The problem of dipole-dipole decoherence of nuclear spins is considered for strongly entangled spin cluster. Our results show that its dynamics can be described as the decoherence due to interaction with a composite bath consisting of fully correlated and uncorrelated parts. The correlated term causes the slower decay of coherence at larger times. The decoherence rate scales up as a square root of the number of spins giving the linear scaling of the resulting error. Our theory is consistent with recent experiment reported in decoherence of correlated spin clusters.The problem of dipole-dipole decoherence of nuclear spins is considered for strongly entangled spin cluster. Our results show that its dynamics can be described as the decoherence due to interaction with a composite bath consisting of fully correlated and uncorrelated parts. The correlated term causes the slower decay of coherence at larger times. The decoherence rate scales up as a square root of the number of spins giving the linear scaling of the resulting error. Our theory is consistent with recent experiment reported in decoherence of correlated spin clusters.

Feb 27, 200516 citations

Robustness of multiqubit entanglement

Leonid Evgenevich Fedichkin, Arkady Fedorov, Vladimir Privman A

We survey results on the decay of multiqubit entanglement due to internal interactions between qubits. Dipole-dipole interaction induces decoherence of strongly entangled nuclear spins. The dynamics of spin clusters can be described as quantum decoherence due to an effective composite bath consisting of fully correlated and uncorrelated parts. The rate of decoherence scales up as a square root of the number of entangled spins, resulting in linear scaling of a measure of quantum noise. Our theory is consistent with a recent experiment.We survey results on the decay of multiqubit entanglement due to internal interactions between qubits. Dipole-dipole interaction induces decoherence of strongly entangled nuclear spins. The dynamics of spin clusters can be described as quantum decoherence due to an effective composite bath consisting of fully correlated and uncorrelated parts. The rate of decoherence scales up as a square root of the number of entangled spins, resulting in linear scaling of a measure of quantum noise. Our theory is consistent with a recent experiment.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEMay 5, 20063 citations

Quantum many-body theory of qubit decoherence in a finite-size spin bath

Wen Yang, Ren‐Bao Liu

Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. We develop a cluster-correlation expansion (CCE) theory for the spin-bath dynamics relevant to the qubit decoherence problem. A cluster-correlation term is recursively defined as the evolution of a group of bath spins divided by the cluster correlations of all the subgroups. This correlation accounts for the authentic (nonfactorizable) collective excitations within a given group. The bath propagator is the product of all possible cluster correlation terms. For a finite-time evolution as in the qubit decoherence problem, a convergent result can be obtained by truncating the expansion up to a certain cluster size. The two-spin cluster truncation of the CCE corresponds to the pair-correlation approximation developed previously [W. Yao et al., Phys. Rev. B 74, 195301 (2006)]. In terms of the standard linked cluster expansion, a cluster-correlation term is the infinite summation of all the connected diagrams with all and only the spins in the group flip-flopped, and thus the expansion is exact whenever convergence occurs. When the individual contribution of each higher-order correlation term to the decoherence is small (while all the terms combined in product could still contribute substantially), as the usual case for relatively large baths, where the decoherence could complete well within the bath spin flip-flop time, the CCE coincides with the cluster expansion [W. M. Witzel and S. Das Sarma, Phys. Rev. B 74, 035322 (2006)]. For small baths, however, the qubit decoherence may not complete within the bath spin flip-flop time scale and thus individual higher-order cluster correlations could become significant. In such cases, only the CCE converges to the exact coherent dynamics of multispin clusters. We check the accuracy of the CCE in an exactly solvable spin-chain model.Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. We develop a cluster-correlation expansion (CCE) theory for the spin-bath dynamics relevant to the qubit decoherence problem. A cluster-correlation term is recursively defined as the evolution of a group of bath spins divided by the cluster correlations of all the subgroups. This correlation accounts for the authentic (nonfactorizable) collective excitations within a given group. The bath propagator is the product of all possible cluster correlation terms. For a finite-time evolution as in the qubit decoherence problem, a convergent result can be obtained by truncating the expansion up to a certain cluster size. The two-spin cluster truncation of the CCE corresponds to the pair-correlation approximation developed previously [W. Yao et al., Phys. Rev. B 74, 195301 (2006)]. In terms of the standard linked cluster expansion, a cluster-correlation term is the infinite summation of all the connected diagrams with all and only the spins in the group flip-flopped, and thus the expansion is exact whenever convergence occurs. When the individual contribution of each higher-order correlation term to the decoherence is small (while all the terms combined in product could still contribute substantially), as the usual case for relatively large baths, where the decoherence could complete well within the bath spin flip-flop time, the CCE coincides with the cluster expansion [W. M. Witzel and S. Das Sarma, Phys. Rev. B 74, 035322 (2006)]. For small baths, however, the qubit decoherence may not complete within the bath spin flip-flop time scale and thus individual higher-order cluster correlations could become significant. In such cases, only the CCE converges to the exact coherent dynamics of multispin clusters. We check the accuracy of the CCE in an exactly solvable spin-chain model.

arXiv:0806.0098Physical Review BAug 21, 2008209 citations

Decoherence of two entangled spin qubits coupled to an interacting sparse nuclear spin bath: Application to nitrogen vacancy centers

