Scalable architecture for a room temperature solid-state quantum information processor

Two-color electromagnetically induced transparency generated slow light in double-mechanical-mode coupling carbon nanotube resonators

We theoretically propose a multiple-mode-coupling hybrid quantum system comprising two-mode-coupling nanomechanical carbon nanotube (CNT) resonators realized by a phase-dependent phonon-exchange interaction interacting with the same nitrogen-vacancy (NV) center in diamond. We investigate the coherent optical responses of the NV center under the condition of resonance and detuning. In particular, two-color electromagnetically induced transparency (EIT) can be achieved by controlling the system parameters and coupling regimes. Combining the spin-phonon interactions and phonon-phonon coupling with the modulation phase, the switching of one and two EIT windows has been demonstrated, which generates a light delay or advance. The slow-to-fast and fast-to-slow light transitions have been studied in different coupling regimes, and the switch between slow and fast light can be controlled periodically by tuning the modulation phase. The study can be applied to phonon-mediated optical information storage or information processing with spin qubits based on multiple-mode hybrid quantum systems.

Complexity Phase Diagram for Interacting and Long-Range Bosonic Hamiltonians

We classify phases of a bosonic lattice model based on the computational complexity of classically simulating the system. We show that the system transitions from being classically simulable to classically hard to simulate as it evolves in time, extending previous results to include on-site number-conserving interactions and long-range hopping. Specifically, we construct a complexity phase diagram with easy and hard "phases" and derive analytic bounds on the location of the phase boundary with respect to the evolution time and the degree of locality. We find that the location of the phase transition is intimately related to upper bounds on the spread of quantum correlations and protocols to transfer quantum information. Remarkably, although the location of the transition point is unchanged by on-site interactions, the nature of the transition point does change. Specifically, we find that there are two kinds of transitions, sharp and coarse, broadly corresponding to interacting and noninteracting bosons, respectively. Our Letter motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.

Wide field imaging of van der Waals ferromagnet Fe3GeTe2 by spin defects in hexagonal boron nitride

Emergent color centers with accessible spins hosted by van der Waals materials have attracted substantial interest in recent years due to their significant potential for implementing transformative quantum sensing technologies. Hexagonal boron nitride (hBN) is naturally relevant in this context due to its remarkable ease of integration into devices consisting of low-dimensional materials. Taking advantage of boron vacancy spin defects in hBN, we report nanoscale quantum imaging of low-dimensional ferromagnetism sustained in Fe₃GeTe₂/hBN van der Waals heterostructures. Exploiting spin relaxometry methods, we have further observed spatially varying magnetic fluctuations in the exfoliated Fe₃GeTe₂ flake, whose magnitude reaches a peak value around the Curie temperature. Our results demonstrate the capability of spin defects in hBN of investigating local magnetic properties of layered materials in an accessible and precise way, which can be extended readily to a broad range of miniaturized van der Waals heterostructure systems.

Hexagonal boron nitride (h-BN) has been used extensively to encapsulate other van der Waals materials, protecting them from environmental degradation, and allowing integration into more complex heterostructures. Here, the authors make use of boron vacancy spin defects in h-BN using them to image the magnetic properties of a Fe₃GeTe₂ flake.

Sub-10 nm Precision Engineering of Solid-State Defects via Nanoscale Aperture Array Mask

Engineering a strongly interacting uniform qubit cluster would be a major step toward realizing a scalable quantum system for quantum sensing and a node-based qubit register. For a solid-state system that uses a defect as a qubit, various methods to precisely position defects have been developed, yet the large-scale fabrication of qubits within the strong coupling regime at room temperature continues to be a challenge. In this work, we generate nitrogen vacancy (NV) color centers in diamond with sub-10 nm scale precision using a combination of nanoscale aperture arrays (NAAs) with a high aspect ratio of 10 and a secondary E-beam hole pattern used as an ion-blocking mask. We perform optical and spin measurements on a cluster of NV spins and statistically investigate the effect of the NAAs during an ion-implantation process. We discuss how this technique is effective for constructing a scalable system.

Entanglement of dark electron-nuclear spin defects in diamond

A promising approach for multi-qubit quantum registers is to use optically addressable spins to control multiple dark electron-spin defects in the environment. While recent experiments have observed signatures of coherent interactions with such dark spins, it is an open challenge to realize the individual control required for quantum information processing. Here, we demonstrate the heralded initialisation, control and entanglement of individual dark spins associated to multiple P1 centers, which are part of a spin bath surrounding a nitrogen-vacancy center in diamond. We realize projective measurements to prepare the multiple degrees of freedom of P1 centers-their Jahn-Teller axis, nuclear spin and charge state-and exploit these to selectively access multiple P1s in the bath. We develop control and single-shot readout of the nuclear and electron spin, and use this to demonstrate an entangled state of two P1 centers. These results provide a proof-of-principle towards using dark electron-nuclear spin defects as qubits for quantum sensing, computation and networks.

