Scholars@Duke
Norbert Matthias Linke

Norbert Matthias Linke

Professor of Physics
Physics
norbert.linke@duke.edu
Box 90305, Durham, NC 27701
701 W. Main Street, Durham, NC 27701

Selected Publications

Realizing two-qubit gates through mode engineering on a trapped-ion quantum computer

Journal Article Physical Review A · February 1, 2025 Two-qubit gates are a fundamental constituent of a quantum computer and typically its most challenging operation. In a trapped-ion quantum computer, this is typically implemented with laser beams which are modulated in amplitude, frequency, phase, or a com ... Full text Cite

Pairwise-Parallel Entangling Gates on Orthogonal Modes in a Trapped-Ion Chain

Journal Article Advanced Quantum Technologies · November 1, 2023 Parallel operations are important for both near-term quantum computers and larger-scale fault-tolerant machines because they reduce execution time and qubit idling. This study proposes and implements a pairwise-parallel gate scheme on a trapped-ion quantum ... Full text Cite

Let the ions sing

Journal Article Nature Physics · June 1, 2023 Full text Cite

Bespoke pulse design for robust rapid two-qubit gates with trapped ions

Journal Article Physical Review Research · April 1, 2023 Two-qubit gate performance is vital for scaling up ion-trap quantum computing. Optimized quantum control is needed to achieve reductions in gate duration and gate error rate. We describe two-qubit gates with addressed Raman beams within a linear trapped-io ... Full text Cite

Multi-round QAOA and advanced mixers on a trapped-ion quantum computer

Journal Article Quantum Science and Technology · January 1, 2023 Combinatorial optimization problems on graphs have broad applications in science and engineering. The quantum approximate optimization algorithm (QAOA) is a method to solve these problems on a quantum computer by applying multiple rounds of variational cir ... Full text Cite

Analog-Digital Hybrid Computations with Trapped Ions

Conference 2023 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2023 · January 1, 2023 Universal digital quantum computers are able to approximate any Hamiltonian evolution as a digital quantum circuit consisting of discrete time steps. Strongly interacting physics models, for example in high-energy physics or materials science, make this a ... Full text Cite

Analog-Digital Hybrid Computations with Trapped Ions

Conference European Quantum Electronics Conference, EQEC 2023 in Proceedings Conference on Lasers and Electro-Optics/Europe, CLEO/Europe 2023 and European Quantum Electronics Conference EQEC 2023, Part of Conference on Lasers and Electro-Optics/Europe, CLEO/Europe 2023 and European Quantum Electroni · January 1, 2023 Cite

Cross-platform comparison of arbitrary quantum states.

Journal Article Nature communications · November 2022 As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can be easily verifie ... Full text Cite

Real-time Quantum Calculations of Phase Shifts On NISQ Hardware Platforms Using Wavepacket Time Delay

Conference Proceedings of Science · July 8, 2022 We introduce a new method to calculate phase shifts on noisy intermediate scale quantum (NISQ) hardware platforms using a wave packet edge time delay. The method uses the early and intermediate stages of the collision because the standard method based on t ... Cite

Quantum computational advantage attested by nonlocal games with the cyclic cluster state

Journal Article Physical Review Research · July 1, 2022 We propose a set of Bell-type nonlocal games that can be used to prove an unconditional quantum advantage in an objective and hardware-agnostic manner. In these games, the circuit depth needed to prepare a cyclic cluster state and measure a subset of its P ... Full text Cite

Many-Body Quantum Teleportation via Operator Spreading in the Traversable Wormhole Protocol

Journal Article Physical Review X · July 1, 2022 By leveraging shared entanglement between a pair of qubits, one can teleport a quantum state from one particle to another. Recent advances have uncovered an intrinsically many-body generalization of quantum teleportation, with an elegant and surprising con ... Full text Cite

Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions

Journal Article PRX Quantum · June 1, 2022 Tracking the dynamics of physical systems in real time is a prime application of quantum computers. Using a trapped-ion system with up to six qubits, we simulate the real-time dynamics of a lattice gauge theory in 1+1 dimensions, i.e., the lattice Schwinge ... Full text Cite

Experimental Measurement of Out-of-Time-Ordered Correlators at Finite Temperature.

