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Tim H. Taminiau

Publications and source records attributed to Tim H. Taminiau.

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High-fidelity two-qubit gates in a 7-qubit register for quantum networks

Quantum networks based on optically active solid-state spins may enable quantum technologies including long-range quantum communication and distributed quantum computing. Network nodes containing multiple high-fidelity qubits can facilitate large-scale fault-tolerant operation. However, the stringent error thresholds remain out of reach for multi-qubit registers. In this work, we demonstrate high-fidelity two-qubit gates in a 7-qubit register, based on nuclear spins coupled to a nitrogen-vacancy (NV) center in diamond. We analyze crosstalk in highly connected spin systems, develop an efficient optimization procedure, and characterize the gates using gate set tomography. The two-qubit gate fidelities (best: 99.61(5)%, average: 99.18(2)%) demonstrate a multi-qubit register at the threshold for distributed quantum computation. Finally, as an example application, we perform a variational quantum eigensolver (VQE) simulation of the ground-state energy of H2 and LiH molecules. These results demonstrate one of the key prerequisites for scalable quantum networks based on solid-state spins.

quant-ph

A multi-dimensional quantum estimation and model learning framework based on variational Bayesian inference

The advancement and scaling of quantum technology has made the learning and identification of quantum systems and devices in highly-multidimensional parameter spaces a pressing task for a variety of applications. In many cases, the integration of real-time feedback control and adaptive choice of measurement settings places strict demands on the speed of this task. Here we present a joint model selection and parameter estimation algorithm that is fast and operable on a large number of model parameters. The algorithm is based on variational Bayesian inference (VBI), which approximates the target posterior distribution by optimizing a tractable family of distributions, making it more scalable than exact inference methods relying on sampling and that generally suffer from high variance and computational cost in high-dimensional spaces. We show how a regularizing prior can be used to select between competing models, each comprising a different number of parameters, identifying the simplest model that explains the experimental data. The regularization can further separate the degrees of freedom, e.g. quantum systems in the environment or processes, which contribute to major features in the observed dynamics, with respect to others featuring small coupling, which only contribute to a background. As an application of the introduced framework, we consider the problem of the identification of multiple individual nuclear spins with a single electron spin quantum sensor, relevant for nanoscale nuclear magnetic resonance. With the number of environmental spins unknown a priori, our Bayesian approach is able to correctly identify the model, i.e. the number of spins and their couplings. We benchmark the algorithm on both simulated and experimental data, using standard figures of merit, and demonstrating that we can estimate dozens of parameters within minutes.

quant-ph

Ten-Second Electron-Spin Coherence in Isotopically Engineered Diamond

Solid-state spin defects are a promising platform for quantum networks. A key requirement is to combine long ground-state spin-coherence times with a coherent optical transition for spin-photon entanglement. Here, we investigate the spin and optical coherence of single nitrogen-vacancy (NV) centres in (111)-grown isotopically engineered diamond. Our diamond-growth process yields a precisely controlled $^{13}\mathrm{C}$ concentration and low-ppb nitrogen concentrations. Combined with the mitigation of 50 Hz noise using a real-time feedforward scheme and tailored decoupling sequences, this enables record defect-electron-spin coherence times of $T_2 = 6.8(1)$ ms for a Hahn echo and of $T_2^{DD} = 11.2(8)$ s under dynamical decoupling. In addition, we observe coherent optical transitions with a near-lifetime-limited homogeneous linewidth of 16.9(4) MHz and characterize the spectral diffusion dynamics. These results provide new avenues to investigate the incorporation of impurities in diamond and new opportunities for improved spin-qubit control for quantum networks and other quantum technologies.

quant-ph

Trans-dimensional Hamiltonian model selection and parameter estimation from sparse, noisy data

High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and model dimensions are consistent with available data. This ill-posed regime may render traditional machine learning and deterministic methods unreliable or intractable, particularly in high-dimensional, nonlinear, and mixed continuous and discrete parameter spaces. To address these challenges, we present a Bayesian framework that hybridizes several Markov chain Monte Carlo (MCMC) sampling techniques to estimate both parameters and model dimension from sparse, noisy data. By integrating sampling for mixed continuous and discrete parameter spaces, reversible-jump MCMC to estimate model dimension, and parallel tempering to accelerate exploration of complex posteriors, our approach enables principled parameter estimation and model selection in data-limited regimes. We apply our framework to a specific ill-posed problem in quantum information science: recovering the locations and hyperfine couplings of nuclear spins surrounding a spin-defect in a semiconductor from sparse, noisy coherence data. We show that a hybridized MCMC method can recover meaningful posterior distributions over physical parameters using an order of magnitude less data than existing approaches, and we validate our results on experimental measurements. More generally, our work provides a flexible, extensible strategy for solving a broad class of ill-posed inverse problems under realistic experimental constraints.

