Lattice gauge theory and dynamical quantum phase transitions using noisy intermediate-scale quantum devices

Pedersen, Simon Panyella; Zinner, N. T.

doi:10.1103/physrevb.103.235103

Cited by 10 publications

(8 citation statements)

References 122 publications

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“…The latter determines the gauge connection

, characterized by the generalized canonical commutation relation

. The lattice model Hamiltonian for a finite lattice with N sites reads [ 4 , 31 , 32 , 33 , 49 ]

where periodic boundary conditions [ 50 , 51 ] require the identification

. The model involves staggered (Kogut–Susskind) fermions [ 61 ], described by single-component spinors

, with negative-mass components encoded in odd- x sites.…”

Section: The Lattice Schwinger Modelmentioning

confidence: 99%

“…The physical subspace

is spanned by states

satisfying the Gauss law constraint

at all sites x , where, for a

gauge group,

The electric field was simulated in the following through a

discretization of U

[ 31 , 32 , 33 , 49 , 52 , 53 ] with

. Unlike in the quantum link models [ 50 , 51 ], where the electric field is replaced by a spin operator, the

model is based on replacing gauge connections with permutation matrices [ 49 ]. In the case of

, the electric field in each link

can have two eigenstates, which will be labeled as

, with

while the gauge connections act as [ 31 , 32 , 33 ]

An immediate implication of the

model is the irrelevance in the Hamiltonian ( 1 ) of the electric field energy, which becomes a constant.…”

Section: The Lattice Schwinger Modelmentioning

confidence: 99%

“…We aimed at studying the non-equilibrium dynamics of the described lattice Schwinger model following a quantum quench [ 50 , 51 , 57 ]. Generally, in this protocol, one considers a family of Hamiltonians

that depends on a tunable parameter and prepares an initial state coinciding with the ground state

.…”

Section: The Lattice Schwinger Modelmentioning

confidence: 99%

“…This paper aimed at testing the superconducting qubit systems available in the IBM Quantum platform [ 1 ] in a simple lattice gauge theory application. We implemented digital evolutions generated by the QED Hamiltonian in

dimensions, consisting of non-commuting local contributions [ 4 , 31 , 32 , 33 , 37 , 41 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 ] and displaying the occurrence of dynamical quantum phase transitions (DQPTs) [ 57 , 58 , 59 ] in specific cases of quantum quenches. A discretization of the electromagnetic field is required to implement gauge degrees of freedom in the quantum simulator: accomplishing such a task by replacing the continuous

gauge group with one of the cyclic groups

guarantees a unitary implementation of the gauge connections [ 49 ]; another possible choice is represented by the family of quantum link models [ 60 ].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Dynamical Quantum Phase Transitions of the Schwinger Model: Real-Time Dynamics on IBM Quantum

Pomarico

Cosmai

Facchi

et al. 2023

Entropy

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Simulating the real-time dynamics of gauge theories represents a paradigmatic use case to test the hardware capabilities of a quantum computer, since it can involve non-trivial input states’ preparation, discretized time evolution, long-distance entanglement, and measurement in a noisy environment. We implemented an algorithm to simulate the real-time dynamics of a few-qubit system that approximates the Schwinger model in the framework of lattice gauge theories, with specific attention to the occurrence of a dynamical quantum phase transition. Limitations in the simulation capabilities on IBM Quantum were imposed by noise affecting the application of single-qubit and two-qubit gates, which combine in the decomposition of Trotter evolution. The experimental results collected in quantum algorithm runs on IBM Quantum were compared with noise models to characterize the performance in the absence of error mitigation.

