NMR Techniques for Quantum Control and Computation

Abstract

Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclear spin dynamics has recently been taken to a new level, motivated by the interest in quantum information processing. NMR has been the workhorse for the experimental implementation of quantum protocols, allowing exquisite control of systems up to seven qubits in size. Here, we survey and summarize a broad variety of pulse control and tomographic techniques which have been developed for and used in NMR quantum computation. Many of these will be useful in other quantum systems now being considered for implementation of quantum information processing tasks.

33 pages, accepted for publication in Rev. Mod. Phys., added subsection on T_{1,ρ} (V.A.6) and on time-optimal pulse sequences (III.A.6), redid some figures, made many small changes, expanded references

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• Coherent control in the ground and optically excited state of an ensemble of erbium dopants
• Accurate and robust unitary transformation of a high-dimensional quantum system
• Dynamically corrected gates for qubits with always-on Ising couplings: Error model and fault-tolerance with the toric code
• Spin-Orbit Interaction Enabled High-Fidelity Two-Qubit Gates
• Entanglement of a nuclear spin qubit register in silicon photonics
• Temporally correlated quantum noise in driven quantum systems
• Detect genuine multipartite entanglement in the one-dimensional transverse-field Ising model
• Rating the performance of noisy teleportation using fluctuations in fidelity
• Fast high-fidelity geometric gates for singlet-triplet qubits
• Quantized Thouless pumps protected by interactions in dimerized Rydberg tweezer arrays
• Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems
• Platonic dynamical decoupling sequences for interacting spin systems
• Shortcuts to adiabatic population inversion via time-rescaling: stability and thermodynamic cost
• Normalization procedure for relaxation studies in NMR quantum information processing
• Emergence of entanglement with temperature and time in factorization-surface states
• Many-particle confinement by constructed disorder and quantum computing
• Greenberger-Horne-Zeilinger state generation in qubit-chains via a single $\pi /2$-pulse
• Enhancing a Near-Term Quantum Accelerator's Instruction Set Architecture for Materials Science Applications
• Single qubit gates by selective excitation with Jump and Return sequences
• Writing electronic ferromagnetic states in a high-temperature paramagnetic nuclear spin system
• Dynamical uncertainty propagation with noisy quantum parameters
• Quantum Gates Robust to Secular Amplitude Drifts
• General off-resonance error robust symmetric composite pulses with three elementary operations
• Three-state coherent control using narrowband and passband sequences
• Generalized Hamiltonian to describe imperfections in ion-light interaction
• Quantum control of Hubbard excitons
• Experimental Implementation of a Codeword Stabilized Quantum Code
• Subsystem Pseudo-pure States
• Ultrahigh-fidelity composite quantum phase gates
• Entangled coherent states under dissipation
• Group twirling and noise tailoring for multi-qubit controlled phase gates
• Fast noise-resistant control of donor nuclear spin qubits in silicon
• Improved Electron-Nuclear Quantum Gates for Spin Sensing and Control
• Entangling efficiency of linear-optical quantum gates
• Algebraic structure of path-independent quantum control
• Scalable fast benchmarking for individual quantum gates with local twirling
• Quantum Control of d-Dimensional Quantum Systems with Application to Alkali Atomic Spins
• Universal quantum processors in spin systems via robust local pulse sequences
• Transitionless quantum driving in spin echo
• Cold highly charged ions in a radio-frequency trap with superconducting magnetic shielding
• Random Pulse Sequences for Qubit Noise Spectroscopy
• Experimental Preparation of Topologically Ordered States via Adiabatic Evolution
• Two-atom quantum gate in hybrid cavity optomechanics
• Experimental Simulation of Bosonic Creation and Annihilation Operators in a Quantum Processor
• Macroscopic Schrödinger Cat Resistant to Particle Loss and Local Decoherence
• SpinQ Gemini: a desktop quantum computer for education and research
• Superiority in dense coding through non-Markovian stochasticity
• Multimode Brownian oscillators: Exact solutions to heat transport
• Manipulation of the dynamics of many-body systems via quantum control methods
• Magnetic hot-spots generation at optical frequencies in all-dielectric mesoscale Janus particles
• How efficient is transport of quantum cargo through multiple highways?
