The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Hartmut Neven - One of the best experts on this subject based on the ideXlab platform.
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Path-integral quantum Monte Carlo simulation with Open-Boundary conditions
Physical Review A, 2017Co-Authors: Zhang Jiang, Vadim Smelyanskiy, Sergio Boixo, Hartmut NevenAbstract:The tunneling decay event of a metastable state in a fully connected quantum spin model can be simulated efficiently by path integral quantum Monte Carlo (QMC) [Isakov $et~al.$, Phys. Rev. Lett. ${\bf 117}$, 180402 (2016).]. This is because the exponential scaling with the number of spins of the thermally-assisted quantum tunneling rate and the Kramers escape rate of QMC are identical [Jiang $et~al.$, Phys. Rev. A ${\bf 95}$, 012322 (2017).], a result of a dominant instantonic tunneling path. In Ref. [1], it was also conjectured that the escape rate in Open-Boundary QMC is quadratically larger than that of conventional periodic-Boundary QMC, therefore, Open-Boundary QMC might be used as a powerful tool to solve combinatorial optimization problems. The intuition behind this conjecture is that the action of the instanton in Open-Boundary QMC is a half of that in periodic-Boundary QMC. Here, we show that this simple intuition---although very useful in interpreting some numerical results---deviates from the actual situation in several ways. Using a fully connected quantum spin model, we derive a set of conditions on the positions and momenta of the endpoints of the instanton, which remove the extra degrees of freedom due to Open boundaries. In comparison, the half-instanton conjecture incorrectly sets the momenta at the endpoints to zero. We also found that the instantons in Open-Boundary QMC correspond to quantum tunneling events in the symmetric subspace (maximum total angular momentum) at all temperatures, whereas the instantons in periodic-Boundary QMC typically lie in subspaces with lower total angular momenta at finite temperatures. This leads to a lesser than quadratic speedup at finite temperatures. We also outline the generalization of the instantonic tunneling method to many-qubit systems without permutation symmetry using spin-coherent-state path integrals.
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Path-Integral Quantum Monte Carlo with Open-Boundary Conditions
arXiv: Quantum Physics, 2017Co-Authors: Zhang Jiang, Vadim Smelyanskiy, Sergio Boixo, Hartmut NevenAbstract:The tunneling decay event of a metastable state in a fully connected quantum spin model can be simulated efficiently by path integral quantum Monte Carlo (QMC) (Phys. Rev. Lett. ${\bf 117}$, 180402 [1]). This is because the exponential scaling with the number of spins of the thermally-assisted quantum tunneling rate and the Kramers escape rate of QMC are identical (Phys. Rev. A ${\bf 95}$, 012322 [2]), a result of a dominant instantonic tunneling path. In Ref. [1], it was also conjectured that the escape rate in Open-Boundary QMC is quadratically larger than that of conventional periodic-Boundary QMC, therefore, Open-Boundary QMC might be used as a powerful tool to solve combinatorial optimization problems. The intuition behind this conjecture is that the action of the instanton in Open-Boundary QMC is a half of that in periodic-Boundary QMC. Here, we show that this simple intuition---although very useful in interpreting some numerical results---deviates from the actual situation in several ways. Using a fully connected quantum spin model, we derive a set of conditions on the positions and momenta of the endpoints of the instanton, which remove the extra degrees of freedom due to Open boundaries. In comparison, the half-instanton conjecture incorrectly sets the momenta at the endpoints to zero. We also found that the instantons in Open-Boundary QMC correspond to quantum tunneling events in the symmetric subspace (maximum total angular momentum) at all temperatures, whereas the instantons in periodic-Boundary QMC typically lie in subspaces with lower total angular momenta at finite temperatures. This leads to a lesser than quadratic speedup at finite temperatures. We also outline the generalization of the instantonic tunneling method to many-qubit systems without permutation symmetry using spin-coherent-state path integrals.
Jie She - One of the best experts on this subject based on the ideXlab platform.