Materials challenges and opportunities for quantum computing hardware

Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.

Indirect overgrowth as a synthesis route for superior diamond nano sensors

The negatively charged nitrogen-vacancy ([Formula: see text]) center shows excellent spin properties and sensing capabilities on the nanoscale even at room temperature. Shallow implanted [Formula: see text] centers can effectively be protected from surface noise by chemical vapor deposition (CVD) diamond overgrowth, i.e. burying them homogeneously deeper in the crystal. However, the origin of the substantial losses in [Formula: see text] centers after overgrowth remains an open question. Here, we use shallow [Formula: see text] centers to exclude surface etching and identify the passivation reaction of NV to NVH centers during the growth as the most likely reason. Indirect overgrowth featuring low energy (2.5-5 keV) nitrogen ion implantation and CVD diamond growth before the essential annealing step reduces this passivation phenomenon significantly. Furthermore, we find higher nitrogen doses to slow down the NV-NVH conversion kinetics, which gives insight into the sub-surface diffusion of hydrogen in diamond during growth. Finally, nano sensors fabricated by indirect overgrowth combine tremendously enhanced [Formula: see text] and [Formula: see text] times with an outstanding degree of depth-confinement which is not possible by implanting with higher energies alone. Our results improve the understanding of CVD diamond overgrowth and pave the way towards reliable and advanced engineering of shallow [Formula: see text] centers for future quantum sensing devices.

Simulating Large Quantum Circuits on a Small Quantum Computer

Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than available, is both of theoretical and practical importance. In this Letter, we introduce cluster parameters K and d of a quantum circuit. The tensor network of such a circuit can be decomposed into clusters of size at most d with at most K qubits of inter-cluster quantum communication. We propose a cluster simulation scheme that can simulate any (K,d)-clustered quantum circuit on a d-qubit machine in time roughly 2^{O(K)}, with further speedups possible when taking more fine-grained circuit structure into account. We show how our scheme can be used to simulate clustered quantum systems-such as large molecules-that can be partitioned into multiple significantly smaller clusters with weak interactions among them. By using a suitable clustered ansatz, we also experimentally demonstrate that a quantum variational eigensolver can still achieve the desired performance for estimating the energy of the BeH_{2} molecule while running on a physical quantum device with half the number of required qubits.

Enhancing Spin-Phonon and Spin-Spin Interactions Using Linear Resources in a Hybrid Quantum System

Hybrid spin-mechanical setups offer a versatile platform for quantum science and technology, but improving the spin-phonon as well as the spin-spin couplings of such systems remains a crucial challenge. Here, we propose and analyze an experimentally feasible and simple method for exponentially enhancing the spin-phonon and the phonon-mediated spin-spin interactions in a hybrid spin-mechanical setup, using only linear resources. Through modulating the spring constant of the mechanical cantilever with a time-dependent pump, we can acquire a tunable and nonlinear (two-phonon) drive to the mechanical mode, thus amplifying the mechanical zero-point fluctuations and directly enhancing the spin-phonon coupling. This method allows the spin-mechanical system to be driven from the weak-coupling regime to the strong-coupling regime, and even the ultrastrong coupling regime. In the dispersive regime, this method gives rise to a large enhancement of the phonon-mediated spin-spin interactions between distant solid-state spins, typically two orders of magnitude larger than that without modulation. As an example, we show that the proposed scheme can apply to generating entangled states of multiple spins with high fidelities even in the presence of large dissipations.

Coupling a single dipole to a long-range surface plasmon device

Embedding a thin layer of a noble metal between two symmetric media results in the hybridization of the surface plasmons, leading to the existence of a long-range surface plasmon (LRSP). In this Letter, we investigate numerically the coupling of a single dipole, as a probe, to this LRSP. Different de-excitation channels are available such as free space radiation and plasmonic modes in different proportions. In a more realistic approach, with finite layers, guided modes in the dielectric may also be excited. The study of the local density of optical states allows us to separate, identify, and reconstruct the different modes. The critical role of the orientation as well as the position of the dipole leads to an interplay between the LRSP and the guided modes. The coupling efficiency with these modes is evaluated. Besides providing a deep understanding of a LRSP in realistic devices, these results could be used as guidelines for future optoelectronic device designs.

