NMR Quantum Information Processing

Abstract

Nuclear Magnetic Resonance (NMR) has provided a valuable experimental testbed for quantum information processing (QIP). Here, we briefly review the use of nuclear spins as qubits, and discuss the current status of NMR-QIP. Advances in the techniques available for control are described along with the various implementations of quantum algorithms and quantum simulations that have been performed using NMR. The recent application of NMR control techniques to other quantum computing systems are reviewed before concluding with a description of the efforts currently underway to transition to solid state NMR systems that hold promise for scalable architectures.

Mixed-state Pauli-channel parameter estimation

“…For example, NMR systems used in quantum information processing provide different dephasing times among the system qubits (for examples from NMR quantum information processing see Refs. [42][43][44][45][46]). It remains to be seen what gains methods like those of this article will yield in such cases.…”

“…Additionally Eqs. (46) and (45) imply that G → 1 as r → 1 and that G → n as r → 0. The striking observation is that for sufficiently small polarizations and a single phase-flip invocation, the correlated state protocol increases the estimation accuracy by a factor of approximately n regardless of the value of the parameter.…”

Implementation of State Transfer Hamiltonians in Spin Chains with Magnetic Resonance Techniques

“…Since the very start of experimental QIP, NMR has played an important role in implementing the first proof-of-principle demonstrations, thanks to the fact that it is mature technology [19][20][21][22]. Indeed, NMR is unique in that simple implementations based on liquid-state NMR have been able to control up to 12 spin qubits [23] with commercially available technology.…”

Quantum simulation of spin ordering with nuclear spins in a solid-state lattice

“…The potential of nuclear magnetic resonance (NMR) techniques 6,7 for simulating an artificial many-body Hamiltonian is theoretically explored. Nuclear spins interact predominantly via a magnetic dipolar interaction, which can be modulated by varying the orientation of the crystal relative to the applied magnetic field, applying NMR pulse sequences, or using different material systems.…”