NMR techniques for quantum control and computation

2004/04/30 by Lieven M. K. Vandersypen, L. M. K. Vandersypen, Isaac L. Chuang +1 · 1,233 citations
Computer Science · Physics and Astronomy · #Open quantum system #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum computer #Quantum information #Quantum mechanics #Quantum technology #Qubit #Spectroscopy and Quantum Chemical Studies #quant-ph

paper · pdf · doi:10.1103/revmodphys.76.1037

published in Reviews of Modern Physics 76(4), 1037-1069 (American Physical Society) · 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

arxiv created 2004/06/10 · openalex publication_date 2005/01/12 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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. This article surveys and summarizes 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 the implementation of quantum information processing tasks.

Citations

• On the exponential solution of differential equations for a linear operator
• A Simplex Method for Function Minimization

Cited by

• Sensitivity optimization for NV-diamond magnetometry
• Quantum computing with NMR
• Scalable entanglement of nuclear spins mediated by electron exchange
• Accurate and robust unitary transformation of a high-dimensional quantum system
• On the encoding complexity of quantum numerical integration: an angle-structure characterization
• W- and Dicke-state engineering using optimal global control in nearest-neighbor coupled ring-shaped qubit arrays
• Quantum Reference Frames in Quantum Circuits: Perspective Dependent Entangling Cost and Coherence Entanglement Trade Offs
• Eight-Qubit Operation of a 300 mm SiMOS Foundry-Fabricated Device
• A practical guide for building superconducting quantum devices
• Experimental implementation of quantum information processing by Zeeman perturbed nuclear quadrupole resonance
• Scalable Quantum Computational Science: A Perspective from Block-Encodings and Polynomial Transformations
• Trading athermality for nonstabiliserness
• Quantum Decoherence
• Recent Advances on Nonadiabatic Geometric Quantum Computation
• Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor
• Entanglement and Quantum Error Correction with Superconducting Qubits
• A Review on Quantum Computing: Qubits, Cryogenic Electronics and Cryogenic MOSFET Physics
• The Phase-Coupled Caldeira-Leggett Model: Non-Markovian Open Quantum Dynamics beyond Linear Dissipation
• Universal Relations in Long-range Quantum Spin Chains
• Semiconductor Spin Qubits
• Digital adiabatic evolution is universally accurate
• Characterizing and Harnessing Correlations Featuring Independent Qubit Devices
• Near-limit quantum control beyond analytic tractability in many-body spin systems
• Quantum control of Hubbard excitons
• Error tolerance in an NMR implementation of Grover’s fixed-point quantum search algorithm
• Identifying an experimental two-state Hamiltonian to arbitrary accuracy
• Stable organic radical qubits and their applications in quantum information science
• Tracking spin qubit frequency variations over 912 days
• Overcoming limitations on gate fidelity in noisy static exchange-coupled surface qubits
• From virtual Z gates to virtual Z pulses
• SpinQ Gemini: a desktop quantum computer for education and research
• High-order Magnus Expansion for Hamiltonian Simulation
• Hierarchical Equations of Motion Solved with the Multiconfigurational Ehrenfest Ansatz
• Parameter Estimation, Model Reduction and Quantum Filtering
• High cooperativity coupling to nuclear spins on a circuit QED architecture
• Quantifying decoherence in continuous variable systems
• Scalable Design of Tailored Soft Pulses for Coherent Control
• Exploring the feasibility of probabilistic and deterministic quantum gates between T centers in silicon
• Taming coherent noise with teleportation
• Towards Efficient Verification of Computation in Quantum Devices
• Heat as a Witness of Quantum Properties
• Dynamical and Emission Properties of Quantum Emitters driven by Ultra-Short Laser Pulses
• Quantum discord determines the interferometric power of quantum states
• Quantum states interrogation using a pre-shaped free electron wavefunction
• Cooperative effects in Josephson junctions in a cavity in the strong coupling regime