• Error-Resilient Floquet Geometric Quantum Computation
• Quantifying Entanglement in Cluster States Built with Error-Prone Interactions
• Suppression of Phase Decoherence in a Single Atomic Qubit
• Quantum non-Markovian behavior at the chaos border
• Nuclear Electric Resonance for Spatially-Resolved Spin Control via Pulsed Optical Excitation in the UV-Visible Spectrum
• Sensitive Magnetic Control of Ensemble Nuclear Spin Hyperpolarisation in Diamond
• Entanglement sudden birth and sudden death in a system of two distant atoms coupled via an optical element
• Discrimination of unitary transformations in the Deutsch-Jozsa algorithm
• Coarse-grained spectral projection (CGSP): a deep learning-assisted approach to quantum unitary dynamics
• Coherence of a dynamically decoupled single neutral atom
• Experimental Virtual Quantum Broadcasting
• Sequential quantum simulation of spin chains with a single circuit QED device
• Robust controllability of two-qubit Hamiltonian dynamics
• Majorana path integral for nonequilibrium dynamics of two-level systems
• Quantum controlled-Z gate for weakly interacting qubits
• Coherent control of a local phonon in trapped ions using dynamical decoupling
• Ultrastrong magnetic light-matter interaction with cavity mode engineering
• Effect of interactions on quantum-limited detectors
• Robust transitionless quantum driving: Concatenated approach
• Interlayer Diffusion of Nuclear Spin Polarization in $\nu =2/3$ Quantum Hall States
• Wavelet correlation noise analysis for qubit operation variable time series
• Low power, fast and broadband ESR quantum control using a stripline resonator
• Separability and parity transitions in $XYZ$ spin systems under nonuniform fields
• Optimal Bounds on State Transfer Under Quantum Channels with Application to Spin System Engineering
• Generalized hyper-Ramsey resonance with spinors
• Local Gradient Optimization of Modular Entangling Sequences
• Quantum compiling with a variational instruction set for accurate and fast quantum computing
• Theory of interaction-dependent instability in quantum detection by means of Luttinger liquid tunnel junction: a rigorous theorem
• Experimental realization of optimal time-reversal on an atom chip for quantum undo operations
• Estimating phase transition of perturbed J1-J2 Heisenberg quantum chain in mixtures of ground and first excited states
• Coarse-grained effective Hamiltonian via the Magnus Expansion for a three-level system
• State-independent robust heat-bath algorithmic cooling of nuclear spins
• Quantum state transfer using 1D Heisenberg Hamiltonian on quasi-1D lattices
• Multi-qubit DC gates over an inhomogeneous array of quantum dots
• Quantum Sensing Using Atomic Clocks for Nuclear and Particle Physics
• Cooperative effects in Josephson junctions in a cavity in the strong coupling regime
• Optical Nuclear Electric Resonance in LiNa: Selective Addressing of Nuclear Spins Through Pulsed Lasers
• Prospects for using integrated atom-photon junctions for quantum information processing
• Pseudospin and Quantum Computation in Semiconductor Nanostructures
• Noise suppression and long-range exchange coupling for gallium arsenide spin qubits
• Control Paradigms for Quantum Engineering
• Optimal generation of single-qubit operation from an always-on interaction by algebraic decoupling
• Excitation of narrow x-ray transitions in thin-film cavities by focused pulses
• A practical guide for building superconducting quantum devices
• Selective Excitation of Superconducting Qubits with a Shared Control Line through Pulse Shaping
• Optical nuclear electric resonance as single qubit gate for trapped neutral atoms
• Parameter Estimation, Model Reduction and Quantum Filtering
• Nuclear Spins in a Nanoscale Device for Quantum Information Processing
• Quasi-Classical Rules for Qubit Spin-Rotation Error Suppression
• Scalable Quantum Computational Science: A Perspective from Block-Encodings and Polynomial Transformations
• PULSEE: A software for the quantum simulation of an extensive set of magnetic resonance observables
• SU(2) hyper-clocks: quantum engineering of spinor interferences for time and frequency metrology
• Implementation of a two-qubit state by an auxiliary qubit on the three-spin system
• High cooperativity coupling to nuclear spins on a circuit QED architecture
• Tailoring the quantumness of a driven qubit
• Quantum gates using electronic and nuclear spins of Yb${}^{+}$ in a magnetic field gradient
• Monogamy relations of entropic non-contextual inequalities and their experimental realization
• Experimental Demonstration of Swift Analytical Universal Control over Nearby Transitions