quant-ph

Unconditionally teleported quantum gates between remote solid-state qubit registers

Quantum networks connecting quantum processing nodes via photonic links enable distributed and modular quantum computation. In this framework, quantum gates between remote qubits can be realized using quantum teleportation protocols. The essential requirements for such non-local gates are remote entanglement, local quantum logic within each processor, and classical communication between nodes to perform operations based on measurement outcomes. Here, we demonstrate an unconditional Controlled-NOT quantum gate between remote diamond-based qubit devices. The control and target qubits are Carbon-13 nuclear spins, while NV electron spins enable local logic, readout, and remote entanglement generation. We benchmark the system by creating a Greenberger-Horne-Zeilinger state, showing genuine 4-partite entanglement shared between nodes. Using deterministic logic, single-shot readout, and real-time feed-forward, we implement non-local gates without post-selection. These results demonstrate a key capability for solid-state quantum networks, enabling exploration of distributed quantum computing and testing of complex network protocols on fully integrated systems.

quant-ph

Quadrupolar resonance spectroscopy of individual nuclei using a room-temperature quantum sensor

Nuclear quadrupolar resonance (NQR) spectroscopy reveals chemical bonding patterns in materials and molecules through the unique coupling between nuclear spins and local fields. However, traditional NQR techniques require macroscopic ensembles of nuclei to yield a detectable signal, which precludes the study of individual molecules and obscures molecule-to-molecule variations due to local perturbations or deformations. Optically active electronic spin qubits, such as the nitrogen-vacancy (NV) center in diamond, facilitate the detection and control of individual nuclei through their local magnetic couplings. Here, we use NV centers to perform NQR spectroscopy on their associated nitrogen-14 ($^{14}$N) nuclei at room temperature. In mapping the nuclear quadrupolar Hamiltonian, we resolve minute variations between individual nuclei. The measurements further reveal correlations between the parameters in the NV center's electronic spin Hamiltonian and the $^{14}$N quadropolar Hamiltonian, as well as a previously unreported Hamiltonian term that results from symmetry breaking. We further design pulse sequences to initialize, readout, and control the quantum evolution of the $^{14}$N nuclear state using the nuclear quadrupolar Hamiltonian.

cond-mat.mes-hall

Control of solid-state nuclear spin qubits using an electron spin-1/2

Solid-state quantum registers consisting of optically active electron spins with nearby nuclear spins are promising building blocks for future quantum technologies. For electron spin-1 registers, dynamical decoupling (DD) quantum gates have been developed that enable the precise control of multiple nuclear spin qubits. However, for the important class of electron spin-1/2 systems, this control method suffers from intrinsic selectivity limitations, resulting in reduced nuclear spin gate fidelities. Here we demonstrate improved control of single nuclear spins by an electron spin-1/2 using Dynamically Decoupled Radio Frequency (DDRF) gates. We make use of the electron spin-1/2 of a diamond tin-vacancy center, showing high-fidelity single-qubit gates, single-shot readout, and spin coherence beyond a millisecond. The DD control is used as a benchmark to observe and control a single carbon-13 nuclear spin. Using the DDRF control method, we demonstrate improved control on that spin. In addition, we find and control an additional nuclear spin that is insensitive to the DD control method. Using these DDRF gates, we show entanglement between the electron and the nuclear spin with 72(3)% state fidelity. Our extensive simulations indicate that DDRF gate fidelities well in excess are feasible. Finally, we employ time-resolved photon detection during readout to quantify the hyperfine coupling for the electron's optically excited state. Our work provides key insights into the challenges and opportunities for nuclear spin control in electron spin-1/2 systems, opening the door to multi-qubit experiments on these promising qubit platforms.

quant-ph

Thresholds for the distributed surface code in the presence of memory decoherence

In the search for scalable, fault-tolerant quantum computing, distributed quantum computers are promising candidates. These systems can be realized in large-scale quantum networks or condensed onto a single chip with closely situated nodes. We present a framework for numerical simulations of a memory channel using the distributed toric surface code, where each data qubit of the code is part of a separate node, and the error-detection performance depends on the quality of four-qubit Greenberger-Horne-Zeilinger (GHZ) states generated between the nodes. We quantitatively investigate the effect of memory decoherence and evaluate the advantage of GHZ creation protocols tailored to the level of decoherence. We do this by applying our framework for the particular case of color centers in diamond, employing models developed from experimental characterization of nitrogen-vacancy centers. For diamond color centers, coherence times during entanglement generation are orders of magnitude lower than coherence times of idling qubits. These coherence times represent a limiting factor for applications, but previous surface code simulations did not treat them as such. Introducing limiting coherence times as a prominent noise factor makes it imperative to integrate realistic operation times into simulations and incorporate strategies for operation scheduling. Our model predicts error probability thresholds for gate and measurement reduced by at least a factor of three compared to prior work with more idealized noise models. We also find a threshold of $4\cdot10^2$ in the ratio between the entanglement generation and the decoherence rates, setting a benchmark for experimental progress.