• Fault-tolerant dynamically-decoupled hyper-Ramsey spectroscopy of ultra-narrow clock transitions
• Cyclicity of interaction frame transformations
• Quantum circuits as a game: A reinforcement learning agent for quantum compilation and its application to reconfigurable neutral atom arrays
• Mechanism behind creating qubit gates expressed as interfering quantum pathway amplitudes
• Quantum Control of d-Dimensional Quantum Systems with Application to Alkali Atomic Spins
• Electron Localization and Energy Levels' Oscillations Induced by Controlled Deformation
• Realizing Bloch Dynamics in a Low-Cost Electrically Driven Acoustic Two-Level System
• Infinite dimensional semiclassical analysis and applications to a model in NMR
• Engineering protected cavity-QED interactions through pulsed dynamical decoupling
• Tailoring the quantumness of a driven qubit
• Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots
• Spin adaptation of the cumulant expansions of reduced density matrices
• Microwave Engineering of Tunable Spin Interactions with Superconducting Qubits
• Exact S-matrices for higher dimensional representations of generalized Landau-Zener Hamiltonians
• Digital quantum simulation of spin models with circuit quantum electrodynamics
• Anyonic interferometry and protected memories in atomic spin lattices
• 1/fnoise: Implications for solid-state quantum information
• Iterative quantum-state transfer along a chain of nuclear spin qubits
• Pseudo-spin quantum computation in semiconductor nanostructures
• Subsystem pseudopure states
• Effect of system level structure and spectral distribution of the environment on the decoherence rate
• How to enhance dephasing time in superconducting qubits
• Optimization of short coherent control pulses
• The Magnus expansion and some of its applications
• Optimal generation of single-qubit operation from an always-on interaction by algebraic decoupling
• Accurate microwave control and real-time diagnostics of neutral-atom qubits
• Attainable entanglement of unitary transformed thermal states in liquid-state nuclear magnetic resonance with the chemical shift
• Exact results on dynamical decoupling by π pulses in quantum information processes
• Implementation of quantum gates via optimal control
• Error-detection-based quantum fault tolerance against discrete Pauli noise
• Experimental multiparticle entanglement dynamics induced by decoherence
• Robust state preparation of a single trapped ion by adiabatic passage
• Liquid-state nuclear magnetic resonance as a testbed for developing quantum control methods
• Optimal tuning of solid-state quantum gates: A universal two-qubit gate
• Parahydrogen Cooling of Nuclear Spin Chains at Hypogeomagnetic Fields
• Quantum spin models with electrons in Penning traps
• High-fidelity one-qubit operations under random telegraph noise
• Ramsey’s method of separated oscillating fields and its application to gravitationally induced quantum phase shifts
• Speedup of quantum-state transfer by three-qubit interactions: Implementation by nuclear magnetic resonance
• Dynamic Polarization of Single Nuclear Spins by Optical Pumping of Nitrogen-Vacancy Color Centers in Diamond at Room Temperature
• Generation of quantum logic operations from physical Hamiltonians
• Spin decoherence from Hamiltonian dynamics in quantum dots
• Linear optical scheme to demonstrate genuine multipartite entanglement for single-particleWstates
• Demonstration of a Compiled Version of Shor’s Quantum Factoring Algorithm Using Photonic Qubits
• DISTRIBUTED QUANTUM COMPUTATION ARCHITECTURE USING SEMICONDUCTOR NANOPHOTONICS
• Atomic swap gate, driven by position fluctuations, in dispersive cavity optomechanics
• DYNAMICS OF QUANTUM CORRELATIONS IN TWO-QUBIT SYSTEMS WITHIN NON-MARKOVIAN ENVIRONMENTS
• Experimental Approximation of the Jones Polynomial with One Quantum Bit
• Generalized pulse design in Floquet engineering: Application to interacting spin systems
• Deterministic generation of large scale atomic W states
• Cavity-based quantum networks with single atoms and optical photons
• Distributed quantum computation based on small quantum registers
• Realization of the Quantum Toffoli Gate with Trapped Ions
• High-fidelity resonant gating of a silicon-based quantum dot hybrid qubit
• Local Convertibility and the Quantum Simulation of Edge States in Many-Body Systems
