The Experts below are selected from a list of 3162 Experts worldwide ranked by ideXlab platform

Yaakov S. Weinstein - One of the best experts on this subject based on the ideXlab platform.

  • Encoding an arbitrary state in a [7,1,3] quantum error correction code
    Quantum Information Processing, 2013
    Co-Authors: Sidney D. Buchbinder, Channing L. Huang, Yaakov S. Weinstein
    Abstract:

    We calculate the fidelity with which an arbitrary state can be encoded into a [7, 1, 3] Calderbank-Shor-Steane quantum error correction code in a non-equiprobable Pauli Operator error environment with the goal of determining whether this encoding can be used for practical implementations of quantum computation. The determination of usability is accomplished by applying ideal error correction to the encoded state which demonstrates the correctability of errors that occurred during the encoding process. We also apply single-qubit Clifford gates to the encoded state and determine the accuracy with which these gates can be implemented. Finally, fault tolerant noisy error correction is applied to the encoded states allowing us to compare noisy (realistic) and perfect error correction implementations. We find the encoding to be usable for the states $${|0\rangle, |1\rangle}$$ , and $${|\pm\rangle = |0\rangle\pm|1\rangle}$$ . These results have implications for when non-fault tolerant procedures may be used in practical quantum computation and whether quantum error correction must be applied at every step in a quantum protocol.

  • encoding an arbitrary state in a 7 1 3 quantum error correction code
    arXiv: Quantum Physics, 2011
    Co-Authors: Sidney D. Buchbinder, Channing L. Huang, Yaakov S. Weinstein
    Abstract:

    We calculate the fidelity with which an arbitrary state can be encoded into a [7,1,3] CSS quantum error correction code in a non-equiprobable Pauli Operator error environment with the goal of determining whether this encoding can be used for practical implementations of quantum computation. This determination is accomplished by applying ideal error correction to the encoded state which demonstrates the correctability of errors that occurred during the encoding process. We then apply single-qubit Clifford gates to the encoded state and determine the accuracy with which these gates can be applied. Finally, fault tolerant noisy error correction is applied to the encoded states in the non-equiprobable Pauli Operator error environment allowing us to compare noisy (realistic) and perfect error correction implementations. We note that this maintains the fidelity of the encoded state for certain error-probability values. These results have implications for when non-fault tolerant procedures may be used in practical quantum computation and whether quantum error correction should be applied at every step in a quantum protocol.

  • logical zeros for the seven qubit quantum error correction code
    Proceedings of SPIE, 2011
    Co-Authors: Gerald Gilbert, Yaakov S. Weinstein
    Abstract:

    ABSTRACT Inthisworkwecomparetheaccuracyoftwomethodsusedtocon structa logicalzerostate appropriateforthe [7;1;3] CSSquantum error correction code in a non-equiprobablePauli o perator error environment. The r st method is to apply errorcorrection, via syndrome measurement, on seven physical qu bits all in the state zero. To do the syndrome measurementsin a fault-tolerant fashion requires the construction of fo ur qubit Shor states. These Shor states are also assumed to beconstructedin anon-equiprobablePauliOperatorerrorenv ironmentandit is these thatareusedtoimplementthe syndro memeasurement. The second construction method is to implemen t the [7;1;3] encoding gate sequence, also in the non-equiprobable Pauli Operator error environment. The d elit y of the output states is calculated for each of these methods .With respect to the Shor state construction we n d that the im plementation of (noisy) parity based veric ations does notnecessarily raise the d elity of the resulting Shor state. W e also n d that the second logical zero construction methodoutputs a seven qubit state with a respectfully higher d eli ty than the r st (fault tolerant) method. However, the d eli ty ofthe single qubit of stored informationhas almost equivalen td elity from the two constructionmethods.Keywords: cluster state, entanglement,decoherence,superOperator

Laszlo Erdős - One of the best experts on this subject based on the ideXlab platform.

