In order to investigate the effects of nonmagnetic impurities in strongly correlated systems, quantum Monte Carlo (QMC) simulations have been carried out for the doped two-dimensional Hubbard model with one nonmagnetic impurity. Using a bare impurity potential which is onsite and attractive, magnetic and single-particle properties have been calculated. The QMC results show that giant oscillations develop in the Knight shift response around the impurity site due to the short-range antiferromagnetic correlations. These results are useful for interpreting the NMR data on Li- and Zn-substituted layered cuprates.In order to investigate the effects of nonmagnetic impurities in strongly correlated systems, quantum Monte Carlo (QMC) simulations have been carried out for the doped two-dimensional Hubbard model with one nonmagnetic impurity. Using a bare impurity potential which is onsite and attractive, magnetic and single-particle properties have been calculated. The QMC results show that giant oscillations develop in the Knight shift response around the impurity site due to the short-range antiferromagnetic correlations. These results are useful for interpreting the NMR data on Li- and Zn-substituted layered cuprates.

arXiv:cond-mat/0308074Physical review. B, Condensed matterDec 9, 20035 citations

Quantum control with NMR methods: Application to quantum simulations

C. Negrevergne

Jan 1, 20020 citations

NMR simulation of Quantum Pigeonhole Effect

V. S. Anjusha, Swathi S. Hegde, T. S. Mahesh

Quantum simulators based on nuclear spin-systems controlled by NMR techniques have been used for studying various quantum phenomena. In this work, using a four-qubit NMR quantum simulator, we investigate the recently postulated quantum pigeon-hole effect. In mathematics, the pigeonhole effect is described by a set of three objects being allocated with only two containers. Classically, one would expect at least one container to accommodate more than one object. However, recently it was predicted that there exist quantum scenarios wherein three quantum particles appear to reside in two containers in such a way that no two particles can be simultaneously assigned with a single container. In our experiments, quantum pigeons are emulated by three nuclear qubits whose states are probed jointly and noninvasively by an ancillary spin. The qubit-states $\{\ket{0}$ , $\ket{1}\}$ emulate the two containers available for each of the qubits. The experimental results are in good agreement with quantum theoretical predictions.Quantum simulators based on nuclear spin-systems controlled by NMR techniques have been used for studying various quantum phenomena. In this work, using a four-qubit NMR quantum simulator, we investigate the recently postulated quantum pigeon-hole effect. In mathematics, the pigeonhole effect is described by a set of three objects being allocated with only two containers. Classically, one would expect at least one container to accommodate more than one object. However, recently it was predicted that there exist quantum scenarios wherein three quantum particles appear to reside in two containers in such a way that no two particles can be simultaneously assigned with a single container. In our experiments, quantum pigeons are emulated by three nuclear qubits whose states are probed jointly and noninvasively by an ancillary spin. The qubit-states $\{\ket{0}$, $\ket{1}\}$ emulate the two containers available for each of the qubits. The experimental results are in good agreement with quantum theoretical predictions.

arXiv:1509.03963Sep 14, 20150 citations

The effects of shot noise on the quantum computation of NMR spectra

Sebastian Walch, Keith R. Fratus, Jan-Michael Reiner +1 more

Recent advances in the field of quantum computing hardware motivate the search for applications which demonstrate so-called quantum advantage. One promising use case that has been identified is the simulation of quantum many-body systems. The computational resources required for performing such a simulation on a classical computer generally grow exponentially with the size of the system being modeled, which is ultimately due to the exponential growth of the Hilbert space in which the dynamics of such a system take place. While digital quantum computers natively evolve quantum states directly in such a Hilbert space, thus naively avoiding this problem, the result of such a computation is typically not obtained as a deterministic output. Rather, it requires projective measurements which are fundamentally affected by shot noise. Any desired expectation values must therefore be reconstructed from repeated measurements, making the number of those measurements a relevant computational resource, and thus an important consideration for any potential claims of quantum advantage. In this work, we study how this resource scales with system size (a scaling which itself depends on the desired accuracy of the final result), using the simulation of nuclear magnetic resonance (NMR) spectra as a test case. We study this scaling for both real-world molecules, as well as a class of model NMR Hamiltonians which allow for efficient large-scale simulations with one-dimensional, two-dimensional, and all-to-all interactions. We find that the required resources increase only weakly with molecular size, far below the exponential growth of the underlying Hilbert space. This result suggests that shot noise should not pose a fundamental barrier to achieving quantum advantage in the simulation of NMR systems, and perhaps for many-body systems more broadly.Recent advances in the field of quantum computing hardware motivate the search for applications which demonstrate so-called quantum advantage. One promising use case that has been identified is the simulation of quantum many-body systems. The computational resources required for performing such a simulation on a classical computer generally grow exponentially with the size of the system being modeled, which is ultimately due to the exponential growth of the Hilbert space in which the dynamics of such a system take place. While digital quantum computers natively evolve quantum states directly in such a Hilbert space, thus naively avoiding this problem, the result of such a computation is typically not obtained as a deterministic output. Rather, it requires projective measurements which are fundamentally affected by shot noise. Any desired expectation values must therefore be reconstructed from repeated measurements, making the number of those measurements a relevant computational resource, and thus an important consideration for any potential claims of quantum advantage. In this work, we study how this resource scales with system size (a scaling which itself depends on the desired accuracy of the final result), using the simulation of nuclear magnetic resonance (NMR) spectra as a test case. We study this scaling for both real-world molecules, as well as a class of model NMR Hamiltonians which allow for efficient large-scale simulations with one-dimensional, two-dimensional, and all-to-all interactions. We find that the required resources increase only weakly with molecular size, far below the exponential growth of the underlying Hilbert space. This result suggests that shot noise should not pose a fundamental barrier to achieving quantum advantage in the simulation of NMR systems, and perhaps for many-body systems more broadly.

quant-pharXiv:2609.20406Sep 18, 20260 citations

Quantum Simulation of Quantum Channels in NMR

Xin Tao, Shijie Wei, Julen Simon Pedernales +2 more

Apr 19, 20170 citations

\{\ket{0}

\ket{1}\}

emulate the two containers available for each of the qubits. The experimental results are in good agreement with quantum theoretical predictions.