Vid Stojevic - Academia.edu (original) (raw)
Papers by Vid Stojevic
npj Quantum Information
Tensor networks permit computational and entanglement resources to be concentrated in interesting... more Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translates infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution of arbitrary one-dimensional systems. The illustrative simulated output of these codes for achievable circuit sizes is given.
Physical Review B, 2015
In this paper we apply the formalism of translation invariant (continuous) matrix product states ... more In this paper we apply the formalism of translation invariant (continuous) matrix product states in the thermodynamic limit to (1 + 1) dimensional critical models. Finite bond dimension bounds the entanglement entropy and introduces an effective finite correlation length, so that the state is perturbed away from criticality. The assumption that the scaling hypothesis holds for this kind of perturbation is known in the literature as finite entanglement scaling. We provide further evidence for the validity of finite entanglement scaling and based on this formulate a scaling algorithm to estimate the central charge and critical exponents of the conformally invariant field theories describing the critical models under investigation. The algorithm is applied to three exemplary models; the cMPS version to the non-relativistic Lieb-Liniger model and the relativistic massless boson, and MPS version to the one-dimensional quantum Ising model at the critical point. Another new aspect to our approach is that we directly use the (c)MPS induced correlation length rather than the bond dimension as scaling parameter. This choice is motivated by several theoretical arguments as well as by the remarkable accuracy of our results. CONTENTS I. Introduction 1 II. Scaling hypothesis 2 III. Recipe for Finite Entanglement Scaling 4 A. Critical Exponents 4 B. Central Charge 6 IV. Exemplary Models 6 A. Lieb-Liniger Model 7 B. Massless Relativistic Boson 8 C. Quantum Ising Model 9 V. Conclusions 10 Acknowledgments 11 A. Review of Continuous Matrix Product States 11 B. Details of the Lieb-Liniger Field-Field Exponent Calculation 12 C. Central charge estimates from D-scaling 14 References 15
We introduce a variational method for calculating dispersion relations of translation invariant (... more We introduce a variational method for calculating dispersion relations of translation invariant (1+1)-dimensional quantum field theories. The method is based on continuous matrix product states and can be implemented efficiently. We study the critical Lieb-Liniger model as a benchmark and excelent agreement with the exact solution is found. Additionally, we observe solitonic signatures of Lieb's Type II excitation. In addition, a non-integrable model is introduced where a U(1)-symmetry breaking term is added to the Lieb-Liniger Hamiltonian. For this model we find evidence of a non-trivial bound-state excitation in the dispersion relation.
We study a generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) formulation of t... more We study a generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) formulation of the A- and B-models which involves a doubling of coordinates, and can be understood as a complexification of the Poisson sigma\sigmasigma-model underlying these. In the flat space limit the construction contains models obtained by twisting an N=2 supersymmetric sigma\sigmasigma-model on Hull's doubled geometry. The curved space generalization involves a product of two diffeomorphic Calabi-Yau manifolds, and the O(d,d)O(d,d)O(d,d) metric can be understood as a complexification of the CY metric. In addition, we consider solutions that can not be obtained by twisting the above sigma\sigmasigma-model. For these it is possible to interpolate between a model evaluated on holomorphic maps and one evaluated on constant maps by different choices of gauge fixing fermion. Finally, we discuss some intriguing similarities between aspects of the doubled formulation and topological M-theory, and a possible relation with results from the theory of Lie and Courant algebroids, where a doubled formulation plays a role in relating two- and three-dimensional topological theories.
In this paper we apply the formalism of translation invariant (continuous) matrix product states ... more In this paper we apply the formalism of translation invariant (continuous) matrix product states in the thermodynamic limit to (1 + 1) dimensional critical models. Finite bond dimension bounds the entanglement entropy and introduces an effective finite correlation length, so that the state is perturbed away from criticality. The assumption that the scaling hypothesis holds for this kind of perturbation is known in the literature as finite entanglement scaling. We provide further evidence for the validity of finite entanglement scaling and based on this formulate a scaling algorithm to estimate the central charge and critical exponents of the conformally invariant field theories describing the critical models under investigation. The algorithm is applied to three exemplary models; the cMPS version to the non-relativistic Lieb-Liniger model and the relativistic massless boson, and MPS version to the one-dimensional quantum Ising model at the critical point. Another new aspect to our approach is that we directly use the (c)MPS induced correlation length rather than the bond dimension as scaling parameter. This choice is motivated by several theoretical arguments as well as by the remarkable accuracy of our results.
Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy... more Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a field dependent sense. The thesis explores various aspects of the special holonomy symmetries.
