Decoherence in solid-state qubits

The interaction of solid-state qubits with environmental degrees of freedom strongly affects the qubit dynamics, and leads to decoherence. In quantum information processing with solid-state qubits, decoherence significantly limits the performances of such devices. Therefore, it is necessary to fully understand the mechanisms that lead to decoherence. In this review, we discuss how decoherence affects two of the most successful realizations of solid-state qubits, namely, spin qubits and superconducting qubits. In the former, the qubit is encoded in the spin 1/2 of the electron, and it is implemented by confining the electron spin in a semiconductor quantum dot. Superconducting devices show quantum behaviour at low temperatures, and the qubit is encoded in the two lowest energy levels of a superconducting circuit. The electron spin in a quantum dot has two main decoherence channels, a (Markovian) phonon-assisted relaxation channel, due to the presence of a spin–orbit interaction, and a (non-Markovian) spin bath constituted by the spins of the nuclei in the quantum dot that interact with the electron spin via the hyperfine interaction. In a superconducting qubit, decoherence takes place as a result of fluctuations in the control parameters, such as bias currents, applied flux and bias voltages, and via losses in the dissipative circuit elements.     

High-Field Phenomena of Qubits

Electron and nuclear spins are very promising candidates to serve as quantum bits (qubits) for proposed quantum computers, as the spin degrees of freedom are relatively isolated from their surroundings and can be coherently manipulated, e.g., through pulsed electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR). For solid-state spin systems, impurities in crystals based on carbon and silicon in various forms have been suggested as qubits, and very long relaxation rates have been observed in such systems. We have investigated a variety of these systems at high magnetic fields in our multifrequency pulsed EPR/ENDOR (electron nuclear double resonance) spectrometer. A high magnetic field leads to large electron spin polarizations at helium temperatures, giving rise to various phenomena that are of interest with respect to quantum computing. For example, it allows the initialization of both the electron spin as well as hyperfine-coupled nuclear spins in a well-defined state by combining millimeter and radio-frequency radiation. It can increase the T ₂ relaxation times by eliminating decoherence due to dipolar interaction and lead to new mechanisms for the coherent electrical readout of electron spins. We will show some examples of these and other effects in Si:P, SiC:N and nitrogen-related centers in diamond.     

Quantum Cryptography in Spin Networks

In this paper we propose a new scheme of long-distance quantum cryptography based on spin networks with qubits stored in electron spins of quantum dots. By＂ conditional Faraday- rotation, single photon polarization measurement, and quantum state transfer, maximal-entangled Bell states for quantum cryptography between two long-distance parties are created. Meanwhile, efficient quantum state transfer over arbitrary＂ distances is obtained in a spin chain by＂ a proper choice of coupling strengths and using spin memory- technique improved. We also analyse the security＂ of the scheme against the cloning-based attack which can be also implemented in spin network and discover that this spin network cloning coincides with the optimal fidelity- achieved by＂ an eavesdropper for entanglement-based cryptography.     

Polarization-Dependent Mode Analyzer and Controlled-Z Gate in Ti:LiNbO3 Quantum Photonic Circuits

Abstract

On-chip integrated photonic circuits are crucial for further progress toward quantum technologies and in the science of quantum optics. The quantum controlled-Z gate is an example of the maximally entangling gate, which is universal for quantum computing when coupled with single-qubit gates. This article demonstrates a deterministic controlled-Z photonic quantum gate based on titanium in-diffused channel waveguides in which polarization and modal degrees of freedom of a single photon are used for encoding the control and target qubits, respectively.     

基于金刚石氮-空位色心自旋系综与超导量子电路混合系统的量子节点纠缠

量子纠缠是实现量子计算和量子通信的核心基础,本文提出了在金刚石氮-空位色心(NV centers)自旋系综与超导量子电路耦合的混合系统中实现两个分离量子节点之间纠缠的理论方案.在该混合系统中,把金刚石NV centers自旋系综和与之耦合的超导共面谐振器视为一个量子节点,两个量子节点之间通过一个空的超导共面谐振器连接.具有较长相干时间的NV centers自旋系综作为一个量子存储器,用于制备、存储和发送量子信息;易于外部操控的超导量子电路可执行量子逻辑门操作,快速调控量子信息.为了实现两个分离量子节点之间的纠缠,首先对系统的哈密顿量进行正则变换,将其等价为两个NV centers自旋系综与同一个超导共面谐振器之间的JC耦合;然后采用NV centers自旋-光子混合比特编码的方式,通过调节超导共面谐振器的谐振频率,精确控制体系演化时间,高保真度地实现了两个分离量子节点之间的量子纠缠.本方案还可以进一步扩展和集成,用于构建多节点纠缠的分布式量子网络.     