Journal Article Physical review letters · April 2022 Out-of-time-ordered correlators (OTOCs) are a key observable in a wide range of interconnected fields including many-body physics, quantum information science, and quantum gravity. Measuring OTOCs using near-term quantum simulators will extend our ability ... Full text Cite

Multiplexed quantum repeaters based on dual-species trapped-ion systems

Journal Article Physical Review A · February 1, 2022 Trapped ions form an advanced technology platform for quantum information processing with long qubit coherence times, high-fidelity quantum logic gates, optically active qubits, and a potential to scale up in size while preserving a high level of connectiv ... Full text Cite

Bounds on the recurrence probability in periodically -driven quantum systems

Journal Article Quantum · January 1, 2022 Periodically-driven systems are ubiquitous in science and technology. In quantum dynamics, even a small number of periodically-driven spins leads to complicated dynamics. Hence, it is of interest to understand what constraints such dynamics must satisfy. W ... Full text Cite

Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware

Journal Article Physical Review A · December 1, 2021 Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks (DTQWs) and sh ... Full text Cite

Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach

Journal Article Physical Review Research · December 1, 2021 Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical co ... Full text Cite

Real-time quantum calculations of phase shifts using wave packet time delays

Journal Article Physical Review D · September 1, 2021 We present a method to extract the phase shift of a scattering process using the real-time evolution in the early and intermediate stages of the collision in order to estimate the time delay of a wave packet. This procedure is convenient when using noisy q ... Full text Cite

Demonstration of Shor Encoding on a Trapped-Ion Quantum Computer

Journal Article Physical Review Applied · August 1, 2021 Fault-tolerant quantum error correction (QEC) is crucial for unlocking the true power of quantum computers. QEC codes use multiple physical qubits to encode a logical qubit, which is protected against errors at the physical qubit level. Here, we use a trap ... Full text Cite

Many-body thermodynamics on quantum computers via partition function zeros.

Journal Article Science advances · August 2021 Partition functions are ubiquitous in physics: They are important in determining the thermodynamic properties of many-body systems and in understanding their phase transitions. As shown by Lee and Yang, analytically continuing the partition function to the ... Full text Cite

Efficient Stabilized Two-Qubit Gates on a Trapped-Ion Quantum Computer.

Journal Article Physical review letters · June 2021 In order to scale up quantum processors and achieve a quantum advantage, it is crucial to economize on the power requirement of two-qubit gates, make them robust to drift in experimental parameters, and shorten the gate times. Applicable to all quantum com ... Full text Cite

Programmable quantum simulations of spin systems with trapped ions

Journal Article Reviews of Modern Physics · April 7, 2021 Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect effici ... Full text Cite

Probing many-body localization on a noisy quantum computer

Journal Article Physical Review A · March 1, 2021 A disordered quantum system of interacting particles exhibits localized behavior when the disorder is large compared to the interaction strength. Studying this phenomenon on a quantum computer with no, or limited, error correction is challenging because ev ... Full text Cite

Seletalisib for Activated PI3Kδ Syndromes: Open-Label Phase 1b and Extension Studies.

Journal Article Journal of immunology (Baltimore, Md. : 1950) · December 2020 Mutations in two genes can result in activated PI3Kδ syndrome (APDS), a rare immunodeficiency disease with limited therapeutic options. Seletalisib, a potent, selective PI3Kδ inhibitor, was evaluated in patients with APDS1 and APDS2. In the phase 1b study ... Full text Cite

Generation of thermofield double states and critical ground states with a quantum computer.

Journal Article Proceedings of the National Academy of Sciences of the United States of America · October 2020 Finite-temperature phases of many-body quantum systems are fundamental to phenomena ranging from condensed-matter physics to cosmology, yet they are generally difficult to simulate. Using an ion trap quantum computer and protocols motivated by the quantum ... Full text Cite

Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer.

Journal Article Nature communications · July 2020 The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range of quantum algor ... Full text Cite

Mit Ionen ist zu rechnen

Journal Article Physik in unserer Zeit · July 2020 ZusammenfassungQuantencomputer versprechen, spezielle, für Anwendungen hochinteressante Aufgaben zu lösen. An diesen NP‐harten Problemen scheitern herkömmliche Supercomputer. Eine Technik, die intensiv erforscht wird, ist d ... Full text Cite

Architecting Noisy Intermediate-Scale Quantum Computers: A Real-System Study

Journal Article IEEE Micro · May 1, 2020 Current quantum computers have very different qubit implementations, instruction sets, qubit connectivity, and noise characteristics. Using real-system evaluations on seven quantum systems from three leading vendors, our work explores fundamental design qu ... Full text Cite

Toward convergence of effective-field-theory simulations on digital quantum computers

Journal Article Physical Review A · December 16, 2019 We report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansatze have been used to compute ... Full text Cite

Training of quantum circuits on a hybrid quantum computer.