Damian Kwiatkowski, Łukasz Cywiński

We consider pure dephasing of Bell states of electron spin qubits interacting with a sparse bath of nuclear spins. Using the newly developed two-qubit generalization of cluster-correlation expansion method, we calculate the spin-echo decay of $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ and $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$ states for various interqubit distances. Comparing the results with calculations in which dephasing of each qubit is treated independently, we identify signatures of influence of common part of the bath on the two qubits. At large interqubit distances, this common part consists of many nuclei weakly coupled to both qubits, so that decoherence caused by it can be modeled by considering multiple uncorrelated sources of noise (clusters of nuclei), each of them weakly affecting the qubits. Consequently, the resulting genuinely two-qubit contribution to decoherence can be described as being caused by classical Gaussian noise. On the other hand, for small interqubit distances the common part of the environment contains clusters of spins that are strongly coupled to both qubits, and their contribution to two-qubit dephasing has visibly non-Gaussian character. We show that one can easily obtain information about non-Gaussianity of environmental noise affecting the qubits from the comparison of dephasing of $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ and $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$ Bell states. Numerical results are obtained for two nitrogen vacancy centers interacting with a bath of $^{13}\mathrm{C}$ nuclei of natural concentration, for which we obtain that Gaussian description of a correlated part of environmental noise starts to hold for centers separated by about 3 nm.We consider pure dephasing of Bell states of electron spin qubits interacting with a sparse bath of nuclear spins. Using the newly developed two-qubit generalization of cluster-correlation expansion method, we calculate the spin-echo decay of $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ and $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$ states for various interqubit distances. Comparing the results with calculations in which dephasing of each qubit is treated independently, we identify signatures of influence of common part of the bath on the two qubits. At large interqubit distances, this common part consists of many nuclei weakly coupled to both qubits, so that decoherence caused by it can be modeled by considering multiple uncorrelated sources of noise (clusters of nuclei), each of them weakly affecting the qubits. Consequently, the resulting genuinely two-qubit contribution to decoherence can be described as being caused by classical Gaussian noise. On the other hand, for small interqubit distances the common part of the environment contains clusters of spins that are strongly coupled to both qubits, and their contribution to two-qubit dephasing has visibly non-Gaussian character. We show that one can easily obtain information about non-Gaussianity of environmental noise affecting the qubits from the comparison of dephasing of $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ and $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$ Bell states. Numerical results are obtained for two nitrogen vacancy centers interacting with a bath of $^{13}\mathrm{C}$ nuclei of natural concentration, for which we obtain that Gaussian description of a correlated part of environmental noise starts to hold for centers separated by about 3 nm.

arXiv:1806.06845Physical review. B./Physical review. BOct 5, 201832 citations

Multiple Quantum Coherence and Entanglement Dynamics in Spin Clusters

G. B. Furman, V. Meerovich, Vladimir Sokolovsky

With the purpose to reveal consistency between multiple quantum (MQ) coherences and entanglement, we investigate numerically the dynamics of these phenomena in one-dimensional linear chains and ring of nuclear spins 1/2 coupled by dipole dipole interactions. As opposed to the calculation of the MQ coherence intensity based on the density matrix describing the spin system as a whole, we consider the "differentiated" intensity related only to the chosen spin pair based on the reduced density matrix. It is shown that the entanglement and the MQ coherence have similar dynamics only for nearest neighbors while we did not obtained any consistency for remote spins.With the purpose to reveal consistency between multiple quantum (MQ) coherences and entanglement, we investigate numerically the dynamics of these phenomena in one-dimensional linear chains and ring of nuclear spins 1/2 coupled by dipole dipole interactions. As opposed to the calculation of the MQ coherence intensity based on the density matrix describing the spin system as a whole, we consider the "differentiated" intensity related only to the chosen spin pair based on the reduced density matrix. It is shown that the entanglement and the MQ coherence have similar dynamics only for nearest neighbors while we did not obtained any consistency for remote spins.

arXiv:0905.3826May 23, 20090 citations

Scaling of Decoherence in Wide NMR Quantum Registers

Hans Georg Krojanski, Dieter Suter

Among the most important parameters for the usefulness of quantum computers are the size of the quantum register and the decoherence time for the quantum information. The decoherence time is expected to get shorter with the number of correlated qubits, but experimental data are only available for small numbers of qubits. Solid-state nuclear magnetic resonance allows one to correlate large numbers of qubits (several hundred) and measure their decoherence rates. We use a modified magnetic dipole-dipole interaction to correlate the proton spins in a solid sample and observe the decay of the resulting highly correlated states. By systematically varying the number of correlated spins, we measure the increase of the decoherence rate with the size of the quantum register.Among the most important parameters for the usefulness of quantum computers are the size of the quantum register and the decoherence time for the quantum information. The decoherence time is expected to get shorter with the number of correlated qubits, but experimental data are only available for small numbers of qubits. Solid-state nuclear magnetic resonance allows one to correlate large numbers of qubits (several hundred) and measure their decoherence rates. We use a modified magnetic dipole-dipole interaction to correlate the proton spins in a solid sample and observe the decay of the resulting highly correlated states. By systematically varying the number of correlated spins, we measure the increase of the decoherence rate with the size of the quantum register.

Physical Review LettersAug 24, 2004135 citations

^{13}\mathrm{C}

nuclei of natural concentration, for which we obtain that Gaussian description of a correlated part of environmental noise starts to hold for centers separated by about 3 nm.