We study a generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) formulation of t... more We study a generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) formulation of the A- and B-models which involves a doubling of coordinates, and can be understood as a complexification of the Poisson sigma\sigmasigma-model underlying these. In the flat space limit the construction contains models obtained by twisting an N=2 supersymmetric sigma\sigmasigma-model on Hull's doubled geometry. The curved space generalization involves a product of two diffeomorphic Calabi-Yau manifolds, and the O(d,d)O(d,d)O(d,d) metric can be understood as a complexification of the CY metric. In addition, we consider solutions that can not be obtained by twisting the above sigma\sigmasigma-model. For these it is possible to interpolate between a model evaluated on holomorphic maps and one evaluated on constant maps by different choices of gauge fixing fermion. Finally, we discuss some intriguing similarities between aspects of the doubled formulation and topological M-theory, and a possible relation with results from...
ABSTRACT We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-d... more ABSTRACT We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum field theories. This generalization is obtained by applying the Dirac-Frenkel time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of the many body system including entanglement and correlations and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for one-dimensional systems.
Physical Review B, 2015
In this paper we apply the formalism of translation invariant (continuous) matrix product states ... more In this paper we apply the formalism of translation invariant (continuous) matrix product states in the thermodynamic limit to (1 + 1) dimensional critical models. Finite bond dimension bounds the entanglement entropy and introduces an effective finite correlation length, so that the state is perturbed away from criticality. The assumption that the scaling hypothesis holds for this kind of perturbation is known in the literature as finite entanglement scaling. We provide further evidence for the validity of finite entanglement scaling and based on this formulate a scaling algorithm to estimate the central charge and critical exponents of the conformally invariant field theories describing the critical models under investigation. The algorithm is applied to three exemplary models; the cMPS version to the non-relativistic Lieb-Liniger model and the relativistic massless boson, and MPS version to the one-dimensional quantum Ising model at the critical point. Another new aspect to our approach is that we directly use the (c)MPS induced correlation length rather than the bond dimension as scaling parameter. This choice is motivated by several theoretical arguments as well as by the remarkable accuracy of our results.
Journal of High Energy Physics, 2006
Journal of High Energy Physics, 2008
Journal of High Energy Physics, 2006
Physical Review Letters, 2013
We introduce a variational method for calculating dispersion relations of translation invariant (... more We introduce a variational method for calculating dispersion relations of translation invariant (1+1)-dimensional quantum field theories. The method is based on continuous matrix product states and can be implemented efficiently. We study the critical Lieb-Liniger model as a benchmark and excelent agreement with the exact solution is found. Additionally, we observe solitonic signatures of Lieb's Type II excitation. In addition, a non-integrable model is introduced where a U (1)-symmetry breaking term is added to the Lieb-Liniger Hamiltonian. For this model we find evidence of a nontrivial bound-state excitation in the dispersion relation.
npj Quantum Information
Tensor networks permit computational and entanglement resources to be concentrated in interesting... more Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translates infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution of arbitrary one-dimensional systems. The illustrative simulated output of these codes for achievable circuit sizes is given.
Physical Review B, 2015
In this paper we apply the formalism of translation invariant (continuous) matrix product states ... more In this paper we apply the formalism of translation invariant (continuous) matrix product states in the thermodynamic limit to (1 + 1) dimensional critical models. Finite bond dimension bounds the entanglement entropy and introduces an effective finite correlation length, so that the state is perturbed away from criticality. The assumption that the scaling hypothesis holds for this kind of perturbation is known in the literature as finite entanglement scaling. We provide further evidence for the validity of finite entanglement scaling and based on this formulate a scaling algorithm to estimate the central charge and critical exponents of the conformally invariant field theories describing the critical models under investigation. The algorithm is applied to three exemplary models; the cMPS version to the non-relativistic Lieb-Liniger model and the relativistic massless boson, and MPS version to the one-dimensional quantum Ising model at the critical point. Another new aspect to our approach is that we directly use the (c)MPS induced correlation length rather than the bond dimension as scaling parameter. This choice is motivated by several theoretical arguments as well as by the remarkable accuracy of our results. CONTENTS I. Introduction 1 II. Scaling hypothesis 2 III. Recipe for Finite Entanglement Scaling 4 A. Critical Exponents 4 B. Central Charge 6 IV. Exemplary Models 6 A. Lieb-Liniger Model 7 B. Massless Relativistic Boson 8 C. Quantum Ising Model 9 V. Conclusions 10 Acknowledgments 11 A. Review of Continuous Matrix Product States 11 B. Details of the Lieb-Liniger Field-Field Exponent Calculation 12 C. Central charge estimates from D-scaling 14 References 15
We introduce a variational method for calculating dispersion relations of translation invariant (... more We introduce a variational method for calculating dispersion relations of translation invariant (1+1)-dimensional quantum field theories. The method is based on continuous matrix product states and can be implemented efficiently. We study the critical Lieb-Liniger model as a benchmark and excelent agreement with the exact solution is found. Additionally, we observe solitonic signatures of Lieb's Type II excitation. In addition, a non-integrable model is introduced where a U(1)-symmetry breaking term is added to the Lieb-Liniger Hamiltonian. For this model we find evidence of a non-trivial bound-state excitation in the dispersion relation.