Signaling and scrambling with strongly long-range interactions

Strongly long-range interacting quantum systems-those with interactions decaying as a power law 1/r α in the distance r on a D-dimensional lattice for α ⩽ D-have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum-information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. In a step towards rectifying this problem, we prove two Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for α ⩽ D/2. Our second bound pertains to generic long-range interacting spin Hamiltonians and gives a tight lower bound for the signaling time to extensive subsets of the system for all α< D. This many-site signaling time lower bounds the scrambling time in strongly long-range interacting systems.

Ultrafast Orbital Depolarization and Defect-Localized Phonon Dynamics Induced by Quantum Resonance between Multi-Nitrogen Vacancy Defects

Proximate nitrogen-vacancy (NV) defects with interdefect interaction may establish a new kind of quantum qubit network to explore controlled multibody quantum dynamics. In particular, by introducing the critical distance and favorable orientation between a pair of NV defects, the quantum resonance (QR) can be induced. Here, we present the first real-time depolarization and phonon dynamics on the excited state at ambient temperature which are intrinsic to the proximate multi-NV defects. We computationally demonstrate that the QR can effectively change the major properties of the multi-NV defects, such as orbital degeneracy, orbital delocalization, local phonon modes, electron-phonon coupling, and orbital depolarization dynamics, elucidating the physical mechanisms and finding the key factors to control them. The physical insights provide a starting point for the positioning accuracy of NV defects and creation protocols with broad implications for magnetometry, quantum information, nanophotonics, sensing, and spectroscopy, allowing the QR to be a new means of physical manipulation.

Triple nitrogen-vacancy centre fabrication by C5N4Hn ion implantation

Quantum information processing requires quantum registers based on coherently interacting quantum bits. The dipolar couplings between nitrogen vacancy (NV) centres with nanometre separation makes them a potential platform for room-temperature quantum registers. The fabrication of quantum registers that consist of NV centre arrays has not advanced beyond NV pairs for several years. Further scaling up of coupled NV centres by using nitrogen implantation through nanoholes has been hampered because the shortening of the separation distance is limited by the nanohole size and ion straggling. Here, we demonstrate the implantation of C₅N₄H_n from an adenine ion source to achieve further scaling. Because the C₅N₄H_n ion may be regarded as an ideal point source, the separation distance is solely determined by straggling. We successfully demonstrate the fabrication of strongly coupled triple NV centres. Our method may be extended to fabricate small quantum registers that can perform quantum information processing at room temperature.

Quantum Control and Sensing of Nuclear Spins by Electron Spins under Power Limitations

State of the art quantum sensing experiments targeting frequency measurements or frequency addressing of nuclear spins require one to drive the probe system at the targeted frequency. In addition, there is a substantial advantage to performing these experiments in the regime of high magnetic fields, in which the Larmor frequency of the measured spins is large. In this scenario we are confronted with a natural challenge of controlling a target system with a very high frequency when the probe system cannot be set to resonance with the target frequency. In this contribution we present a set of protocols that are capable of confronting this challenge, even at large frequency mismatches between the probe system and the target system, both for polarization and for quantum sensing.

Quantum reference beacon–guided superresolution optical focusing in complex media

Optical scattering is generally considered to be a nuisance of microscopy that limits imaging depth and spatial resolution. Wavefront shaping techniques enable optical imaging at unprecedented depth, but attaining superresolution within complex media remains a challenge. We used a quantum reference beacon (QRB), consisting of solid-state quantum emitters with spin-dependent fluorescence, to provide subwavelength guidestar feedback for wavefront shaping to achieve a superresolution optical focus. We implemented the QRB-guided imaging with nitrogen-vacancy centers in diamond nanocrystals, which enable optical focusing with a subdiffraction resolution below 186 nanometers (less than half the wavelength). QRB-assisted wavefront-shaping should find use in a range of applications, including deep-tissue quantum enhanced sensing and individual optical excitation of magnetically coupled spin ensembles for applications in quantum information processing.

Wide dynamic range magnetic field cycler: Harnessing quantum control at low and high fields

We describe the construction of a fast field cycling device capable of sweeping a 4-order-of-magnitude range of magnetic fields, from ∼1 mT to 7 T, in under 700 ms, and which is further extendable to a 1 nT-7 T range. Central to this system is a high-speed sample shuttling mechanism between a superconducting magnet and a magnetic shield, with the capability to access arbitrary fields in between with high resolution. Our instrument serves as a versatile platform to harness the inherent dichotomy of spin dynamics on offer at low and high fields-in particular, the low anisotropy, fast spin manipulation, and rapid entanglement growth at low field as well as the long spin lifetimes, spin specific control, and efficient inductive measurement possible at high fields. Exploiting these complementary capabilities in a single device opens up applications in a host of problems in quantum control, sensing, and information storage, besides in nuclear hyperpolarization, relaxometry, and imaging. In particular, in this paper, we focus on the ability of the device to enable low-field hyperpolarization of ¹³C nuclei in diamond via optically pumped electronic spins associated with nitrogen vacancy defect centers.

