Observation of higher-order topological states on a quantum computer
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 a particularly suitable platform 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 mid-gap spectra to a high degree
of accuracy, as benchmarked by reference exact diagonalization data. The time
and memory needed with our approach scale favorably with system size and
dimensionality compared to exact diagonalization on classical computers.
Jin Ming Koh Tommy Tai Ching Hua Lee