance (NMR) as an example of a quantum technology; we consider in particular detail the implementation of quantum computers using NMR. We begin by outlining the physical principles underlying NMR, and give an introduction to the quantum mechanics involved. We next discuss the general characteristics of quantum technologies and the ways and extent to which these characteristics are expressed in NMR. We then give an introduction to the subject of quantum computation and its implementation using NMR. Finally, we describe some spectroscopy techniques which also exploit the quantum nature of NMR.     

Implementation of the quantum Fourier transform

A quantum Fourier transform (QFT) has been implemented on a three qubit nuclear magnetic resonance (NMR) quantum computer to extract the periodicity of an input state. Implementation of a QFT provides a first step towards the realization of Shor's factoring and other quantum algorithms. The experimental implementation of the QFT on a periodic state is presented along with a quantitative measure of its efficiency measured through state tomography. Experimentally realizing the QFT is a clear demonstration of the ability of NMR to control quantum systems.     

Nuclear magnetic resonance for quantum computing: Techniques and recent achievements

Rapid developments in quantum information processing have been made, and remarkable achievements have been obtained in recent years, both in theory and experiments. Coherent control of nuclear spin dynamics is a powerful tool for the experimental implementation of quantum schemes in liquid and solid nuclear magnetic resonance(NMR) system,especially in liquid-state NMR. Compared with other quantum information processing systems, the NMR platform has the advantages such as the long coherence time, the precise manipulation, and well-developed quantum control techniques,which make it possible to accurately control a quantum system with up to 12-qubits. Extensive applications of liquid-state NMR spectroscopy in quantum information processing such as quantum communication, quantum computing, and quantum simulation have been thoroughly studied over half a century. This article introduces the general principles of NMR quantum information processing, and reviews the new-developed techniques. The review will also include the recent achievements of the experimental realization of quantum algorithms for machine learning, quantum simulations for high energy physics, and topological order in NMR. We also discuss the limitation and prospect of liquid-state NMR spectroscopy and the solid-state NMR systems as quantum computing in the article.     

Experimental realization of quantum games on a quantum computer

We generalize the quantum prisoner's dilemma to the case where the players share a nonmaximally entangled states. We show that the game exhibits an intriguing structure as a function of the amount of entanglement with two thresholds which separate a classical region, an intermediate region, and a fully quantum region. Furthermore this quantum game is experimentally realized on our nuclear magnetic resonance quantum computer.     

Experimental realization of discrete fourier transformation on NMR quantum computers

We report the experimental implementation of discrete Fourier transformation (DFT) on a nuclear magnetic resonance (NMR) quantum computer. Experimental results agree well with the theoretical ones. With the pulse sequences that we propose and the refocusing pulse sequences that one uses to suppress unwanted one-spin and two-spin interactions, the DFT can, in principle, be realized on anyL-bit quantum number.     

Experimental implementation of the quantum baker's map

This Letter reports on the experimental implementation of the quantum baker's map via a three bit nuclear magnetic resonance quantum information processor. The experiments tested the sensitivity of the quantum chaotic map to perturbations. In the first experiment, the map was iterated forward and then backward to provide benchmarks for intrinsic errors and decoherence. In the second set of experiments, the least significant qubit was perturbed in between the iterations to test the sensitivity of the quantum chaotic map to controlled perturbations. These experiments can be used to investigate existing theoretical predictions for quantum chaotic dynamics.     

All-silicon quantum computer

A solid-state implementation of a quantum computer composed entirely of silicon is proposed. Qubits are 29Si nuclear spins arranged as chains in a 28Si (spin-0) matrix with Larmor frequencies separated by a large magnetic field gradient. No impurity dopants or electrical contacts are needed. Initialization is accomplished by optical pumping, algorithmic cooling, and pseudo-pure state techniques. Magnetic resonance force microscopy is used for ensemble measurement.     