Journal Article Science advances · October 2019 Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum comput ... Full text Cite

2D Quantum Metamaterials

Conference · September 2019 Full text Cite

Two-qubit entangling gates within arbitrarily long chains of trapped ions

Journal Article Physical Review A · August 26, 2019 Ion trap quantum computers are based on modulating the Coulomb interaction between atomic ion qubits using external forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large num ... Full text Open Access Cite

Parallel entangling operations on a universal ion-trap quantum computer.

Journal Article Nature · August 2019 The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations1. The ability to execute parallel entangling quantum gates offers efficiency gai ... Full text Cite

Full-stack, real-system quantum computer studies: Architectural comparisons and design insights

Conference Proceedings - International Symposium on Computer Architecture · June 22, 2019 In recent years, Quantum Computing (QC) has progressed to the point where small working prototypes are available for use. Termed Noisy Intermediate-Scale Quantum (NISQ) computers, these prototypes are too small for large benchmarks or even for Quantum Erro ... Full text Cite

Validating and certifying stabilizer states

Journal Article Physical Review A · April 30, 2019 We propose a measurement scheme that validates the preparation of an n-qubit stabilizer state. The scheme involves a measurement of n Pauli observables, a priori determined from the stabilizer state and which can be realized using single-qubit gates. Based ... Full text Cite

Verified quantum information scrambling.

Journal Article Nature · March 2019 Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout an entire system. This concept accompanies the dynamics of thermalization in closed quantum systems, and has recently emer ... Full text Cite

Quantum computing and simulation with trapped atomic ions

Conference Optics InfoBase Conference Papers · January 1, 2019 I will review some of the latest results in both gate-based quantum computing and analog quantum simulation, speculating on how this platform can realistically be scaled in the near future. ... Full text Cite

Measuring the Rényi entropy of a two-site Fermi-Hubbard model on a trapped ion quantum computer

Journal Article Physical Review A · November 26, 2018 The efficient simulation of correlated quantum systems is a promising near-term application of quantum computers. Here, we present a measurement of the second Rényi entropy of the ground state of the two-site Fermi-Hubbard model on a five-qubit programmabl ... Full text Cite

Machine learning assisted readout of trapped-ion qubits

Journal Article Journal of Physics B: Atomic, Molecular and Optical Physics · August 17, 2018 We reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the incor ... Full text Cite

Demonstration of a Bayesian quantum game on an ion-trap quantum computer

Journal Article Quantum Science and Technology · July 10, 2018 We demonstrate a Bayesian quantum game on an ion-trap quantum computer with five qubits. The players share an entangled pair of qubits and perform rotations on their qubit as the strategy choice. Two five-qubit circuits are sufficient to run all 16 possibl ... Full text Cite

Observation of Hopping and Blockade of Bosons in a Trapped Ion Spin Chain.

Journal Article Physical review letters · February 2018 The local phonon modes in a Coulomb crystal of trapped ions can represent a Hubbard system of coupled bosons. We selectively prepare single excitations at each site and observe free hopping of a boson between sites, mediated by the long-range Coulomb inter ... Full text Cite

Robust 2-Qubit Gates in a Linear Ion Crystal Using a Frequency-Modulated Driving Force.

Journal Article Physical review letters · January 2018 In an ion trap quantum computer, collective motional modes are used to entangle two or more qubits in order to execute multiqubit logical gates. Any residual entanglement between the internal and motional states of the ions results in loss of fidelity, esp ... Full text Open Access Cite

Complete 3-Qubit Grover search on a programmable quantum computer.

Journal Article Nature communications · December 2017 The Grover quantum search algorithm is a hallmark application of a quantum computer with a well-known speedup over classical searches of an unsorted database. Here, we report results for a complete three-qubit Grover search algorithm using the scalable qua ... Full text Cite

Fault-tolerant quantum error detection.

Journal Article Science advances · October 2017 Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple physical qubits. ... Full text Cite

Experimental comparison of two quantum computing architectures.

