Observation of higher-order topological states on a quantum computer

Abstract

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.

An exact local mapping from clock-spins to fermions

“…Interestingly, chains of interacting fermions like the one described by the Hamiltonian in Eq. ( 79) can be effectively simulated on quantum computers [58].…”

Observation of higher-order time-dislocation topological modes

“…As critical subsystems that straddle different topological phases, topological interfaces are host to exotic phenomena ranging from robust chiral anomalies to percolating edge states 1,2 . Particularly in higher dimensions, such interfaces become especially rich due to the directional interplay between different localization mechanisms, as epitomized by higher-order [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and hybrid skintopological states [20][21][22][23][24][25] . Of late, the prospect of timeperiodic (Floquet) driving has introduced yet another new level of complexity by opening up the temporal dimension [26][27][28][29][30][31][32][33][34][35][36] .…”