Collective Effects in Casimir-Polder Forces

We study cooperative phenomena in the fluctuation-induced forces between a surface and a system of neutral two-level quantum emitters prepared in a coherent collective state, showing that the total Casimir-Polder force on the emitters can be modified via their mutual correlations. Particularly, we find that a one-dimensional chain of emitters prepared in a super- or subradiant state experiences an enhanced or suppressed collective vacuum-induced force, respectively. The collective nature of dispersion forces can be understood as resulting from the interference between the different processes contributing to the surface-modified resonant dipole-dipole interaction. Such cooperative fluctuation forces depend singularly on the surface response at the resonance frequency of the emitters, thus being easily maneuverable. Our results demonstrate the potential of collective phenomena as a new tool to selectively tailor vacuum forces.

Nanoscale Mapping and Control of Antenna-Coupling Strength for Bright Single Photon Sources

Cavity quantum electrodynamics is the art of enhancing light-matter interaction of photon emitters in cavities with opportunities for sensing, quantum information, and energy capture technologies. To boost emitter-cavity interaction, that is, coupling strength g, ultrahigh quality cavities have been concocted yielding photon trapping times of microsecondsy to milliseconds. However, such high- Q cavities give poor photon output, hindering applications. To preserve high photon output, it is advantageous to strive for highly localized electric fields in radiatively lossy cavities. Nanophotonic antennas are ideal candidates combining low- Q factors with deeply localized mode volumes, allowing large g, provided the emitter is positioned exactly right inside the nanoscale mode volume. Here, with nanometer resolution, we map and tune the coupling strength between a dipole nanoantenna-cavity and a single molecule, obtaining a coupling rate of g_max ∼ 200 GHz. Together with accelerated single photon output, this provides ideal conditions for fast and pure nonclassical single photon emission with brightness exceeding 10⁹ photons/sec. Clearly, nanoantennas acting as "bad" cavities offer an optimal regime for strong coupling g to deliver bright on-demand and ultrafast single photon nanosources for quantum technologies.

Fault-tolerant interface between quantum memories and quantum processors

Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow straightforward gate implementation needed for data processing. To exploit the particular advantages of different topological codes for fault-tolerant quantum computation, it is necessary to be able to switch between them. Here we propose a practical solution, subsystem lattice surgery, which requires only two-body nearest-neighbor interactions in a fixed layout in addition to the indispensable error correction. This method can be used for the fault-tolerant transfer of quantum information between arbitrary topological subsystem codes in two dimensions and beyond. In particular, it can be employed to create a simple interface, a quantum bus, between noise resilient surface code memories and flexible color code processors.

In the quest for fault-tolerant quantum computation, being able to interface different topological codes such as surface and color codes would allow to get the best of each code. Here, the authors show how to interface arbitrary topological quantum error correction codes in two dimensions.

Evolution-Free Hamiltonian Parameter Estimation through Zeeman Markers

We provide a protocol for Hamiltonian parameter estimation which relies only on the Zeeman effect. No time-dependent quantities need to be measured; it fully suffices to observe spectral shifts induced by fields applied to local "markers." We demonstrate the idea with a simple tight-binding Hamiltonian and numerically show stability with respect to Gaussian noise on the spectral measurements. Then we generalize the result to show applicability to a wide range of systems, including quantum spin chains, networks of qubits, and coupled harmonic oscillators, and suggest potential experimental implementations.

Depolarization Dynamics in a Strongly Interacting Solid-State Spin Ensemble

We study the depolarization dynamics of a dense ensemble of dipolar interacting spins, associated with nitrogen-vacancy centers in diamond. We observe anomalously fast, density-dependent, and nonexponential spin relaxation. To explain these observations, we propose a microscopic model where an interplay of long-range interactions, disorder, and dissipation leads to predictions that are in quantitative agreement with both current and prior experimental results. Our results pave the way for controlled many-body experiments with long-lived and strongly interacting ensembles of solid-state spins.