Journal Article Proceedings of the National Academy of Sciences of the United States of America · March 2017 We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www.Researchibm.com/ibm-q) with limited connectivity ... Full text Cite

High-fidelity spatial and polarization addressing of Ca + 43 qubits using near-field microwave control

Journal Article Physical Review A · February 27, 2017 Individual addressing of qubits is essential for scalable quantum computation. Spatial addressing allows unlimited numbers of qubits to share the same frequency, while enabling arbitrary parallel operations. We demonstrate addressing of long-lived Ca+43 "a ... Full text Cite

Comparing the architectures of the first programmable quantum computers

Conference Optics InfoBase Conference Papers · January 1, 2017 Cite

Demonstration of a small programmable quantum computer with atomic qubits.

Journal Article Nature · August 2016 Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular ... Full text Cite

High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits.

Journal Article Physical review letters · August 2016 We demonstrate laser-driven two-qubit and single-qubit logic gates with respective fidelities 99.9(1)% and 99.9934(3)%, significantly above the ≈99% minimum threshold level required for fault-tolerant quantum computation, using qubits stored in hyperfine g ... Full text Cite

Hybrid quantum logic and a test of Bell's inequality using two different atomic isotopes.

Journal Article Nature · December 2015 Entanglement is one of the most fundamental properties of quantum mechanics, and is the key resource for quantum information processing (QIP). Bipartite entangled states of identical particles have been generated and studied in several experiments, and pos ... Full text Cite

High-Fidelity Preparation, Gates, Memory, and Readout of a Trapped-Ion Quantum Bit.

Journal Article Physical review letters · November 2014 We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine "atomic clock" states of ^{43}Ca^{+}. We measure a combined qubi ... Full text Cite

Microwave control electrodes for scalable, parallel, single-qubit operations in a surface-electrode ion trap

Journal Article Applied Physics B: Lasers and Optics · January 1, 2014 We propose a surface ion trap design incorporating microwave control electrodes for near-field single-qubit control. The electrodes are arranged so as to provide arbitrary frequency, amplitude and polarization control of the microwave field in one trap zon ... Full text Cite

Injection locking of two frequency-doubled lasers with 3.2 GHz offset for driving Raman transitions with low photon scattering in 43Ca+.

Journal Article Optics letters · December 2013 We describe the injection locking of two infrared (794 nm) laser diodes that are each part of a frequency-doubled laser system. An acousto-optic modulator in the injection path gives an offset of 1.6 GHz between the lasers for driving Raman transitions bet ... Full text Cite

A microfabricated ion trap with integrated microwave circuitry

Journal Article Applied Physics Letters · January 28, 2013 We describe the design, fabrication, and testing of a surface-electrode ion trap, which incorporates microwave waveguides, resonators, and coupling elements for the manipulation of trapped ion qubits using near-field microwaves. The trap is optimised to gi ... Full text Cite

Background-free detection of trapped ions

Journal Article Applied Physics B: Lasers and Optics · June 1, 2012 We demonstrate a Doppler cooling and detection scheme for ions with low-lying D levels which almost entirely suppresses scattered laser light background, while retaining a high fluorescence signal and efficient cooling. We cool a single ion with a laser on ... Full text Cite

Heating rate and electrode charging measurements in a scalable, microfabricated, surface-electrode ion trap

Journal Article Applied Physics B: Lasers and Optics · June 1, 2012 We characterise the performance of a surfaceelectrode ion "chip" trap fabricated using established semiconductor integrated circuit and micro-electro-mechanicalsystem (MEMS) microfabrication processes, which are in principle scalable to much larger ion tra ... Full text Cite

Implementation of a symmetric surface-electrode ion trap with field compensation using a modulated Raman effect

Journal Article New Journal of Physics · May 17, 2010 We describe a new electrode design for a surface-electrode Paul trap, which allows rotation of the normal modes out of the trap plane, and a technique for micromotion compensation in all directions using a two-photon process, which avoids the need for an u ... Full text Cite

Optimised focusing ion optics for an ultracold deterministic single ion source targeting nm resolution

Journal Article Journal of Modern Optics · October 1, 2009 Using a segmented ion trap with mK laser-cooled ions we have realised a novel single ion source which can deterministically deliver a wide range of ion species, isotopes or ionic molecules [Schnitzler et al. Phys. Rev. Lett. 2009, 102, 070501]. Experimenta ... Full text Cite

Deterministic ultracold ion source targeting the Heisenberg limit.

Journal Article Physical review letters · February 2009 The major challenges to fabricate quantum processors and future nano-solid-state devices are material modification techniques with nanometer resolution and suppression of statistical fluctuations of dopants or qubit carriers. Based on a segmented ion trap ... Full text Cite