  • uniform lieb thirring inequality for the three dimensional Pauli Operator with a strong non homogeneous magnetic field
    Annales Henri Poincaré, 2004
    Co-Authors: Laszlo Erdős, Jan Philip Solovej
    Abstract:

    The Pauli Operator describes the energy of a nonrelativistic quantum particle with spin $$ 1 \over 2 $$ in a magnetic field and an external potential. A new Lieb- Thirring type inequality on the sum of the negative eigenvalues is presented. The main feature compared to earlier results is that in the large field regime the present estimate grows with the optimal (first) power of the strength of the magnetic field. As a byproduct of the method, we also obtain an optimal upper bound on the pointwise density of zero energy eigenfunctions of the Dirac Operator. The main technical tools are: (i) a new localization scheme for the square of the resolvent of a general class of second order elliptic Operators; (ii) a geometric construction of a Dirac Operator with a constant magnetic field that approximates the original Dirac Operator in a tubular neighborhood of a fixed field line. The errors may depend on the regularity of the magnetic field but they are uniform in the field strength.

  • Pauli Operator and aharonov casher theorem for measure valued magnetic fields
    Communications in Mathematical Physics, 2002
    Co-Authors: Laszlo Erdős, Vitali Vougalter
    Abstract:

    We define the two dimensional Pauli Operator and identify its core for magnetic fields that are regular Borel measures. The magnetic field is generated by a scalar potential hence we bypass the usual A∈L 2 loc condition on the vector potential, which does not allow to consider such singular fields. We extend the Aharonov–Casher theorem for magnetic fields that are measures with finite total variation and we present a counterexample in case of infinite total variation. One of the key technical tools is a weighted L 2 estimate on a singular integral Operator.

  • semiclassical eigenvalue estimates for the Pauli Operator with strong non homogeneous magnetic fields ii leading order asymptotic estimates
    Communications in Mathematical Physics, 1997
    Co-Authors: Laszlo Erdős, Jan Philip Solovej
    Abstract:

    We give the leading order semiclassical asymptotics for the sum of the negative eigenvalues of the Pauli Operator (in dimension two and three) with a strong non-homogeneous magnetic field. As in [LSY-II] for homogeneous field, this result can be used to prove that the magnetic Thomas-Fermi theory gives the leading order ground state energy of large atoms. We develop a new localization scheme well suited to the anisotropic character of the strong magnetic field. We also use the basic Lieb-Thirring estimate obtained in our companion paper [ES-I].

  • ground state density of the Pauli Operator in the large field limit
    Letters in Mathematical Physics, 1993
    Co-Authors: Laszlo Erdős
    Abstract:

    The ground-state density of the Pauli Operator in the case of a nonconstant magnetic field with constant direction is studied. It is shown that in the large field limit, the naturally rescaled ground-state density function is bounded from above by the megnetic field, and under some additional conditions, the limit density function is equal to the magnetic field. A restatement of this result yields an estimate on the density of complex orthogonal polynomials with respect to a fairly general weight function. We also prove a special case of the paramagnetic inequality.

Mikael Persson Sundqvist - One of the best experts on this subject based on the ideXlab platform.

  • On the semiclassical analysis of the ground state energy of the Dirichlet Pauli Operator III: magnetic fields that change sign
    Letters in Mathematical Physics, 2019
    Co-Authors: Bernard Helffer, Hynek Kovařík, Mikael Persson Sundqvist
    Abstract:

    We consider the semiclassical Dirichlet Pauli Operator in bounded connected domains in the plane. Rather optimal results have been obtained in previous papers by Ekholm–Kovařík–Portmann and Helffer–Sundqvist for the asymptotics of the ground state energy in the semiclassical limit when the magnetic field has constant sign. In this paper, we focus on the case when the magnetic field changes sign. We show, in particular, that the ground state energy of this Pauli Operator will be exponentially small as the semiclassical parameter tends to zero and give lower bounds and upper bounds for this decay rate. Concrete examples of magnetic fields changing sign on the unit disk are discussed. Various natural conjectures are disproved, and this leaves the research of an optimal result in the general case still open.