We study a generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) formulation of t... more We study a generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) formulation of the A- and B-models which involves a doubling of coordinates, and can be understood as a complexification of the Poisson sigma\sigmasigma-model underlying these. In the flat space limit the construction contains models obtained by twisting an N=2 supersymmetric sigma\sigmasigma-model on Hull's doubled geometry. The curved space generalization involves a product of two diffeomorphic Calabi-Yau manifolds, and the O(d,d)O(d,d)O(d,d) metric can be understood as a complexification of the CY metric. In addition, we consider solutions that can not be obtained by twisting the above sigma\sigmasigma-model. For these it is possible to interpolate between a model evaluated on holomorphic maps and one evaluated on constant maps by different choices of gauge fixing fermion. Finally, we discuss some intriguing similarities between aspects of the doubled formulation and topological M-theory, and a possible relation with results from the theory of Lie and Courant algebroids, where a doubled formulation plays a role in relating two- and three-dimensional topological theories.
In this paper we apply the formalism of translation invariant (continuous) matrix product states ... more In this paper we apply the formalism of translation invariant (continuous) matrix product states in the thermodynamic limit to (1 + 1) dimensional critical models. Finite bond dimension bounds the entanglement entropy and introduces an effective finite correlation length, so that the state is perturbed away from criticality. The assumption that the scaling hypothesis holds for this kind of perturbation is known in the literature as finite entanglement scaling. We provide further evidence for the validity of finite entanglement scaling and based on this formulate a scaling algorithm to estimate the central charge and critical exponents of the conformally invariant field theories describing the critical models under investigation. The algorithm is applied to three exemplary models; the cMPS version to the non-relativistic Lieb-Liniger model and the relativistic massless boson, and MPS version to the one-dimensional quantum Ising model at the critical point. Another new aspect to our approach is that we directly use the (c)MPS induced correlation length rather than the bond dimension as scaling parameter. This choice is motivated by several theoretical arguments as well as by the remarkable accuracy of our results.
Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy... more Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a field dependent sense. The thesis explores various aspects of the special holonomy symmetries.
We study a generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) formulation of t... more We study a generalization of the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) formulation of the A- and B-models which involves a doubling of coordinates, and can be understood as a complexification of the Poisson sigma\sigmasigma-model underlying these. In the flat space limit the construction contains models obtained by twisting an N=2 supersymmetric sigma\sigmasigma-model on Hull's doubled geometry. The curved space generalization involves a product of two diffeomorphic Calabi-Yau manifolds, and the O(d,d)O(d,d)O(d,d) metric can be understood as a complexification of the CY metric. In addition, we consider solutions that can not be obtained by twisting the above sigma\sigmasigma-model. For these it is possible to interpolate between a model evaluated on holomorphic maps and one evaluated on constant maps by different choices of gauge fixing fermion. Finally, we discuss some intriguing similarities between aspects of the doubled formulation and topological M-theory, and a possible relation with results from...
ABSTRACT We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-d... more ABSTRACT We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum field theories. This generalization is obtained by applying the Dirac-Frenkel time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of the many body system including entanglement and correlations and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for one-dimensional systems.
Physical Review B, 2015
In this paper we apply the formalism of translation invariant (continuous) matrix product states ... more In this paper we apply the formalism of translation invariant (continuous) matrix product states in the thermodynamic limit to (1 + 1) dimensional critical models. Finite bond dimension bounds the entanglement entropy and introduces an effective finite correlation length, so that the state is perturbed away from criticality. The assumption that the scaling hypothesis holds for this kind of perturbation is known in the literature as finite entanglement scaling. We provide further evidence for the validity of finite entanglement scaling and based on this formulate a scaling algorithm to estimate the central charge and critical exponents of the conformally invariant field theories describing the critical models under investigation. The algorithm is applied to three exemplary models; the cMPS version to the non-relativistic Lieb-Liniger model and the relativistic massless boson, and MPS version to the one-dimensional quantum Ising model at the critical point. Another new aspect to our approach is that we directly use the (c)MPS induced correlation length rather than the bond dimension as scaling parameter. This choice is motivated by several theoretical arguments as well as by the remarkable accuracy of our results.
Journal of High Energy Physics, 2006
Journal of High Energy Physics, 2008
Journal of High Energy Physics, 2006
Physical Review Letters, 2013
We introduce a variational method for calculating dispersion relations of translation invariant (... more We introduce a variational method for calculating dispersion relations of translation invariant (1+1)-dimensional quantum field theories. The method is based on continuous matrix product states and can be implemented efficiently. We study the critical Lieb-Liniger model as a benchmark and excelent agreement with the exact solution is found. Additionally, we observe solitonic signatures of Lieb's Type II excitation. In addition, a non-integrable model is introduced where a U (1)-symmetry breaking term is added to the Lieb-Liniger Hamiltonian. For this model we find evidence of a nontrivial bound-state excitation in the dispersion relation.