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a pressure correction scheme for generalized form of energy stable Open Boundary conditions for incompressible flows
Journal of Computational Physics, 2015Co-Authors: Suchua Dong, Jie SheAbstract:We present a generalized form of Open Boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving Open or outflow boundaries. The generalized form represents a family of Open Boundary conditions, which all ensure the energy stability of the system, even in situations where strong vortices or backflows occur at the Open/outflow boundaries. Our numerical algorithm for treating these Open Boundary conditions is based on a rotational pressure correction-type strategy, with a formulation suitable for C 0 spectral-element spatial discretizations. We have introduced a discrete equation and associated Boundary conditions for an auxiliary variable. The algorithm contains constructions that prevent a numerical locking at the Open/outflow Boundary. In addition, we have developed a scheme with a provable unconditional stability for a sub-class of the Open Boundary conditions. Extensive numerical experiments have been presented to demonstrate the performance of our method for several flow problems involving Open/outflow boundaries. We compare simulation results with the experimental data to demonstrate the accuracy of our algorithm. Long-time simulations have been performed for a range of Reynolds numbers at which strong vortices or backflows occur at the Open/outflow boundaries. We show that the Open Boundary conditions and the numerical algorithm developed herein produce stable simulations in such situations.
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error analysis of pressure correction schemes for the time dependent stokes equations with Open Boundary conditions
SIAM Journal on Numerical Analysis, 2005Co-Authors: Jean-luc Guermond, Peter D. Minev, Jie SheAbstract:The incompressible Stokes equations with prescribed normal stress (Open) Boundary conditions on part of the Boundary are considered. It is shown that the standard pressure-correction method is not suitable for approximating the Stokes equations with Open Boundary conditions, whereas the rotational pressure-correction method yields reasonably good error estimates. These results appear to be the first ever published for splitting schemes with Open Boundary conditions. Numerical results in agreement with the error estimates are presented.
Suchuan Dong - One of the best experts on this subject based on the ideXlab platform.
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on a simple and effective thermal Open Boundary condition for convective heat transfer problems
International Journal of Heat and Mass Transfer, 2020Co-Authors: Suchuan DongAbstract:Abstract We present an effective thermal Open Boundary condition for convective heat transfer problems on domains involving outflow/Open boundaries. This Boundary condition is energy-stable, and it ensures that the contribution of the Open Boundary will not cause an “energy-like” temperature functional to increase over time, irrespective of the state of flow on the Open Boundary. It is effective in coping with thermal Open boundaries even in flow regimes where strong vortices or backflows are prevalent on such boundaries, and it is straightforward to implement. Extensive numerical simulations are presented to demonstrate the stability and effectiveness of our method for heat transfer problems with strong vortices and backflows occurring on the Open boundaries. Simulation results are compared with previous works to demonstrate the accuracy of the presented method.
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On a Simple and Effective Thermal Open Boundary Condition for Convective Heat Transfer Problems
arXiv: Fluid Dynamics, 2019Co-Authors: Xiaoyu Liu, Zhi Xie, Suchuan DongAbstract:We present an effective thermal Open Boundary condition for convective heat transfer problems on domains involving outflow/Open boundaries. This Boundary condition is energy-stable, and it ensures that the contribution of the Open Boundary will not cause an ``energy-like'' temperature functional to increase over time, irrespective of the state of flow on the Open Boundary. It is effective in coping with thermal Open boundaries even in flow regimes where strong vortices or backflows are prevalent on such boundaries, and it is straightforward to implement. Extensive numerical simulations are presented to demonstrate the stability and effectiveness of our method for heat transfer problems with strong vortices and backflows occurring on the Open boundaries. Simulation results are compared with previous works to demonstrate the accuracy of the presented method.
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energy stable Boundary conditions based on a quadratic form applications to outflow Open Boundary problems in incompressible flows
Journal of Computational Physics, 2019Co-Authors: Zhiguo Yang, Suchuan DongAbstract:Abstract We present a set of new energy-stable Open Boundary conditions for tackling the backflow instability in simulations of outflow/Open Boundary problems for incompressible flows. These Boundary conditions are developed through two steps: (i) devise a general form of Boundary conditions that ensure the energy stability by re-formulating the Boundary contribution into a quadratic form in terms of a symmetric matrix and computing an associated eigen problem; and (ii) require that, upon imposing the Boundary conditions from the previous step, the scale of Boundary dissipation should match a physical scale. These Open Boundary conditions can be re-cast into the form of a traction-type condition, and therefore they can be implemented numerically using the splitting-type algorithm from a previous work. The current Boundary conditions can effectively overcome the backflow instability typically encountered at moderate and high Reynolds numbers. In general they give rise to a non-zero traction on the entire Open Boundary, unlike previous related methods which only take effect in the backflow regions of the Boundary. Extensive numerical experiments in two and three dimensions are presented to test the effectiveness and performance of the presented methods, and simulation results are compared with the available experimental data to demonstrate their accuracy.