  • on the semi classical analysis of the groundstate energy of the dirichlet Pauli Operator iii magnetic fields that change sign
    arXiv: Spectral Theory, 2017
    Co-Authors: Bernard Helffer, Hynek Kovarik, Mikael Persson Sundqvist
    Abstract:

    We consider the semi-classical Dirichlet Pauli Operator in bounded connected domains in the plane. Rather optimal results have been obtained in previous papers by Ekholm-Kovařik-Portmann and Helffer-Sundqvist for the asymptotics of the ground state energy in the semi-classical limit when the magnetic field has constant sign. In this paper, we focus on the case when the magnetic field changes sign. We show, in particular, that the ground state energy of this Pauli Operator will be exponentially small as the semi-classical parameter tends to zero and give lower bounds and upper bounds for this decay rate. Concrete examples of magnetic fields changing sign on the unit disc are discussed. Various natural conjectures are disproved and this leaves the research of an optimal result in the general case still open.

  • on the semi classical analysis of the ground state energy of the dirichlet Pauli Operator
    Journal of Mathematical Analysis and Applications, 2017
    Co-Authors: Bernard Helffer, Mikael Persson Sundqvist
    Abstract:

    We complete and improve the results of a recent paper by Ekholm, Kovařik and Portmann in connection with a question of C. Guillarmou about the semiclassical expansion of the lowest eigenvalue of the Pauli Operator with Dirichlet conditions. We exhibit connections with the properties of the torsion function in mechanics, the exit time of a Brownian motion and the analysis of the low eigenvalues of some Witten Laplacian.

  • on the semi classical analysis of the groundstate energy of the dirichlet Pauli Operator in non simply connected domains
    arXiv: Spectral Theory, 2017
    Co-Authors: Bernard Helffer, Mikael Persson Sundqvist
    Abstract:

    We consider the Dirichlet Pauli Operator in bounded connected domains in the plane, with a semi-classical parameter. We show, in particular, that the ground state energy of this Pauli Operator will be exponentially small as the semi-classical parameter tends to zero and estimate this decay rate. This extends our results, discussing the results of a recent paper by Ekholm--Kovařik--Portmann, to include also non-simply connected domains.

  • on the semi classical analysis of the groundstate energy of the dirichlet Pauli Operator
    arXiv: Spectral Theory, 2016
    Co-Authors: Bernard Helffer, Mikael Persson Sundqvist
    Abstract:

    We discuss the results of a recent paper by Ekholm, Kova\v{r}\'ik and Portmann in connection with a question of C. Guillarmou about the semiclassical expansion of the lowest eigenvalue of the Pauli Operator with Dirichlet conditions. We exhibit connections with the properties of the torsion function in mechanics, the exit time of a Brownian motion and the analysis of the low eigenvalues of some Witten Laplacian.

Sidney D. Buchbinder - One of the best experts on this subject based on the ideXlab platform.

  • Encoding an arbitrary state in a [7,1,3] quantum error correction code
    Quantum Information Processing, 2013
    Co-Authors: Sidney D. Buchbinder, Channing L. Huang, Yaakov S. Weinstein
    Abstract:

    We calculate the fidelity with which an arbitrary state can be encoded into a [7, 1, 3] Calderbank-Shor-Steane quantum error correction code in a non-equiprobable Pauli Operator error environment with the goal of determining whether this encoding can be used for practical implementations of quantum computation. The determination of usability is accomplished by applying ideal error correction to the encoded state which demonstrates the correctability of errors that occurred during the encoding process. We also apply single-qubit Clifford gates to the encoded state and determine the accuracy with which these gates can be implemented. Finally, fault tolerant noisy error correction is applied to the encoded states allowing us to compare noisy (realistic) and perfect error correction implementations. We find the encoding to be usable for the states $${|0\rangle, |1\rangle}$$ , and $${|\pm\rangle = |0\rangle\pm|1\rangle}$$ . These results have implications for when non-fault tolerant procedures may be used in practical quantum computation and whether quantum error correction must be applied at every step in a quantum protocol.