quant-ph

Roadmap on Nanoscale Magnetic Resonance Imaging

The field of nanoscale magnetic resonance imaging (NanoMRI) was started 30 years ago. It was motivated by the desire to image single molecules and molecular assemblies, such as proteins and virus particles, with near-atomic spatial resolution and on a length scale of 100 nm. Over the years, the NanoMRI field has also expanded to include the goal of useful high-resolution nuclear magnetic resonance (NMR) spectroscopy of molecules under ambient conditions, including samples up to the micron-scale. The realization of these goals requires the development of spin detection techniques that are many orders of magnitude more sensitive than conventional NMR and MRI, capable of detecting and controlling nanoscale ensembles of spins. Over the years, a number of different technical approaches to NanoMRI have emerged, each possessing a distinct set of capabilities for basic and applied areas of science. The goal of this roadmap article is to report the current state of the art in NanoMRI technologies, outline the areas where they are poised to have impact, identify the challenges that lie ahead, and propose methods to meet these challenges. This roadmap also shows how developments in NanoMRI techniques can lead to breakthroughs in emerging quantum science and technology applications.

cond-mat.mes-hall

Optical coherence of diamond nitrogen-vacancy centers formed by ion implantation and annealing

The advancement of quantum optical science and technology with solid-state emitters such as nitrogen-vacancy (NV) centers in diamond critically relies on the coherence of the emitters' optical transitions. A widely employed strategy to create NV centers at precisely controlled locations is nitrogen ion implantation followed by a high-temperature annealing process. We report on experimental data directly correlating the NV center optical coherence to the origin of the nitrogen atom. These studies reveal low-strain, narrow-optical-linewidth ($<500$ MHz) NV centers formed from naturally-occurring $^{14}$N atoms. In contrast, NV centers formed from implanted $^{15}$N atoms exhibit significantly broadened optical transitions ($>1$ GHz) and higher strain. The data show that the poor optical coherence of the NV centers formed from implanted nitrogen is not due to an intrinsic effect related to the diamond or isotope. These results have immediate implications for the positioning accuracy of current NV center creation protocols and point to the need to further investigate the influence of lattice damage on the coherence of NV centers from implanted ions.

cond-mat.mes-hall

Multipartite entanglement generation and contextuality tests using non-destructive three-qubit parity measurements

We report on the realization and application of non-destructive three-qubit parity measurements on nuclear spin qubits in diamond. We use high-fidelity quantum logic to map the parity of the joint state of three nuclear spin qubits onto an electronic spin qubit that acts as an ancilla, followed by single-shot non-destructive readout of the ancilla combined with an electron spin echo to ensure outcome-independent evolution of the nuclear spins. Through the sequential application of three such parity measurements, we demonstrate the generation of genuine multipartite entangled states out of the maximally mixed state. Furthermore, we implement a single-shot version of the GHZ experiment that can generate a quantum versus classical contradiction in each run. Finally, we test a state-independent non-contextuality inequality in eight dimensions. The techniques and insights developed here are relevant for fundamental tests as well as for quantum information protocols such as quantum error correction.

quant-ph

One-second coherence for a single electron spin coupled to a multi-qubit nuclear-spin environment

Single electron spins coupled to multiple nuclear spins provide promising multi-qubit registers for quantum sensing and quantum networks. The obtainable level of control is determined by how well the electron spin can be selectively coupled to, and decoupled from, the surrounding nuclear spins. Here we realize a coherence time exceeding a second for a single electron spin through decoupling sequences tailored to its microscopic nuclear-spin environment. We first use the electron spin to probe the environment, which is accurately described by seven individual and six pairs of coupled carbon-13 spins. We develop initialization, control and readout of the carbon-13 pairs in order to directly reveal their atomic structure. We then exploit this knowledge to store quantum states for over a second by carefully avoiding unwanted interactions. These results provide a proof-of-principle for quantum sensing of complex multi-spin systems and an opportunity for multi-qubit quantum registers with long coherence times.

quant-ph

Repeated quantum error correction on a continuously encoded qubit by real-time feedback

Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be compatible with universal fault-tolerant computations, it is essential that the states remain encoded at all times and that errors are actively corrected. Here we demonstrate such active error correction on a continuously protected qubit using a diamond quantum processor. We encode a logical qubit in three long-lived nuclear spins, repeatedly detect phase errors by non-destructive measurements using an ancilla electron spin, and apply corrections on the encoded state by real-time feedback. The actively error-corrected qubit is robust against errors and multiple rounds of error correction prevent errors from accumulating. Moreover, by correcting correlated phase errors naturally induced by the environment, we demonstrate that encoded quantum superposition states are preserved beyond the dephasing time of the best physical qubit used in the encoding. These results establish a powerful platform for the fundamental investigation of error correction under different types of noise and mark an important step towards fault-tolerant quantum information processing.

quant-ph

Quantum Zeno subspaces by repeated multi-spin projections

Repeated observations inhibit the coherent evolution of quantum states through the quantum Zeno effect. In multi-qubit systems this effect provides new opportunities to control complex quantum states. Here, we experimentally demonstrate that repeatedly projecting joint observables of multiple spins creates coherent quantum Zeno subspaces and simultaneously suppresses dephasing caused by the environment. We encode up to two logical qubits in these subspaces and show that the enhancement of the dephasing time with increasing number of projections follows a scaling law that is independent of the number of spins involved. These results provide new insights into the interplay between frequent multi-spin measurements and non-Markovian noise and pave the way for tailoring the dynamics of multi-qubit systems through repeated projections.

quant-ph

Robust quantum-network memory using decoherence-protected subspaces of nuclear spins

The realization of a network of quantum registers is an outstanding challenge in quantum science and technology. We experimentally investigate a network node that consists of a single nitrogen-vacancy (NV) center electronic spin hyperfine-coupled to nearby nuclear spins. We demonstrate individual control and readout of five nuclear spin qubits within one node. We then characterize the storage of quantum superpositions in individual nuclear spins under repeated application of a probabilistic optical inter-node entangling protocol. We find that the storage fidelity is limited by dephasing during the electronic spin reset after failed attempts. By encoding quantum states into a decoherence-protected subspace of two nuclear spins we show that quantum coherence can be maintained for over 1000 repetitions of the remote entangling protocol. These results and insights pave the way towards remote entanglement purification and the realisation of a quantum repeater using NV center quantum network nodes.

quant-ph

Unconditional quantum teleportation between distant solid-state qubits

Realizing robust quantum information transfer between long-lived qubit registers is a key challenge for quantum information science and technology. Here we demonstrate unconditional teleportation of arbitrary quantum states between diamond spin qubits separated by 3 meters. We prepare the teleporter through photon-mediated heralded entanglement between two distant electron spins and subsequently encode the source qubit in a single nuclear spin. By realizing a fully deterministic Bell-state measurement combined with real-time feed-forward we achieve teleportation in each attempt while obtaining an average state fidelity exceeding the classical limit. These results establish diamond spin qubits as a prime candidate for the realization of quantum networks for quantum communication and network-based quantum computing.

quant-ph

Demonstration of entanglement-by-measurement of solid state qubits

Projective measurements are a powerful tool for manipulating quantum states. In particular, a set of qubits can be entangled by measurement of a joint property such as qubit parity. These joint measurements do not require a direct interaction between qubits and therefore provide a unique resource for quantum information processing with well-isolated qubits. Numerous schemes for entanglement-by-measurement of solid-state qubits have been proposed, but the demanding experimental requirements have so far hindered implementations. Here we realize a two-qubit parity measurement on nuclear spins in diamond by exploiting the electron spin of a nitrogen-vacancy center as readout ancilla. The measurement enables us to project the initially uncorrelated nuclear spins into maximally entangled states. By combining this entanglement with high-fidelity single-shot readout we demonstrate the first violation of Bells inequality with solid-state spins. These results open the door to a new class of experiments in which projective measurements are used to create, protect and manipulate entanglement between solid-state qubits.

quant-ph

Nanorod optical antennas for dipolar transitions

Optical antennas link objects to light. Here, we analyze metal nanorod antennas as cavities with variable reflection coefficients to derive the interaction of dipolar transitions with radiation through the antenna modes. The presented analytical model accurately describes the complete emission process, and is summarized in a phase-matching equation. We show how antenna modes evolve as they become increasingly more bound, i.e. plasmonic. The results illustrate why efficient antennas should not be too plasmonic, and how subradiant even modes can evolve into weakly-interacting dark modes. Our description is valid for the interaction of nanorods with light in general, and is thus widely applicable.

physics.optics