Simulation of Interaction-Induced Chiral Topological Dynamics on a Digital Quantum Computer

Koh, Jin; Tai, Tommy; Lee, Ching Hua

doi:10.1103/physrevlett.129.140502

Cited by 18 publications

(13 citation statements)

References 134 publications

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“…where u α π is now labeled by the parity vector π of lattice coordinates, and the parity operator Recompilation. Circuit recompilation starts from a circuit ansatz, whose parameters are dynamically optimized [76][77][78][79][80]134]. We use a circuit ansatz comprising an initial layer of U3 general single-qubit rotation gates on all qubits followed by K ansatz layers, each comprising a layer of CX gates entangling adjacent qubits and a layer of U3 rotations (see Figure 2e).…”

Section: Methodsmentioning

confidence: 99%

“…However, while straightforward, such an approach yields deep circuits unsuitable for presentgeneration NISQ hardware. To compress the circuits, we utilize a tensor network-aided recompilation technique [76][77][78][79][80]. We exploit the number-conserving symmetries of H dD chain , arising from H dD lattice and the nature of our mapping (see Methods), to enhance circuit construction performance and quality at large circuit breadths (up to 32 qubits).…”

Section: B Simulation On Quantum Hardwarementioning

confidence: 99%

“…We exploit the number-conserving symmetries of H dD chain , arising from H dD lattice and the nature of our mapping (see Methods), to enhance circuit construction performance and quality at large circuit breadths (up to 32 qubits). Moreover, to improve data quality amidst hardware noise, we employ a suite of error mitigation techniques, in particular readout mitigation (RO) that approximately corrects bit-flip errors during measurement [18,81], a post-selection (PS) technique that discards results in unphysical Fock-space sectors [18,77,82], and averaging across machines and qubit chains (see Methods).…”

Section: B Simulation On Quantum Hardwarementioning

confidence: 99%

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Observation of higher-order topological states on a quantum computer

Koh¹,

Tai²,

Lee³

2023

Preprint

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Programmable quantum simulators such as superconducting quantum processors and ultracold atomic lattices represent rapidly developing emergent technology that may one day qualitatively outperform existing classical computers. Yet, apart from a few breakthroughs, the range of viable computational applications with current-day noisy intermediate-scale quantum (NISQ) devices is still significantly limited by gate errors, quantum decoherence and the number of high quality qubits. In this work, we develop an approach that places NISQ hardware as particularly suitable platforms for simulating multi-dimensional condensed matter systems, including lattices beyond three dimensions which are difficult to realize or probe in other settings. By fully exploiting the exponentially large Hilbert space of a quantum chain, we encoded a high-dimensional model in terms of non-local many-body interactions that can further be systematically transcribed into quantum gates. We demonstrate the power of our approach by realizing, on IBM transmon-based quantum computers, higher-order topological states in up to four dimensions, which are exotic phases that have never been realized in any quantum setting. With the aid of in-house circuit compression and error mitigation techniques, we measured the topological state dynamics and their protected midgap spectra to a high degree of accuracy, as benchmarked by reference exact diagonalization data. The time and memory needed with our approach scales favorably with system size and dimensionality compared to exact diagonalization on classical computers.

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Section: Methodsmentioning

confidence: 99%

Section: B Simulation On Quantum Hardwarementioning

confidence: 99%

Section: B Simulation On Quantum Hardwarementioning

confidence: 99%

See 1 more Smart Citation

Observation of higher-order topological states on a quantum computer

Koh¹,

Tai²,

Lee³

2023

Preprint

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“…The rapid development of hardware and algorithms in universal quantum computation also opens up the possibility of implementing our YLES measurement protocol in quantum computers via ancilla-based methods [88][89][90][91]. Moreover, our MPS implementation, which is related to mid-circuit measurements [92][93][94][95], provides an approach to improve the current ancilla-based methods for dynamically simulating various non-Hermitian many-body phenomena [96][97][98][99][100][101][102][103] and unconventional non-Hermitian topology [104][105][106][107][108][109][110][111][112][113][114][115][116][117], on quantum circuits.…”

Section: (B) Upon Obtaining γ ∞mentioning

confidence: 99%

Proposal for observing Yang-Lee criticality in Rydberg atomic arrays

Shen¹,

Chen²,

Qin³

et al. 2023

Preprint

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Yang-Lee edge singularities (YLES) are the edges of the partition function zeros of an interacting spin model in the space of complex control parameters. They play an important role in understanding non-Hermitian phase transitions in many-body physics, as well as characterizing the corresponding non-unitary criticality. Even though such partition function zeroes have been measured in dynamical experiments where time acts as the imaginary control field, experimentally demonstrating such YLES criticality with a physical imaginary field has remained elusive due to the difficulty of physically realizing non-Hermitian many-body models. We provide a protocol for observing the YLES by detecting kinked dynamical magnetization responses due to broken PT symmetry, thus enabling the physical probing of non-unitary phase transitions in non-equilibrium settings. In particular, scaling analyses based on our non-unitary time evolution circuit with matrix product states (tMPS) accurately recover the exponents uniquely associated with the corresponding non-unitary CFT. We provide an explicit proposal for observing YLES criticality in Floquet quenched Rydberg atomic arrays with laser-induced loss, which paves the way towards an universal platform for simulating non-Hermitian many-body dynamical phenomena.

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“…As discussed in Appendix A, although a uniform grounding mechanism can be employed to isolate the topological states isolated from the bulk states, a Chern topolectrical circuit can be designed so that it exhibits clear chiral propagating boundary states in the admittance spectrum without a uniform grounding mechanism. This is due to nontrivial center-of-mass pumping through a Laughlin-style pumping argument [119][120][121][122][123][124], which has been demonstrated in a variety of classical and quantum settings [18,[125][126][127][128][129]. Here, due to the nearest neighbor connections and the onsite capacitors represented by the factor σ z in the Laplacian, the topological states are separated despite the nonuniform grounding.…”

Section: Example: 2d Chern Kink Topolectrical Circuitmentioning

confidence: 99%

Impedance responses and size-dependent resonances in topolectrical circuits via the method of images

Sahin

Siu

Rafi-Ul-Islam

et al. 2022

Preprint

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Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit’s parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits (TEs) such as 1D and 2D Su–Schrieffer–Heeger (SSH) circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite LC circuits. Through the method of images, we study how resonance modes in a multi-dimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally-reduced expressions for the impedance in three dimensions and above.

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Simulation of Interaction-Induced Chiral Topological Dynamics on a Digital Quantum Computer

Cited by 18 publications

References 134 publications

Observation of higher-order topological states on a quantum computer

Observation of higher-order topological states on a quantum computer

Proposal for observing Yang-Lee criticality in Rydberg atomic arrays

Impedance responses and size-dependent resonances in topolectrical circuits via the method of images

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