  • encoding an arbitrary state in a 7 1 3 quantum error correction code
    arXiv: Quantum Physics, 2011
    Co-Authors: Sidney D. Buchbinder, Channing L. Huang, Yaakov S. Weinstein
    Abstract:

    We calculate the fidelity with which an arbitrary state can be encoded into a [7,1,3] CSS quantum error correction code in a non-equiprobable Pauli Operator error environment with the goal of determining whether this encoding can be used for practical implementations of quantum computation. This determination is accomplished by applying ideal error correction to the encoded state which demonstrates the correctability of errors that occurred during the encoding process. We then apply single-qubit Clifford gates to the encoded state and determine the accuracy with which these gates can be applied. Finally, fault tolerant noisy error correction is applied to the encoded states in the non-equiprobable Pauli Operator error environment allowing us to compare noisy (realistic) and perfect error correction implementations. We note that this maintains the fidelity of the encoded state for certain error-probability values. These results have implications for when non-fault tolerant procedures may be used in practical quantum computation and whether quantum error correction should be applied at every step in a quantum protocol.

Jan Philip Solovej - One of the best experts on this subject based on the ideXlab platform.

  • uniform lieb thirring inequality for the three dimensional Pauli Operator with a strong non homogeneous magnetic field
    Annales Henri Poincaré, 2004
    Co-Authors: Laszlo Erdős, Jan Philip Solovej
    Abstract:

    The Pauli Operator describes the energy of a nonrelativistic quantum particle with spin $$ 1 \over 2 $$ in a magnetic field and an external potential. A new Lieb- Thirring type inequality on the sum of the negative eigenvalues is presented. The main feature compared to earlier results is that in the large field regime the present estimate grows with the optimal (first) power of the strength of the magnetic field. As a byproduct of the method, we also obtain an optimal upper bound on the pointwise density of zero energy eigenfunctions of the Dirac Operator. The main technical tools are: (i) a new localization scheme for the square of the resolvent of a general class of second order elliptic Operators; (ii) a geometric construction of a Dirac Operator with a constant magnetic field that approximates the original Dirac Operator in a tubular neighborhood of a fixed field line. The errors may depend on the regularity of the magnetic field but they are uniform in the field strength.

  • uniform lieb thirring inequality for the three dimensional Pauli Operator with a strong non homogeneous magnetic field
    arXiv: Mathematical Physics, 2003
    Co-Authors: Laszlo Erdos, Jan Philip Solovej
    Abstract:

    The Pauli Operator describes the energy of a nonrelativistic quantum particle with spin 1/2 in a magnetic field and an external potential. A new Lieb-Thirring type inequality on the sum of the negative eigenvalues is presented. The main feature compared to earlier results is that in the large field regime the present estimate grows with the optimal (first) power of the strength of the magnetic field. As a byproduct of the method, we also obtain an optimal upper bound on the pointwise density of zero energy eigenfunctions of the Dirac Operator. The main technical tools are: (i) a new localization scheme for the square of the resolvent of a general class of second order elliptic Operators; (ii) a geometric construction of a Dirac Operator with a constant magnetic field that approximates the original Dirac Operator in a tubular neighborhood of a fixed field line. The errors may depend on the regularity of the magnetic field but they are uniform in the field strength.

  • semiclassical eigenvalue estimates for the Pauli Operator with strong non homogeneous magnetic fields ii leading order asymptotic estimates
    Communications in Mathematical Physics, 1997
    Co-Authors: Laszlo Erdős, Jan Philip Solovej
    Abstract:

    We give the leading order semiclassical asymptotics for the sum of the negative eigenvalues of the Pauli Operator (in dimension two and three) with a strong non-homogeneous magnetic field. As in [LSY-II] for homogeneous field, this result can be used to prove that the magnetic Thomas-Fermi theory gives the leading order ground state energy of large atoms. We develop a new localization scheme well suited to the anisotropic character of the strong magnetic field. We also use the basic Lieb-Thirring estimate obtained in our companion paper [ES-I].