Entanglement swapping between electromagnetic field modes and matter qubits

Scalable quantum networks require the capability to create, store and distribute entanglement among distant nodes (atoms, trapped ions, charge and spin qubits built on quantum dots, etc.) by means of photonic channels. We show how the entanglement between qubits and electromagnetic field modes allows generation of entangled states of remotely located qubits. We present analytical calculations of linear entropy and the density matrix for the entangled qubits for the system described by the Jaynes-Cummings model. We also discuss the influence of decoherence. The presented scheme is able to drive an initially separable state of two qubits into an highly entangled state suitable for quantum information processing.     

Spin quantum computation in silicon nanostructures

Proposed silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals because of their long spin coherence times due to their limited interactions with their environments. For these spin qubits, shallow donor exchange gates are frequently invoked to perform two-qubit operations. We discuss in this review a particularly important spin decoherence channel, and bandstructure effects on the exchange gate control. Specifically, we review our work on donor electron spin spectral diffusion due to background nuclear spin flip-flops, and how isotopic purification of silicon can significantly enhance the electron spin dephasing time. We then review our calculation of donor electron exchange coupling in the presence of degenerate silicon conduction band valleys. We show that valley interference leads to orders of magnitude variations in electron exchange coupling when donor configurations are changed on an atomic scale. These studies illustrate the substantial potential that donor electron/nuclear spins in silicon have as candidates for qubits and simultaneously the considerable challenges they pose. In particular, our work on spin decoherence through spectral diffusion points to the possible importance of isotopic purification in the fabrication of scalable solid state quantum computer architectures. We also provide a critical comparison between the two main proposed spin-based solid state quantum computer architectures, namely, shallow donor bound states in Si and localized quantum dot states in GaAs.     

Enhancement of electron spin coherence by optical preparation of nuclear spins

We study a large ensemble of nuclear spins interacting with a single electron spin in a quantum dot under optical excitation and photon detection. At the two-photon resonance between the two electron-spin states, the detection of light scattering from the intermediate exciton state acts as a weak quantum measurement of the effective magnetic (Overhauser) field due to the nuclear spins. In a coherent population trapping state without light scattering, the nuclear state is projected into an eigenstate of the Overhauser field operator, and electron decoherence due to nuclear spins is suppressed: We show that this limit can be approached by adapting the driving frequencies when a photon is detected. We use a Lindblad equation to describe the driven system under photon emission and detection. Numerically, we find an increase of the electron coherence time from 5 to 500 ns after a preparation time of 10 micros.     

Spin interactions,relaxation and decoherence in quantum dots

We review recent studies on spin decoherence of electrons and holes in quasi-two-dimensional quantum dots, as well as electron-spin relaxation in nanowire quantum dots. The spins of confined electrons and holes are considered major candidates for the realization of quantum information storage and processing devices, provided that sufficiently long coherence and relaxation times can be achieved. The results presented here indicate that this prerequisite might be realized in both electron and hole quantum dots, taking one large step towards quantum computation with spin qubits.     

An endohedral fullerene-based nuclear spin quantum computer

We propose a new scalable quantum computer architecture based on endohedral fullerene molecules. Qubits are encoded in the nuclear spins of the endohedral atoms, which posses even longer coherence times than the electron spins which are used as the qubits in previous proposals. To address the individual qubits, we use the hyperfine interaction, which distinguishes two modes (active and passive) of the nuclear spin. Two-qubit quantum gates are effectively implemented by employing the electronic dipolar interaction between adjacent molecules. The electron spins also assist in the qubit initialization and readout. Our architecture should be significantly easier to implement than earlier proposals for spin-based quantum computers, such as the concept of Kane [B.E. Kane, Nature 393 (1998) 133].     

Spin readout and initialization in a semiconductor quantum dot

Electron spin qubits in semiconductors are attractive from the viewpoint of long coherence times. However, single spin measurement is challenging. Several promising schemes incorporate ancillary tunnel couplings that may provide unwanted channels for decoherence. Here, we propose a novel spin-charge transduction scheme, converting spin information to orbital information within a single quantum dot by microwave excitation. The same quantum dot can be used for rapid initialization, gating, and readout. We present detailed modeling of such a device in silicon to confirm its feasibility.     

Measurement of a heavy-hole hyperfine interaction in InGaAs quantum dots using resonance fluorescence

We measure the strength and the sign of hyperfine interaction of a heavy hole with nuclear spins in single self-assembled quantum dots. Our experiments utilize the locking of a quantum dot resonance to an incident laser frequency to generate nuclear spin polarization. By monitoring the resulting Overhauser shift of optical transitions that are split either by electron or exciton Zeeman energy with respect to the locked transition using resonance fluorescence, we find that the ratio of the heavy-hole and electron hyperfine interactions is -0.09 ± 0.02 in three quantum dots. Since hyperfine interactions constitute the principal decoherence source for spin qubits, we expect our results to be important for efforts aimed at using heavy-hole spins in quantum information processing.     

