A paper recently published in Nature Communications demonstrated higher-order topological (HOT) lattice realization on a quantum computer.
Study: Quantum Simulators: A Step Towards Quantum Advantage. Image Credit: Panchenko Vladimir/Shutterstock.com
Quantum Simulators: Progress and Challenges
In recent years, significant progress has been made in developing programmable quantum simulator platforms, such as Rydberg atom arrays, ultracold atomic lattices, trapped ion systems, and superconducting fluxonium—and transmon-based processors.
Several successful demonstrations of these platforms, specifically in the context of quantum many-body dynamics and quantum chemistry, have been reported.
This ongoing research effort has been underpinned by the expectation that programmable quantum simulators/quantum-computational platforms can outperform classical computers/conventional classical counterparts in many useful tasks, enabling new capabilities.
Although quantum advantage breakthroughs in simulational tasks have been reported, existing studies primarily focused on specifically tailored problems, such as boson sampling and random quantum circuit sampling, which hinder their broader applicability.
Currently, the range of viable applications using noisy intermediate-scale quantum (NISQ) devices still needs to be improved by the number of high-quality qubits and gate errors. Thus, pushing the near-term NISQ hardware capabilities and identifying applications for which the quantum platforms offer unique advantages have become necessary.
The Proposed Approach
In this work, researchers developed an approach that establishes digital NISQ hardware as a versatile platform to simulate generic multi-dimensional condensed matter systems/lattice models.
The objective was to use this method to realize HOT phases in high-dimensional lattices of exceptional complexity and size on transmon-based superconducting quantum devices.
The proposed method encoded a high-dimensional lattice on a reduced-dimension model regarding many-body interactions to exploit the full advantage of the host quantum system's exponentially large Hilbert space.
Specifically, a mapping procedure encoded a high-dimensional lattice's single-particle degrees of freedom within an interacting one-dimensional model's many-body Fock space.
This enabled them to exploit the full advantage of the Hilbert space inherently accessible by a quantum computer while substantially reducing the required number of qubits for direct simulation. Unlike earlier quantum simulator studies where topological models were implemented through synthetic dimensions, researchers here aimed to achieve HOT lattices in real space, up to d = 4 dimensions (tesseract).
Classical high-dimensional HOT lattice simulation is expensive, and the quantum simulation's resource complexity was favorable over classical methods like exact diagonalization in entirely general settings.
Researchers measured the protected mid-gap spectra and topological state dynamics of HOT lattices on IBM superconducting quantum processors, up to four dimensions, with high accuracy using error mitigation and circuit optimization techniques. All experiments were performed using IBM transmon-based superconducting quantum devices.
Quantum volume (QV)-32 devices ibmq_brooklyn (65 qubits) and ibmq_manhattan (65 qubits) were utilized for time-evolution on the square lattice, while QV-128 devices ibmq_montreal (27 qubits) and ibmq_mumbai (27 qubits), and QV-32 devices ibmq_toronto (27 qubits) and ibmq_sydney (27 qubits) were used for time-evolution on the cubic and tesseract lattices.
Additionally, the group of QV-128 devices was employed for iterative quantum phase estimation (IQPE). The QV reflected an approximate aggregate capability measure of the machine: the number of qubits, decoherence times, and gate error rates.
Study Contributions
Researchers successfully realized the first HOT Hamiltonian simulation in a fully quantum setting in up to four dimensions by exploiting the exponentially large many-body Hilbert space.
They also accurately measured the initial states' density evolution, displayed their robustness emerging from higher-order topology, and detected their midgap topological energy spectra, which report the number of high-dimensional lattice-hosted degenerate HOT modes on quantum hardware.
This was equivalent to investigating the system's corresponding topological invariant by the renowned bulk-boundary correspondence. Although the topological invariant could be directly measured through holonomy on wavefunctions, such an approach is expensive and challenging to utilize on generic HOT lattices suitably.
Researchers emphasized that performing a digital quantum simulation of Hamiltonians with similar complexity as HOT lattices examined was non-trivial due to experiment limitations, such as decoherence, gate errors, and qubit numbers, on current hardware. The study and results presented were only possible with the approach described in this work.
In this study, the projected resource requirements were favorably scaled with lattice dimensionality and system size compared to classical computation. This indicates a potential route to useful quantum advantage in the long term as quantum simulator platforms continue to improve rapidly.
Such an advantage can lead to a tremendous scientific impact when realized, as the quantum lattice system simulation is a ubiquitous foundational task in engineering and physical contexts. To summarize, this work effectively demonstrated the realization of HOT lattices on a quantum computer.
Journal Reference
Koh, J. M., Tai, T., Lee, C. H. (2024). Realization of higher-order topological lattices on a quantum computer. Nature Communications, 15(1), 1-14. doi: 10.1038/s41467-024-49648-5, https://www.nature.com/articles/s41467-024-49648-5
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