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A convective-like energy-stable Open Boundary condition for simulations of incompressible flows
Journal of Computational Physics, 2015Co-Authors: Suchuan DongAbstract:We present a new energy-stable Open Boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/Open boundaries. This Open Boundary condition ensures the energy stability of the system, even when strong vortices or backflows occur at the outflow Boundary. Under certain situations it can be reduced to a form that can be analogized to the usual convective Boundary condition. One prominent feature of this Boundary condition is that it provides a control over the velocity on the outflow/Open Boundary. This is not available with the other energy-stable Open Boundary conditions from previous works. Our numerical algorithm treats the proposed Open Boundary condition based on a rotational velocity-correction type strategy. It gives rise to a Robin-type condition for the discrete pressure and a Robin-type condition for the discrete velocity on the outflow/Open Boundary, respectively at the pressure and the velocity sub-steps. We present extensive numerical experiments on a canonical wake flow and a jet flow in Open domain to test the effectiveness and performance of the method developed herein. Simulation results are compared with the experimental data as well as with other previous simulations to demonstrate the accuracy of the current method. Long-time simulations are performed for a range of Reynolds numbers, at which strong vortices and backflows occur at the outflow/Open boundaries. The results show that our method is effective in overcoming the backflow instability, and that it allows for the vortices to discharge from the domain in a fairly natural fashion even at high Reynolds numbers.
Zhang Jiang - One of the best experts on this subject based on the ideXlab platform.
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Path-integral quantum Monte Carlo simulation with Open-Boundary conditions
Physical Review A, 2017Co-Authors: Zhang Jiang, Vadim Smelyanskiy, Sergio Boixo, Hartmut NevenAbstract:The tunneling decay event of a metastable state in a fully connected quantum spin model can be simulated efficiently by path integral quantum Monte Carlo (QMC) [Isakov $et~al.$, Phys. Rev. Lett. ${\bf 117}$, 180402 (2016).]. This is because the exponential scaling with the number of spins of the thermally-assisted quantum tunneling rate and the Kramers escape rate of QMC are identical [Jiang $et~al.$, Phys. Rev. A ${\bf 95}$, 012322 (2017).], a result of a dominant instantonic tunneling path. In Ref. [1], it was also conjectured that the escape rate in Open-Boundary QMC is quadratically larger than that of conventional periodic-Boundary QMC, therefore, Open-Boundary QMC might be used as a powerful tool to solve combinatorial optimization problems. The intuition behind this conjecture is that the action of the instanton in Open-Boundary QMC is a half of that in periodic-Boundary QMC. Here, we show that this simple intuition---although very useful in interpreting some numerical results---deviates from the actual situation in several ways. Using a fully connected quantum spin model, we derive a set of conditions on the positions and momenta of the endpoints of the instanton, which remove the extra degrees of freedom due to Open boundaries. In comparison, the half-instanton conjecture incorrectly sets the momenta at the endpoints to zero. We also found that the instantons in Open-Boundary QMC correspond to quantum tunneling events in the symmetric subspace (maximum total angular momentum) at all temperatures, whereas the instantons in periodic-Boundary QMC typically lie in subspaces with lower total angular momenta at finite temperatures. This leads to a lesser than quadratic speedup at finite temperatures. We also outline the generalization of the instantonic tunneling method to many-qubit systems without permutation symmetry using spin-coherent-state path integrals.
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Path-Integral Quantum Monte Carlo with Open-Boundary Conditions
arXiv: Quantum Physics, 2017Co-Authors: Zhang Jiang, Vadim Smelyanskiy, Sergio Boixo, Hartmut NevenAbstract:The tunneling decay event of a metastable state in a fully connected quantum spin model can be simulated efficiently by path integral quantum Monte Carlo (QMC) (Phys. Rev. Lett. ${\bf 117}$, 180402 [1]). This is because the exponential scaling with the number of spins of the thermally-assisted quantum tunneling rate and the Kramers escape rate of QMC are identical (Phys. Rev. A ${\bf 95}$, 012322 [2]), a result of a dominant instantonic tunneling path. In Ref. [1], it was also conjectured that the escape rate in Open-Boundary QMC is quadratically larger than that of conventional periodic-Boundary QMC, therefore, Open-Boundary QMC might be used as a powerful tool to solve combinatorial optimization problems. The intuition behind this conjecture is that the action of the instanton in Open-Boundary QMC is a half of that in periodic-Boundary QMC. Here, we show that this simple intuition---although very useful in interpreting some numerical results---deviates from the actual situation in several ways. Using a fully connected quantum spin model, we derive a set of conditions on the positions and momenta of the endpoints of the instanton, which remove the extra degrees of freedom due to Open boundaries. In comparison, the half-instanton conjecture incorrectly sets the momenta at the endpoints to zero. We also found that the instantons in Open-Boundary QMC correspond to quantum tunneling events in the symmetric subspace (maximum total angular momentum) at all temperatures, whereas the instantons in periodic-Boundary QMC typically lie in subspaces with lower total angular momenta at finite temperatures. This leads to a lesser than quadratic speedup at finite temperatures. We also outline the generalization of the instantonic tunneling method to many-qubit systems without permutation symmetry using spin-coherent-state path integrals.