A review on single photon sources in silicon carbide

This paper summarizes key findings in single-photon generation from deep level defects in silicon carbide (SiC) and highlights the significance of these individually addressable centers for emerging quantum applications. Single photon emission from various defect centers in both bulk and nanostructured SiC are discussed as well as their formation and possible integration into optical and electrical devices. The related measurement protocols, the building blocks of quantum communication and computation network architectures in solid state systems, are also summarized. This includes experimental methodologies developed for spin control of different paramagnetic defects, including the measurement of spin coherence times. Well established doping, and micro- and nanofabrication procedures for SiC may allow the quantum properties of paramagnetic defects to be electrically and mechanically controlled efficiently. The integration of single defects into SiC devices is crucial for applications in quantum technologies and we will review progress in this direction.

Single-spin magnetic resonance in the nitrogen-vacancy center of diamond

Magnetic resonance of single spins has flourished mostly because of the unique properties of the NV center in diamond. This review covers the basic physics of this defect center, introduces the techniques for working with single spins and gives an overview of some applications like quantum information and sensing.

Generation of macroscopic Schrödinger cat state in diamond mechanical resonator

We propose a scheme to generate macroscopic Schrödinger cat state (SCS) in diamond mechanical resonator (DMR) via the dynamical strain-mediated coupling mechanism. In our model, the direct coupling between the nitrogen-vacancy (NV) center and lattice strain field enables coherent spin–phonon interactions in the quantum regime. Based on a cyclic Δ-type transition structure of the NV center constructed by combining the quantized mechanical strain field and a pair of external microwave fields, the populations of the different energy levels can be selectively transferred by controlling microwave fields, and the SCS can be created by adjusting the controllable parameters of the system. Furthermore, we demonstrate the nonclassicality of the mechanical SCS both in non-dissipative case and dissipative case. The experimental feasibility and challenge are justified using currently available technology.

High-speed quantum networking by ship

Networked entanglement is an essential component for a plethora of quantum computation and communication protocols. Direct transmission of quantum signals over long distances is prevented by fibre attenuation and the no-cloning theorem, motivating the development of quantum repeaters, designed to purify entanglement, extending its range. Quantum repeaters have been demonstrated over short distances, but error-corrected, global repeater networks with high bandwidth require new technology. Here we show that error corrected quantum memories installed in cargo containers and carried by ship can provide a exible connection between local networks, enabling low-latency, high-fidelity quantum communication across global distances at higher bandwidths than previously proposed. With demonstrations of technology with sufficient fidelity to enable topological error-correction, implementation of the quantum memories is within reach, and bandwidth increases with improvements in fabrication. Our approach to quantum networking avoids technological restrictions of repeater deployment, providing an alternate path to a worldwide Quantum Internet.

Controllable quantum dynamics of inhomogeneous nitrogen-vacancy center ensembles coupled to superconducting resonators

We explore controllable quantum dynamics of a hybrid system, which consists of an array of mutually coupled superconducting resonators (SRs) with each containing a nitrogen-vacancy center spin ensemble (NVE) in the presence of inhomogeneous broadening. We focus on a three-site model, which compared with the two-site case, shows more complicated and richer dynamical behavior, and displays a series of damped oscillations under various experimental situations, reflecting the intricate balance and competition between the NVE-SR collective coupling and the adjacent-site photon hopping. Particularly, we find that the inhomogeneous broadening of the spin ensemble can suppress the population transfer between the SR and the local NVE. In this context, although the inhomogeneous broadening of the spin ensemble diminishes entanglement among the NVEs, optimal entanglement, characterized by averaging the lower bound of concurrence, could be achieved through accurately adjusting the tunable parameters.

Demonstration of a Coherent Electronic Spin Cluster in Diamond

An obstacle for spin-based quantum sensors is magnetic noise due to proximal spins. However, a cluster of such spins can become an asset, if it can be controlled. Here, we polarize and readout a cluster of three nitrogen electron spins coupled to a single nitrogen-vacancy spin in diamond. We further achieve sub-nm localization of the cluster spins. Finally, we demonstrate coherent spin exchange between the species by simultaneous dressing of the nitrogen-vacancy and the nitrogen states. These results establish the feasibility of environment-assisted sensing and quantum simulations with diamond spins.

Nanoscale Engineering of Closely-Spaced Electronic Spins in Diamond

Numerous theoretical protocols have been developed for quantum information processing with dipole-coupled solid-state spins. Nitrogen vacancy (NV) centers in diamond have many of the desired properties, but a central challenge has been the positioning of NV centers at the nanometer scale that would allow for efficient and consistent dipolar couplings. Here we demonstrate a method for chip-scale fabrication of arrays of single NV centers with record spatial localization of about 10 nm in all three dimensions and controllable inter-NV spacing as small as 40 nm, which approaches the length scale of strong dipolar coupling. Our approach uses masked implantation of nitrogen through nanoapertures in a thin gold film, patterned via electron-beam lithography and dry etching. We verified the position and spin properties of the resulting NVs through wide-field super-resolution optically detected magnetic resonance imaging.

