Roadmap for quantum simulation of the fractional quantum Hall effect

Kaicher, Michael P.; Jäger, Simon B.; Dallaire-Demers, Pierre-Luc; Wilhelm, Frank K.

doi:10.1103/physreva.102.022607

Cited by 6 publications

(4 citation statements)

References 74 publications

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“…A better understanding of the topologically ordered states in the fractional quantum hall effect 164,165 , the nature of the superconducting glue in unconventional superconductors 166,167 , the ability to induce quantum phases "on demand" via ultrafast excitations 3 , and the identification of interesting quantum materials such as topological insulators, superconductors, and spin liquids 168 are fundamental problems that in many cases are hard to describe with classical methods, especially if the corresponding quantum states are highly entangled.…”

Section: Outlook and Applicationsmentioning

confidence: 99%

Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges

Fauseweh

2024

Nat Commun

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Simulating quantum many-body systems is a key application for emerging quantum processors. While analog quantum simulation has already demonstrated quantum advantage, its digital counterpart has recently become the focus of intense research interest due to the availability of devices that aim to realize general-purpose quantum computers. In this perspective, we give a selective overview of the currently pursued approaches, review the advances in digital quantum simulation by comparing non-variational with variational approaches and identify hardware and algorithmic challenges. Based on this review, the question arises: What are the most promising problems that can be tackled with digital quantum simulation? We argue that problems of a qualitative nature are much more suitable for near-term devices then approaches aiming purely for a quantitative accuracy improvement.

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Section: Outlook and Applicationsmentioning

confidence: 99%

Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges

Fauseweh

2024

Nat Commun

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“…20) Given the importance of understanding and exploiting the coupling between an electronic system and an external magnetic field as discussed above, it is desirable to develop methods to incorporate external magnetic fields in the quantum computation of electronic systems. Although such a method has already been proposed for the second-quantized formalism, 21) a first-quantized method remains lacking to our best knowledge. In this study, we employ the operatorsplitting technique used by Watanabe and Tsukada 22) for classical computers to efficiently incorporate a uniform magnetic field in the FQE calculation.…”

Section: Introductionmentioning

confidence: 99%

First-quantized eigensolver for ground and excited states of electrons under a uniform magnetic field

Kosugi

Nishi

Matsushita

2023

Jpn. J. Appl. Phys.

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First-quantized eigensolver (FQE) is a recently proposed quantum computation framework for obtaining the ground state of an interacting electronic system based on probabilistic imaginary-time evolution. Here, we propose a method for introducing a uniform magnetic field to the FQE calculation. Our resource estimation demonstrates that the additional circuit responsible for the magnetic field can be implemented with a linear depth in terms of the number of qubits assigned to each electron. Hence, introduction of the magnetic field has no impact on the leading order of the entire computational cost. The proposed method is validated by numerical simulations of the ground and excited states employing filtration circuits for the energy eigenstates. We also provide a generic construction of the derivative circuits together with measurement-based formulae. We can obtain the electric-current density in an electronic system to gain insights into the microscopic origin of the magnetic response.

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“…The charged excitations in the FQH systems are predicted to carry fractional charge, with anyonic and even non-abelian statistics [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Under the right conditions, these topological properties are expected to be invariant against local disturbance, making them desirable for the robust manipulation of quantum information [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications

Wang

Yang

2022

Phys. Rev. B

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Neutral excitations in a fractional quantum Hall droplet define the incompressibility gap of the topological phase. In this work, we derived a set of analytical results for the energy gap of the graviton modes with two-body and three-body Hamiltonians in both the long-wavelength and thermodynamic limit. These allow us to construct model Hamiltonians for the graviton modes in different FQH phases, and to elucidate a hierarchical structure of conformal Hilbert spaces (null spaces of model Hamiltonians) with respect to the graviton modes and their corresponding ground states. Using the analytical tools developed, we perform numerical analysis with a particular focus on the Laughlin ν = 1/5 and the Gaffnian ν = 2/5 phases. Our calculation shows that for gapped phases, low-lying neutral excitations can undergo a "phase transition" even when the ground state is invariant. We discuss about the compressibility of the Gaffnian phase, the possibility of multiple graviton modes, and the transition from the graviton modes to the "hollow-core" modes, as well as their experimental consequences.

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Roadmap for quantum simulation of the fractional quantum Hall effect

Cited by 6 publications

References 74 publications

Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges

Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges

First-quantized eigensolver for ground and excited states of electrons under a uniform magnetic field

Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications

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