Sergio Boixo - One of the best experts on this subject based on the ideXlab platform.
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Path-integral quantum Monte Carlo simulation with Open-Boundary conditions
Physical Review A, 2017Co-Authors: Zhang Jiang, Vadim Smelyanskiy, Sergio Boixo, Hartmut NevenAbstract:The tunneling decay event of a metastable state in a fully connected quantum spin model can be simulated efficiently by path integral quantum Monte Carlo (QMC) [Isakov $et~al.$, Phys. Rev. Lett. ${\bf 117}$, 180402 (2016).]. This is because the exponential scaling with the number of spins of the thermally-assisted quantum tunneling rate and the Kramers escape rate of QMC are identical [Jiang $et~al.$, Phys. Rev. A ${\bf 95}$, 012322 (2017).], a result of a dominant instantonic tunneling path. In Ref. [1], it was also conjectured that the escape rate in Open-Boundary QMC is quadratically larger than that of conventional periodic-Boundary QMC, therefore, Open-Boundary QMC might be used as a powerful tool to solve combinatorial optimization problems. The intuition behind this conjecture is that the action of the instanton in Open-Boundary QMC is a half of that in periodic-Boundary QMC. Here, we show that this simple intuition---although very useful in interpreting some numerical results---deviates from the actual situation in several ways. Using a fully connected quantum spin model, we derive a set of conditions on the positions and momenta of the endpoints of the instanton, which remove the extra degrees of freedom due to Open boundaries. In comparison, the half-instanton conjecture incorrectly sets the momenta at the endpoints to zero. We also found that the instantons in Open-Boundary QMC correspond to quantum tunneling events in the symmetric subspace (maximum total angular momentum) at all temperatures, whereas the instantons in periodic-Boundary QMC typically lie in subspaces with lower total angular momenta at finite temperatures. This leads to a lesser than quadratic speedup at finite temperatures. We also outline the generalization of the instantonic tunneling method to many-qubit systems without permutation symmetry using spin-coherent-state path integrals.
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Path-Integral Quantum Monte Carlo with Open-Boundary Conditions
arXiv: Quantum Physics, 2017Co-Authors: Zhang Jiang, Vadim Smelyanskiy, Sergio Boixo, Hartmut NevenAbstract:The tunneling decay event of a metastable state in a fully connected quantum spin model can be simulated efficiently by path integral quantum Monte Carlo (QMC) (Phys. Rev. Lett. ${\bf 117}$, 180402 [1]). This is because the exponential scaling with the number of spins of the thermally-assisted quantum tunneling rate and the Kramers escape rate of QMC are identical (Phys. Rev. A ${\bf 95}$, 012322 [2]), a result of a dominant instantonic tunneling path. In Ref. [1], it was also conjectured that the escape rate in Open-Boundary QMC is quadratically larger than that of conventional periodic-Boundary QMC, therefore, Open-Boundary QMC might be used as a powerful tool to solve combinatorial optimization problems. The intuition behind this conjecture is that the action of the instanton in Open-Boundary QMC is a half of that in periodic-Boundary QMC. Here, we show that this simple intuition---although very useful in interpreting some numerical results---deviates from the actual situation in several ways. Using a fully connected quantum spin model, we derive a set of conditions on the positions and momenta of the endpoints of the instanton, which remove the extra degrees of freedom due to Open boundaries. In comparison, the half-instanton conjecture incorrectly sets the momenta at the endpoints to zero. We also found that the instantons in Open-Boundary QMC correspond to quantum tunneling events in the symmetric subspace (maximum total angular momentum) at all temperatures, whereas the instantons in periodic-Boundary QMC typically lie in subspaces with lower total angular momenta at finite temperatures. This leads to a lesser than quadratic speedup at finite temperatures. We also outline the generalization of the instantonic tunneling method to many-qubit systems without permutation symmetry using spin-coherent-state path integrals.