Direct Measurement of Topological Numbers with Spins in Diamond

Topological numbers can characterize the transition between different topological phases, which are not described by Landau's paradigm of symmetry breaking. Since the discovery of the quantum Hall effect, more topological phases have been theoretically predicted and experimentally verified. However, it is still an experimental challenge to directly measure the topological numbers of various predicted topological phases. In this Letter, we demonstrate quantum simulation of topological phase transition of a quantum wire (QW), by precisely modulating the Hamiltonian of a single nitrogen-vacancy (NV) center in diamond. Deploying a quantum algorithm of finding eigenvalues, we reliably extract both the dispersion relations and topological numbers. This method can be further generalized to simulate more complicated topological systems.

Photonic Quantum Networks formed from NV(-) centers

In this article we present a simple repeater scheme based on the negatively-charged nitrogen vacancy centre in diamond. Each repeater node is built from modules comprising an optical cavity containing a single NV⁻, with one nuclear spin from ¹⁵N as quantum memory. The module uses only deterministic processes and interactions to achieve high fidelity operations (>99%), and modules are connected by optical fiber. In the repeater node architecture, the processes between modules by photons can be in principle deterministic, however current limitations on optical components lead the processes to be probabilistic but heralded. Our resource-modest repeater architecture contains two modules at each node, and the repeater nodes are then connected by entangled photon pairs. We discuss the performance of such a quantum repeater network with modest resources and then incorporate more resource-intense strategies step by step. Our architecture should allow large-scale quantum information networks with existing or near future technology.

Memory-built-in quantum cloning in a hybrid solid-state spin register

As a way to circumvent the quantum no-cloning theorem, approximate quantum cloning protocols have received wide attention with remarkable applications. Copying of quantum states to memory qubits provides an important strategy for eavesdropping in quantum cryptography. We report an experiment that realizes cloning of quantum states from an electron spin to a nuclear spin in a hybrid solid-state spin register with near-optimal fidelity. The nuclear spin provides an ideal memory qubit at room temperature, which stores the cloned quantum states for a millisecond under ambient conditions, exceeding the lifetime of the original quantum state carried by the electron spin by orders of magnitude. The realization of a cloning machine with built-in quantum memory provides a key step for application of quantum cloning in quantum information science.

Generation of ensembles of individually resolvable nitrogen vacancies using nanometer-scale apertures in ultrahigh-aspect ratio planar implantation masks

A central challenge in developing magnetically coupled quantum registers in diamond is the fabrication of nitrogen vacancy (NV) centers with localization below ∼20 nm to enable fast dipolar interaction compared to the NV decoherence rate. Here, we demonstrate the targeted, high throughput formation of NV centers using masks with a thickness of 270 nm and feature sizes down to ∼1 nm. Super-resolution imaging resolves NVs with a full-width maximum distribution of 26 ± 7 nm and a distribution of NV-NV separations of 16 ± 5 nm.

Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin

At its most fundamental level, circuit-based quantum computation relies on the application of controlled phase shift operations on quantum registers. While these operations are generally compromised by noise and imperfections, quantum gates based on geometric phase shifts can provide intrinsically fault-tolerant quantum computing. Here we demonstrate the high-fidelity realization of a recently proposed fast (non-adiabatic) and universal (non-Abelian) holonomic single-qubit gate, using an individual solid-state spin qubit under ambient conditions. This fault-tolerant quantum gate provides an elegant means for achieving the fidelity threshold indispensable for implementing quantum error correction protocols. Since we employ a spin qubit associated with a nitrogen-vacancy colour centre in diamond, this system is based on integrable and scalable hardware exhibiting strong analogy to current silicon technology. This quantum gate realization is a promising step towards viable, fault-tolerant quantum computing under ambient conditions.

Quantum gates based on geometric phase shifts offer a promising approach for the realization of fault-tolerant quantum computing. Using nitrogen-vacancy centre qubits in diamond, this study experimentally realises a high-fidelty, non-adiabatic, non-Abelian holonomic single-qubit gate at room temperature.