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“…The latter determines the gauge connection

, characterized by the generalized canonical commutation relation

. The lattice model Hamiltonian for a finite lattice with N sites reads [ 4 , 31 , 32 , 33 , 49 ]

where periodic boundary conditions [ 50 , 51 ] require the identification

. The model involves staggered (Kogut–Susskind) fermions [ 61 ], described by single-component spinors

, with negative-mass components encoded in odd- x sites.…”

Section: The Lattice Schwinger Modelmentioning

confidence: 99%

“…The physical subspace

is spanned by states

satisfying the Gauss law constraint

at all sites x , where, for a

gauge group,

The electric field was simulated in the following through a

discretization of U

[ 31 , 32 , 33 , 49 , 52 , 53 ] with

. Unlike in the quantum link models [ 50 , 51 ], where the electric field is replaced by a spin operator, the

model is based on replacing gauge connections with permutation matrices [ 49 ]. In the case of

, the electric field in each link

can have two eigenstates, which will be labeled as

, with

while the gauge connections act as [ 31 , 32 , 33 ]

An immediate implication of the

model is the irrelevance in the Hamiltonian ( 1 ) of the electric field energy, which becomes a constant.…”

Section: The Lattice Schwinger Modelmentioning

confidence: 99%

that depends on a tunable parameter and prepares an initial state coinciding with the ground state

.…”

Section: The Lattice Schwinger Modelmentioning

confidence: 99%

gauge group with one of the cyclic groups

guarantees a unitary implementation of the gauge connections [ 49 ]; another possible choice is represented by the family of quantum link models [ 60 ].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamical Quantum Phase Transitions of the Schwinger Model: Real-Time Dynamics on IBM Quantum

Pomarico

Cosmai

Facchi

et al. 2023

Entropy

View full text Add to dashboard Cite

show abstract

“…[87][88][89][90][91][92][93][94][95], and later predicted to occur in gauge theories as well [1,96]. Importantly, this phenomenon is shown to be an ideal candidate for exploration with existing analog and digital devices, since it persists in small systems and on short time scales [1,97,98]. DQPTs are manifest in non-equal time correlation functions and nonequal time wavefunction overlaps (Loschmidt echos), and in the Schwinger model they are related to an underlying topological transition [1].…”

Section: Introductionmentioning

confidence: 99%

Quantum computation of dynamical quantum phase transitions and entanglement tomography in a lattice gauge theory

Mueller¹,

A.²,

Connelly³

et al. 2022

Preprint

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Engineering an effective three-spin Hamiltonian in trapped-ion systems for applications in quantum simulation

Andrade

Davoudi

Graß

et al. 2022

Quantum Sci. Technol.

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Trapped-ion quantum simulators, in analog and digital modes, are considered a primary candidate to achieve quantum advantage in quantum simulation and quantum computation. The underlying controlled ion–laser interactions induce all-to-all two-spin interactions via the collective modes of motion through Cirac–Zoller or Mølmer–Sørensen schemes, leading to effective two-spin Hamiltonians, as well as two-qubit entangling gates. In this work, the Mølmer–Sørensen scheme is extended to induce three-spin interactions via tailored first- and second-order spin–motion couplings. The scheme enables engineering single-, two-, and three-spin interactions, and can be tuned via an enhanced protocol to simulate purely three-spin dynamics. Analytical results for the effective evolution are presented, along with detailed numerical simulations of the full dynamics to support the accuracy and feasibility of the proposed scheme for near-term applications. With a focus on quantum simulation, the advantage of a direct analog implementation of three-spin dynamics is demonstrated via the example of matter-gauge interactions in the U(1) lattice gauge theory within the quantum link model. The mapping of degrees of freedom and strategies for scaling the three-spin scheme to larger systems, are detailed, along with a discussion of the expected outcome of the simulation of the quantum link model given realistic fidelities in the upcoming experiments. The applications of the three-spin scheme go beyond the lattice gauge theory example studied here and include studies of static and dynamical phase diagrams of strongly interacting condensed-matter systems modeled by two- and three-spin Hamiltonians.

show abstract

Lattice gauge theory and dynamical quantum phase transitions using noisy intermediate-scale quantum devices

Cited by 10 publications

References 122 publications

Dynamical Quantum Phase Transitions of the Schwinger Model: Real-Time Dynamics on IBM Quantum

Dynamical Quantum Phase Transitions of the Schwinger Model: Real-Time Dynamics on IBM Quantum

Quantum computation of dynamical quantum phase transitions and entanglement tomography in a lattice gauge theory

Engineering an effective three-spin Hamiltonian in trapped-ion systems for applications in quantum simulation

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