Storage of multiple coherent microwave excitations in an electron spin ensemble

Strong coupling between a microwave photon and electron spins, which could enable a long-lived quantum memory element for superconducting qubits, is possible using a large ensemble of spins. This represents an inefficient use of resources unless multiple photons, or qubits, can be orthogonally stored and retrieved. Here we employ holographic techniques to realize a coherent memory using a pulsed magnetic field gradient and demonstrate the storage and retrieval of up to 100 weak 10?GHz coherent excitations in collective states of an electron spin ensemble. We further show that such collective excitations in the electron spin can then be stored in nuclear spin states, which offer coherence times in excess of seconds.     

"量身定做"单光子波包:在量子网络中控制光子/自旋量子界面

文章简要地介绍了如何在量子网络中控制量子界面动力学以实现静态量子比特和动态量子比特的相互转换．具体言之，该界面由半导体量子点、固体光学微腔以及光学波导管构成，静态及动态比特分别为量子点中的电子自旋和波导管中的单光子波包所携带．界面动力学的控制则是基于对量子点、微腔和波导管耦合系统的量子电动力学的严格求解．据此可实现网络中两个远距离节点间的量子态传输、交换以及确定性的建立量子纠缠等量子操作．上述量子界面亦可用于任意指定波形的单光子源或者单光子探测装置。     

Quantum readout and fast initialization of nuclear spin qubits with electric currents

Nuclear spin qubits have the longest coherence times in the solid state, but their quantum readout and initialization is a great challenge. We present a theory for the interaction of an electric current with the nuclear spins of donor impurities in semiconductors. The theory yields a sensitivity criterion for quantum detection of nuclear spin states using electrically detected magnetic resonance, as well as an all-electrical method for fast nuclear spin qubit initialization.     

Entanglement of remote atomic qubits

We report observations of entanglement of two remote atomic qubits, achieved by generating an entangled state of an atomic qubit and a single photon at site , transmitting the photon to site in an adjacent laboratory through an optical fiber, and converting the photon into an atomic qubit. Entanglement of the two remote atomic qubits is inferred by performing, locally, quantum state transfer of each of the atomic qubits onto a photonic qubit and subsequent measurement of polarization correlations in violation of the Bell inequality [EQUATION: SEE TEXT]. We experimentally determine [EQUATION: SEE TEXT]. Entanglement of two remote atomic qubits, each qubit consisting of two independent spin wave excitations, and reversible, coherent transfer of entanglement between matter and light represent important advances in quantum information science.     

Scaling of decoherence in wide NMR quantum registers

Among the most important parameters for the usefulness of quantum computers are the size of the quantum register and the decoherence time for the quantum information. The decoherence time is expected to get shorter with the number of correlated qubits, but experimental data are only available for small numbers of qubits. Solid-state nuclear magnetic resonance allows one to correlate large numbers of qubits (several hundred) and measure their decoherence rates. We use a modified magnetic dipole-dipole interaction to correlate the proton spins in a solid sample and observe the decay of the resulting highly correlated states. By systematically varying the number of correlated spins, we measure the increase of the decoherence rate with the size of the quantum register.     

Experimental Hamiltonian Learning of an 11-Qubit Solid-State Quantum Spin Register

Learning the Hamiltonian of a quantum system is indispensable for prediction of the system dynamics and realization of high fidelity quantum gates.However,it is a significant challenge to efficiently characterize the Hamiltonian which has a Hilbert space dimension exponentially growing with the system size.Here,we develop and implement an adaptive method to learn the effective Hamiltonian of an 11-qubit quantum system consisting of one electron spin and ten nuclear spins associated with a single nitrogen-vacancy center in a diamond.We validate the estimated Hamiltonian by designing universal quantum gates based on the learnt Hamiltonian and implementing these gates in the experiment.Our experimental result demonstrates a well-characterized 11-qubit quantum spin register with the ability to test quantum algorithms,and shows our Hamiltonian learning method as a useful tool for characterizing the Hamiltonian of the nodes in a quantum network with solid-state spin qubits.     

Quantum computing with spin cluster qubits

We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) antiferromagnetic exchange interaction with uniform and nonuniform coupling constants. We show that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. This qubit is remarkably insensitive to the placement and coupling anisotropy of spins within the cluster. One- and two-qubit quantum gates can be generated by magnetic fields and intercluster exchange, and leakage during quantum gate operation is small. Spin cluster qubits inherit the long decoherence times and short gate operation times of single spins. Control of single spins is hence not necessary for the realization of universal quantum gates.     

Prospects for measurement‐based quantum computing with solid state spins

This article aims to review the developments, both theoretical and experimental, that have in the past decade laid the ground for a new approach to solid state quantum computing. Measurement‐based quantum computing (MBQC) requires neither direct interaction between qubits nor even what would be considered controlled generation of entanglement. Rather it can be achieved using entanglement that is generated probabilistically by the collapse of quantum states upon measurement. Single electronic spins in solids make suitable qubits for such an approach, offering long coherence times and well defined routes to optical measurement. We will review the theoretical basis of MBQC and experimental data for two frontrunner candidate qubits – nitrogen‐vacancy (NV) centres in diamond and semiconductor quantum dots – and discuss the prospects and challenges that lie ahead in realising MBQC in the solid state.