半导体核磁共振显微压力的质子全自旋量子门的实现

以实现质子全自旋量子门、观察半导体核子自旋态和量子计算为目的, 依据样品的自旋-晶格弛豫时间和自旋-自旋弛豫时间,采用脉冲调制序列控制磁共振的条件和翻转旋转框架,计算了共振显微压力. 结果表明,质子全自旋量子门具有高灵敏度和高Q操控性,通过扫描片段和激光干涉可以得到磁共振压力. 共振压力兼具MRI和AFM优点,是一种强有力的通过核自旋实现量子计算获得量子信息的有效方法. 关键词： 空间分辨率 共振显微 半导体光刻 电子束刻印     

Field tuning the g factor in InAs nanowire double quantum dots

We study the effects of magnetic and electric fields on the g factors of spins confined in a two-electron InAs nanowire double quantum dot. Spin sensitive measurements are performed by monitoring the leakage current in the Pauli blockade regime. Rotations of single spins are driven using electric-dipole spin resonance. The g factors are extracted from the spin resonance condition as a function of the magnetic field direction, allowing determination of the full g tensor. Electric and magnetic field tuning can be used to maximize the g-factor difference and in some cases altogether quench the electric-dipole spin resonance response, allowing selective single spin control.     

Concepts of spin quantum computing

Quantum computing is based on two-state quantum systems called qubits. Recent proposals for quantum computing included nuclear spin 1/2 as qubits and implementations of several quantum algorithms were demonstrated by applying liquid-state NMR. Here I want to lay out some of the concepts of spin quantum computing including nuclear and electron spins. This article is intended to serve a dual purpose. It should on one hand introduce the reader who is not familiar with magnetic resonance to the spin quantum computing terminology and the concepts of pulsed magnetic resonance. At the same time I want to introduce the NMR expert to the recent developments in quantum computing.     

Implementation of conditional phase-shift gate for quantum information processing by NMR,using transition-selective pulses

Experimental realization of quantum information processing in the field of nuclear magnetic resonance (NMR) has been well established. Implementation of conditional phase-shift gate has been a significant step, which has lead to realization of important algorithms such as Grover's search algorithm and quantum Fourier transform. This gate has so far been implemented in NMR by using coupling evolution method. We demonstrate here the implementation of the conditional phase-shift gate using transition selective pulses. As an application of the gate, we demonstrate Grover's search algorithm and quantum Fourier transform by simulations and experiments using transition selective pulses.     

Efficient decomposition of quantum gates

Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit which is optimal in the sense of fully controlled single-qubit gates and yet is equivalent with the multiqubit gate. In the second step of the optimization, superfluous control bits are eliminated, which eventually results in a smaller total number of the elementary gates. In our scheme the number of controlled NOT gates is O(4(n)) which coincides with the theoretical lower bound.     

Spin-polarized current in double quantum dots

We analyze the transport through asymmetric double quantum dots with an inhomogeneous Zeeman splitting in the presence of crossed dc and ac magnetic fields.A strong spin-polarized current can be obtained by changing the dc magnetic field.It is mainly due to the resonant tunnelling.But for the ferromagnetic right electrode,the electron spin resonance also plays an important role in transport.We show that the double quantum dots with three-level mixing under crossed dc and ac magnetic fields can act not only as a bipolar spin filter but also as a spin inverter under suitable conditions.     

Adder on ternary base elements for a quantum computer

A circuit consisting of elementary quantum logic operators has been proposed for an adder in the ternary number system. A sequence of RF magnetic field pulses has been found for its implementation by the nuclear magnetic resonance method on a chain of quadrupole nuclei with spin I = 1. The numerical simulation of the adder operation has been performed.     

Optically detected resonance spectroscopy of interface fluctuation quantum dots

We have performed optically detected resonance (ODR) spectroscopy on modulation-doped GaAs/AlGaAs quantum wells of different widths in which lateral fluctuations of the well width were purposely introduced by growth interruption at the interfaces. These monolayer fluctuations form quantum dots for which confinement and Coulomb correlation energies are comparable. By monitoring resonant changes of the dot ensemble photoluminescence induced by far-infrared (FIR) radiation in a magnetic field, we have observed cyclotron resonance (CR) of free electrons in the widest wells, as well as internal transitions of mobile and localized charged excitons. The latter, which are forbidden by magnetic translational invariance, have previously not been observed. For the narrower wells the effects of non-parabolicity and carrier localization on the CR and CR-like transitions have to be included for a proper interpretation of the measurements.