Long-distance transfer and routing of static magnetic fields

We show how the static magnetic field of a finite source can be transferred and routed to arbitrary long distances. This is achieved by using transformation optics, which results in a device made of a material with a highly anisotropic magnetic permeability. We show that a simplified version of the device, made by a superconducting-ferromagnet hybrid, also leads to an excellent transfer of the magnetic field. The latter is demonstrated with a proof-of-principle experiment where a ferromagnet tube coated with a superconductor improves the transfer of static magnetic fields with respect to conventional methods by a 400% factor over distances of 14 cm.

Mapping of topological quantum circuits to physical hardware

Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires strategic measurement in accordance with a topological circuit specification. The specification is a geometric structure that defines encoded information and fault-tolerant operations. The compilation of a topological circuit is one important aspect of programming a quantum computer, another is the mapping of the topological circuit into the operations performed by the hardware. Each qubit has to be controlled, and measurement results are needed to propagate encoded quantum information from input to output. In this work, we introduce an algorithm for mapping an topological circuit to the operations needed by the physical hardware. We determine the control commands for each qubit in the computer and the relevant measurements that are needed to track information as it moves through the circuit.

Topological quantum computing with a very noisy network and local error rates approaching one percent

A scalable quantum computer could be built by networking together many simple processor cells, thus avoiding the need to create a single complex structure. The difficulty is that realistic quantum links are very error prone. A solution is for cells to repeatedly communicate with each other and so purify any imperfections; however prior studies suggest that the cells themselves must then have prohibitively low internal error rates. Here we describe a method by which even error-prone cells can perform purification: groups of cells generate shared resource states, which then enable stabilization of topologically encoded data. Given a realistically noisy network (≥10% error rate) we find that our protocol can succeed provided that intra-cell error rates for initialisation, state manipulation and measurement are below 0.82%. This level of fidelity is already achievable in several laboratory systems.

High-resolution correlation spectroscopy of ¹³C spins near a nitrogen-vacancy centre in diamond

Spin complexes comprising the nitrogen-vacancy centre and neighbouring spins are being considered as a building block for a new generation of spintronic and quantum information processing devices. As assembling identical spin clusters is difficult, new strategies are being developed to determine individual node structures with the highest precision. Here we use a pulse protocol to monitor the time evolution of the (13)C ensemble in the vicinity of a nitrogen-vacancy centre. We observe long-lived time correlations in the nuclear spin dynamics, limited by nitrogen-vacancy spin-lattice relaxation. We use the host (14)N spin as a quantum register and demonstrate that hyperfine-shifted resonances can be separated upon proper nitrogen-vacancy initialization. Intriguingly, we find that the amplitude of the correlation signal exhibits a sharp dependence on the applied magnetic field. We discuss this observation in the context of the quantum-to-classical transition proposed recently to explain the field dependence of the spin cluster dynamics.

Ultrafast optical control of individual quantum dot spin qubits

Single spins in semiconductor quantum dots form a promising platform for solid-state quantum information processing. The spin-up and spin-down states of a single electron or hole, trapped inside a quantum dot, can represent a single qubit with a reasonably long decoherence time. The spin qubit can be optically coupled to excited (charged exciton) states that are also trapped in the quantum dot, which provides a mechanism to quickly initialize, manipulate and measure the spin state with optical pulses, and to interface between a stationary matter qubit and a 'flying' photonic qubit for quantum communication and distributed quantum information processing. The interaction of the spin qubit with light may be enhanced by placing the quantum dot inside a monolithic microcavity. An entire system, consisting of a two-dimensional array of quantum dots and a planar microcavity, may plausibly be constructed by modern semiconductor nano-fabrication technology and could offer a path toward chip-sized scalable quantum repeaters and quantum computers. This article reviews the recent experimental developments in optical control of single quantum dot spins for quantum information processing. We highlight demonstrations of a complete set of all-optical single-qubit operations on a single quantum dot spin: initialization, an arbitrary SU(2) gate, and measurement. We review the decoherence and dephasing mechanisms due to hyperfine interaction with the nuclear-spin bath, and show how the single-qubit operations can be combined to perform spin echo sequences that extend the qubit decoherence from a few nanoseconds to several microseconds, more than 5 orders of magnitude longer than the single-qubit gate time. Two-qubit coupling is discussed, both within a single chip by means of exchange coupling of nearby spins and optically induced geometric phases, as well as over longer-distances. Long-distance spin-spin entanglement can be generated if each spin can emit a photon that is entangled with the spin, and these photons are then interfered. We review recent work demonstrating entanglement between a stationary spin qubit and a flying photonic qubit. These experiments utilize the polarization- and frequency-dependent spontaneous emission from the lowest charged exciton state to single spin Zeeman sublevels.