• Survival of the fittest in the coherent evolution of quantum ensembles
• Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit
• Experimental simulation of quantum superchannels
• Microwave Engineering of Tunable Spin Interactions with Superconducting Qubits
• Local gradient optimization of leakage-suppressing entangling sequences
• Efimov Effect in Long-range Quantum Spin Chains
• High-fidelity Nuclear Coherent Population Transfer via the Mixed-State Inverse Engineering
• Quantum state reconstruction with imperfect rotations on an inhomogeneously broadened ensemble of qubits
• Overcoming limitations on gate fidelity in noisy static exchange-coupled surface qubits
• Highly efficient nuclear population transfer through physics-informed neural networks
• Implementing Finite Impulse Response Filters on Quantum Computers
• Resource state generation for a multispin register in a hybrid matter-photon quantum information processor
• Pulse-controlled quantum gate sequences on a strongly coupled qubit chain
• Mitigation of systematic amplitude error in nonadiabatic holonomic operations
• Entanglement manipulation by a local magnetic pulse
• Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins
• Infinite dimensional semiclassical analysis and applications to a model in NMR
• Phonon-induced entanglement dynamics of two donor-based charge quantum bits
• Statistical comparison of ensemble implementations of Grover's search algorithm to classical sequential searches
• Quantum probes for quantum wells
• Cooling classical many-spin systems using feedback control
• True experimental reconstruction of quantum states and processes via convex optimization
• openMMF: a library for multimode driven quantum systems
• Zero- to ultralow-field nuclear magnetic resonance and its applications
• Universal quantum computation with quantum-dot cellular automata in dephasing-free subspace
• Cyclicity of interaction frame transformations
• Measurement-based cooling of many-body quantum systems
• Implementation of Liouville space search algorithm on strongly dipolar coupled nuclear spins
• Optimal finite-time processes in weakly driven overdamped Brownian motion
• Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor
• Electron Localization and Energy Levels' Oscillations Induced by Controlled Deformation
• Realizing the Petz Recovery Map on an NMR Quantum Processor
• Simultaneous control of populations and coherence phase of open two-level quantum systems with a single pulse
• Protected Rabi oscillation induced by natural interactions among physical qubits
• Controllable conditional quantum oscillations and synchronization in superconducting flux qubits
• Experimental implementation of quantum information processing by Zeeman perturbed nuclear quadrupole resonance
• Advantage of flexible catalysis for entanglement and quantum thermodynamics
• Quantum states interrogation using a pre-shaped free electron wavefunction
• Quantum dynamics of spin-J particles in static and rotating magnetic fields: Entanglement resonances and kinks
• Geometric and holonomic quantum computation
• Robust gigahertz-range ac magnetometry with an ensemble of NV centers in diamond using concatenated continuous dynamical decoupling
• Universal Relations in Long-range Quantum Spin Chains
• Collection efficiency of optical photons generated from microwave excitations of a Bose-Einstein condensate
• Attainable entanglement of unitary transformed thermal states in liquid-state nuclear magnetic resonance with the chemical shift
• Scaling of Computational Order Parameters in Rydberg Atom Graph States
• Resilience-Runtime Tradeoff Relations for Quantum Algorithms
• Detecting Initial System-Environment Correlations from a Single Observable
• Exploring the physical limits of saturation contrast in Magnetic Resonance Imagign
• Benchmarking quantum devices beyond classical capabilities
• Tomographic entanglement indicators from NMR experiments
• Constructing Qudits from Infinite Dimensional Oscillators by Coupling to Qubits
• Generalized pulse design in Floquet engineering: Application to interacting spin systems
• Diverging scaling with converging multisite entanglement in odd and even quantum Heisenberg ladders
• Spin adaptation of the cumulant expansions of reduced density matrices
• Simulated Randomized Benchmarking of a Dynamically Corrected Cross-Resonance Gate
• Preparation of two-qubit entangled states on a spin-1/2 Ising-Heisenberg diamond spin cluster by controlling the measurement
• Hyper Ramsey-Bordé matter-wave interferometry for robust quantum sensors