• Robust Two-Qubit Gates for Donors in Silicon Controlled by Hyperfine Interactions
• Chiral quantum walks
• Concept of deterministic single ion doping with sub-nm spatial resolution
• Room-Temperature Implementation of the Deutsch-Jozsa Algorithm with a Single Electronic Spin in Diamond
• Manipulation of the dynamics of many-body systems via quantum control methods
• Measuring Bipartite Quantum Correlations of an Unknown State
• Quantum simulation of the general semi-classical Rabi model in regimes of arbitrarily strong driving
• Environment-Induced Sudden Transition in Quantum Discord Dynamics
• Efficient assessment of process fidelity
• Detect genuine multipartite entanglement in the one-dimensional transverse-field Ising model
• Controllable Conditional Quantum Oscillations and Quantum Gate Operations in Superconducting Flux Qubits
• Measurement of linear response functions in Nuclear Magnetic Resonance
• High-Fidelity Single-Qubit Gates for Two-Electron Spin Qubits in GaAs
• High-fidelity quantum gates in Si/SiGe double quantum dots
• Simulated randomized benchmarking of a dynamically corrected cross-resonance gate
• Spin Based Heat Engine: Demonstration of Multiple Rounds of Algorithmic Cooling
• Fidelity benchmarks for two-qubit gates in silicon
• Experimental Benchmarking of Quantum Control in Zero-Field Nuclear Magnetic Resonance
• Experimental simulation of shift operators in a quantum processor
• Majorana path integral for nonequilibrium dynamics of two-level systems
• Room-temperature manipulation and decoherence of a single spin in diamond
• Graphane with carbon dimer defects: Robust in-gap states and a scalable two-dimensional platform for quantum computation
• Universal Set of Scalable Dynamically Corrected Gates for Quantum Error Correction with Always-on Qubit Couplings
• Robust entanglement in antiferromagnetic Heisenberg chains by single-spin optimal control
• Quantum process estimation via generic two-body correlations
• Assessing Non-Markovian Quantum Dynamics
• Entanglement of a nuclear spin qubit register in silicon photonics
• Quantum-information-processing architecture with endohedral fullerenes in a carbon nanotube
• Improved quantum state tomography for systems with XX+YY couplings and Z readouts
• Numerical analysis of optimized coherent control pulses
• Quantum controlled-Zgate for weakly interacting qubits
• Broadband noise-free optical quantum memory with neutral nitrogen-vacancy centers in diamond
• Impact of Classical Control Electronics on Qubit Fidelity
• Spins in few-electron quantum dots
• Observation of interaction induced blockade and local spin freezing in a NMR quantum simulator
• Quantum Control in the Cs6S1/2Ground Manifold Using Radio-Frequency and Microwave Magnetic Fields
• Experimental simulation of anyonic fractional statistics with an NMR quantum-information processor
• Integration of spectator qubits into quantum computer architectures for hardware tune-up and calibration
• Optimized Compilation of Aggregated Instructions for Realistic Quantum Computers
• Landau-Majorana-Stückelberg-Zener dynamics driven by coupling for two interacting qutrit systems
• Quantum dynamics of a microwave driven superconducting phase qubit coupled to a two-level system
• Composite two-qubit gates
• Catalytic Coherence
• Rating the performance of noisy teleportation using fluctuations in fidelity
• Driven coherent oscillations of a single electron spin in a quantum dot
• Simultaneous time-optimal control of the inversion of two spin-12particles
• Hybrid quantum-classical approach to enhanced quantum metrology
• Second-order shaped pulses for solid-state quantum computation
• Advantage of flexible catalysis for entanglement and quantum thermodynamics
• Nuclear spin squeezing via electric quadrupole interaction
• Quantum-Dot-Based Resonant Exchange Qubit
• Interlayer diffusion of nuclear spin polarization inν=23quantum Hall states
• Realization of geometric Landau-Zener-Stückelberg interferometry
• Three-electron spin qubits

Related

• Introduction to NMR Quantum Information Processing
• NMR quantum information processing
• Quantum computing with NMR
• Nuclear Spins as Quantum Testbeds: Singlet States, Quantum Correlations, and Delayed-choice Experiments
• NMR Quantum Computation