Quantum error correction for beginners

Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspects of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large-scale quantum computers. The introduction of quantum error correction in 1995 showed that active techniques could be employed to mitigate this fatal problem. However, quantum error correction and fault-tolerant computation is now a much larger field and many new codes, techniques, and methodologies have been developed to implement error correction for large-scale quantum algorithms. In response, we have attempted to summarize the basic aspects of quantum error correction and fault-tolerance, not as a detailed guide, but rather as a basic introduction. The development in this area has been so pronounced that many in the field of quantum information, specifically researchers who are new to quantum information or people focused on the many other important issues in quantum computation, have found it difficult to keep up with the general formalisms and methodologies employed in this area. Rather than introducing these concepts from a rigorous mathematical and computer science framework, we instead examine error correction and fault-tolerance largely through detailed examples, which are more relevant to experimentalists today and in the near future.

Efficient coupling of a single diamond color center to propagating plasmonic gap modes

We report on coupling of a single nitrogen-vacancy (NV) center in a nanodiamond to the propagating gap mode of two parallel placed chemically grown silver nanowires. The coupled NV-center nanowire system is made by manipulating nanodiamonds and nanowires with the tip of an atomic force microscope cantilever. An efficient coupling of an NV-center to an easily accessible gap plasmon mode is demonstrated and we measure an enhancement of the spontaneous emission decay rate by a factor of 8.3.

Practicality of spin chain wiring in diamond quantum technologies

Coupled spin chains are promising candidates for wiring up qubits in solid-state quantum computing (QC). In particular, two nitrogen-vacancy centers in diamond can be connected by a chain of implanted nitrogen impurities; when driven by suitable global fields the chain can potentially enable quantum state transfer at room temperature. However, our detailed analysis of error effects suggests that foreseeable systems may fall far short of the fidelities required for QC. Fortunately the chain can function in the more modest role as a mediator of noisy entanglement, enabling QC provided that we use subsequent purification. For instance, a chain of 5 spins with interspin distances of 10 nm has finite entangling power as long as the T(2) time of the spins exceeds 0.55 ms. Moreover we show that repurposing the chain this way can remove the restriction to nearest-neighbor interactions, so eliminating the need for complicated dynamical decoupling sequences.

Collectively enhanced interactions in solid-state spin qubits

We propose and analyze a technique to collectively enhance interactions between solid-state quantum registers composed from random networks of spin qubits. In such systems, disordered dipolar interactions generically result in localization. Here, we demonstrate the emergence of a single collective delocalized eigenmode as one turns on a transverse magnetic field. The interaction strength between this symmetric collective mode and a remote spin qubit is enhanced by the square root of the number of spins participating in the delocalized mode. Mediated by such collective enhancement, long-range quantum logic between remote spin registers can occur at distances consistent with optical addressing. A specific implementation utilizing nitrogen-vacancy defects in diamond is discussed and the effects of decoherence are considered.

Bandwidth-limited control and ringdown suppression in high-Q resonators

We describe how the transient behavior of a tuned and matched resonator circuit and a ringdown suppression pulse may be integrated into an optimal control theory (OCT) pulse-design algorithm to derive control sequences with limited ringdown that perform a desired quantum operation in the presence of resonator distortions of the ideal waveform. Inclusion of ringdown suppression in numerical pulse optimizations significantly reduces spectrometer deadtime when using high quality factor (high-Q) resonators, leading to increased signal-to-noise ratio (SNR) and sensitivity of inductive measurements. To demonstrate the method, we experimentally measure the free-induction decay of an inhomogeneously broadened solid-state free radical spin system at high Q. The measurement is enabled by using a numerically optimized bandwidth-limited OCT pulse, including ringdown suppression, robust to variations in static and microwave field strengths. We also discuss the applications of pulse design in high-Q resonators to universal control of anisotropic-hyperfine coupled electron-nuclear spin systems via electron-only modulation even when the bandwidth of the resonator is significantly smaller than the hyperfine coupling strength. These results demonstrate how limitations imposed by linear response theory may be vastly exceeded when using a sufficiently accurate system model to optimize pulses of high complexity.

Coherence-protected quantum gate by continuous dynamical decoupling in diamond

In order to achieve reliable quantum-information processing results, we need to protect quantum gates along with the qubits from decoherence. Here we demonstrate experimentally on a nitrogen-vacancy system that by using a continuous-wave dynamical decoupling method, we might not only prolong the coherence time by about 20 times but also protect the quantum gates for the duration of the controlling time. This protocol shares the merits of retaining the superiority of prolonging the coherence time and at the same time easily combining with quantum logic tasks. This method can be useful in tasks where the duration of quantum controlling exceeds far beyond the dephasing time.