Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers

Kirmani, Ammar; Bull, Kieran; Hou, Chang-Yu; Saravanan, Vedika; Saeed, Samah Mohamed; Papić, Zlatko; Rahmani, Armin; Ghaemi, Pouyan

doi:10.1103/physrevlett.129.056801

Cited by 12 publications

(8 citation statements)

References 89 publications

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“…(2.5). Intriguingly, this constraint also emerges in theoretical descriptions of the ν = 1/3 Laughlin fractional quantum Hall (FQH) state in a particular quasi-1D limit [59][60][61][62]. In fact, the ground state of the system in this limit is unitarily equivalent to |ξ for a particular choice of the parameter ξ [59].…”

Section: Model and State Preparation Tasksmentioning

confidence: 93%

Preparing quantum-many body scars on a quantum computer

Gustafson,

Li,

Kahn

et al. 2023

Preprint

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Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware.

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Section: Model and State Preparation Tasksmentioning

confidence: 93%

Preparing quantum-many body scars on a quantum computer

Gustafson,

Li,

Kahn

et al. 2023

Preprint

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“…Still, detecting the anyonic statistics of FQH states by directly braiding one excitation around the other through adiabatic Hamiltonian evolution remains an open experimental challenge. Meanwhile, there have been extensive advancements in theoretical models for the fractional Hall states, such as one-dimensional (1D) model Hamiltonians [6][7][8][9][10] that are particularly suitable for implementation on small, noisy quantum devices [11,12], that capture two-dimensional (2D) physics. Such devices have been used for studying topological braiding in the toric and surface codes without emulating Hamiltonian evolution [13,14].…”

Section: Introductionmentioning

confidence: 99%

Braiding fractional quantum Hall quasiholes on a superconducting quantum processor

Kirmani¹,

Wang²,

Ghaemi³

et al. 2023

Preprint

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Direct experimental detection of anyonic exchange statistics in fractional quantum Hall systems by braiding the excitations and measuring the wave-function phase is an enormous challenge. Here, we use a small, noisy quantum computer to emulate direct braiding within the framework of a simplified model applicable to a thin cylinder geometry and measure the topological phase. Our algorithm first prepares the ground state with two quasiholes. It then applies a unitary operation controlled by an ancilla, corresponding to a sequence of adiabatic evolutions that take one quasihole around the other. We finally extract the phase of the wave function from measuring the ancilla with a compound error mitigation strategy. Our results open a new avenue for studying braiding statistics in fractional Hall states.

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“…have been adapted for studying the FQHE, but because of the strongcoupling nature of this problem, the largest system size available for numerical calculations is still far away from the usual experiments, let al one the thermodynamic limit. Recently, quantum computers have also been found to be an available platform for the simulation of FQH states and their dynamics, the difficulty of which, however, is that the construction of these states involves non-unitary operators, so only the simplest states like the Laughlin states have been realized on quantum computers so far [186,187].…”

Section: Topological Models and New Platforms: 2004 -2007mentioning

confidence: 99%

“…An acoustic crystalline wave is also predicted to act like a gravitational wave, which can interact with the graviton modes as a probe [323]. Furthermore, an optimal-control-based variational quantum algorithm has been designed for realizing the graviton mode in quantum computers [187]. There has also been much interest in the graviton mode due to its spin structure, allowing it to couple selectively to circularly polarized light, making them useful for experimentally distinguishing different topological phases [324].…”

Section: Gravitons As Quasiparticlesmentioning

confidence: 99%

“…While Lorentz invariance is absent in this (2 + 1)-dimensional space-time, these 2D graviton modes encode topological information about their respective FQH phases, and their dynamics lead to rich physics ranging from ground state incompressibility to the dynamical phase transitions of the low-lying excitations [140,354]. The effective field theory studying the graviton modes has been proposed by using the Newton-Carton metric, and various experimental proposals for the observation of these modes have been put forward [187,236,238,318,321,322,[324][325][326]355]. In this chapter, we will reveal the origin of the graviton modes from the metric fluctuations within CHSs [52,199,230].…”

Section: Microscopic Theory Of Multiple Graviton Modesmentioning

confidence: 99%

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Graviton modes in fractional quantum hall liquids

Wang¹

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The fractional quantum Hall fluid is a two-dimensional quantum fluid of electrons subject to a strong magnetic field at low temperatures. Neutral excitations in a fractional quantum Hall droplet define the incompressibility gap of the topological phase. Among these states, there are some specific modes in the long-wavelength limit that can be understood as "spin-2 gravitons". In this thesis, we will introduce a set of analytical results for the energy gap of the graviton modes for model Hamiltonians in the thermodynamic limit, which is governed by a well-defined and universal characteristic tensor. These results can help to construct model Hamiltonians for the graviton modes of different FQH phases and elucidate a hierarchical structure of conformal Hilbert spaces (null spaces of model Hamiltonians) containing the graviton modes and their corresponding ground states. An isomorphism can be defined for these conformal Hilbert spaces, and the mapping between them can be regarded as a more rigorous and general reinterpretation of the composite fermionization of FQH states, with naturally emergent composite fermions (each consisting of one electron and an even number of fluxes). The results from exact diagonalization will be shown, which confirm that for gapped phases, low-lying neutral excitations can undergo a phase transition even when the ground state remains in the same phase. Furthermore, the gaplessness of the Gaffnian state could be testified based on this formalism with further numerical experiments. Recently there has been numerical evidence implying the signature of multiple graviton modes. We will introduce the microscopic theory for the emergence of multiple gravitons in fractional quantum Hall droplets based on composite fermionization and the well-defined particle-hole conjugate within a specific conformal Hilbert space. This reveals the dynamical nature of this phenomenon and provides theoretical insights into the chirality and the "merging and splitting" behaviors of the graviton modes. The experimental relevance of multiple graviton modes will be discussed. The microscopic theory of gravitons can also provide valuable insights into the field-theoretical approaches.

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Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers

Cited by 12 publications

References 89 publications

Preparing quantum-many body scars on a quantum computer

Preparing quantum-many body scars on a quantum computer

Braiding fractional quantum Hall quasiholes on a superconducting quantum processor

Graviton modes in fractional quantum hall liquids

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