Provable Advantage in Quantum Phase Learning via Quantum Kernel Alphatron

The use of quantum computation to speed-up machine learning algorithms is among the most exciting prospective applications in the NISQ era. Here, we focus on the quantum phase learning problem, which is crucially important in understanding many-particle quantum systems. We prove that, under widely believed complexity theory assumptions, quantum phase learning problem cannot be efficiently solved by machine learning algorithms using classical resources and classical data. Whereas using quantum data, we prove the universality of quantum kernel Alphatron in efficiently predicting quantum phases, indicating clear quantum advantages in such learning problems. We numerically benchmark the algorithm for a variety of problems, including recognizing symmetry-protected topological phases and symmetry-broken phases. Our results highlight the capability of quantum machine learning in efficient prediction of quantum phases of many-particle systems.

Symmetry-protected sign problem and magic in quantum phases of matter

We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic to study the complexity of symmetry-protected topological (SPT) phases of matter. In particular, we say a state has a symmetry-protected sign problem or symmetry-protected magic, if finite-depth quantum circuits composed of symmetric gates are unable to transform the state into a non-negative real wave function or stabilizer state, respectively. We prove that states belonging to certain SPT phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, we find that one-dimensional Z2×Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have symmetry-protected magic. Furthermore, we comment on the relation between a symmetry-protected sign problem and the computational wire property of one-dimensional SPT states. In an appendix, we also introduce explicit decorated domain wall models of SPT phases, which may be of independent interest.

Superconductivity coexisting with ferromagnetism in a quasi-one dimensional non-centrosymmetric (TaSe4)3I

Low-dimensional materials with broken inversion symmetry and strong spin-orbit coupling can give rise to fascinating quantum phases and phase transitions. Here we report coexistence of superconductivity and ferromagnetism below 2.5 K in the quasione dimensional crystals of non-centrosymmetric (TaSe4)3I (space group: P¯421c). The unique phase is a direct consequence of inversion symmetry breaking as the same material also stabilizes in a centro-symmetric structure (space group: P4/mnc) where it behaves like a non-magnetic insulator[1–4]. The coexistence here upfront contradicts the popular belief that superconductivity and ferromagnetism are two apparently antagonistic phenomena. Notably, here, for the first time, we have clearly detected Meissner effect in the superconducting state despite the coexisting ferromagnetic order. The coexistence of superconductivity and ferromagnetism projects non-centrosymmetric (TaSe4)3I as a host for complex ground states of quantum matter including possible unconventional superconductivity with elusive spin-triplet pairing[5–8].

Gate-tunable magnetoresistance in six-septuple-layer MnBi2Te4

The recently discovered antiferromagnetic topological insulator MnBi2Te4 hosts many exotic topological quantum phases such as the axion insulator and Chern insulator. Here we report systematic gate voltage dependent magneto transport studies in six septuple-layer MnBi2Te4. In p-type carrier regime, we observe positive linear magnetoresistance when MnBi2Te4 is polarized in the ferromagnetic state by an out-of-plane magnetic field. Whereas in the n-type regime, distinct negative magnetoresistance behaviors are observed. The behaviors of magnetoresistance in both regimes are highlyrobust against temperature up to the Néel temperature. Within the antiferromagnetic regime, the behavior of magnetoresistance exhibits a transition from negative to positive under the control of gate voltage. The boundaries of the magnetoresistance phase diagram can be explicitly marked by the gate-voltage-independent magnetic fields that characterize the processes of the spin-flop transition. The rich transport phenomena demonstrate the intricate interplay between topology, magnetism and dimensionality in MnBi2Te4.

Detection of Magnetic Gap in Topological Surface States of MnBi2Te4

Recently, intrinsic antiferromagnetic topological insulator MnBi2Te4 has drawn intense research interest and leads to plenty of significant progress in physics and materials science by hosting quantum anomalous Hall effect, axion insulator state, and other quantum phases. An essential ingredient to realize these quantum states is the magnetic gap in the topological surface states induced by the out-of-plane ferromagnetism on the surface of MnBi2Te4. However, the experimental observations of the surface gap remain controversial. Here, we report the observation of the surface gap via the point contact tunneling spectroscopy. In agreement with theoretical calculations, the gap size is around 50 meV, which vanishes as the sample becomes paramagnetic with increasing temperature. The magnetoresistance hysteresis is detected through the point contact junction on the sample surface with an out-of-plane magnetic field, substantiating the surface ferromagnetism. Furthermore, the non-zero transport spin polarization coming from the ferromagnetism is determined by the point contact Andreev reflection spectroscopy. Combining these results, the magnetism-induced gap in topological surface states of MnBi2Te4 is revealed.

Altermagnetism: spin-momentum locked phase protected by non-relativistic symmetries

The search for novel magnetic quantum phases, phenomena and functional materials has been guided by relativistic magnetic-symmetry groups in coupled spin and real space from the dawn of the field in 1950s to the modern era of topological matter. However, the magnetic groups cannot disentangle non-relativistic phases and effects, such as the recently reported unconventional spin physics in collinear antiferromagnets, from the typically weak relativistic spin-orbit coupling phenomena. Here we discover that more general spin symmetries in decoupled spin and crystal space categorize non-relativistic collinear magnetism in three phases: conventional ferromagnets and antiferromangets, and a third distinct phase combining zero net magnetization with an alternating spin-momentum locking in energy bands, which we dub "altermagnetic". For this third basic magnetic phase, which is omitted by the relativistic magnetic groups, we develop a spin-group theory describing six characteristic types of the altermagnetic spin-momentum locking. We demonstrate an extraordinary spin-splitting mechanism in altermagnetic bands originating from a local electric crystal field, which contrasts with the conventional magnetic or relativistic splitting by global magnetization or inversion asymmetry. Based on first-principles calculations, we identify altermagnetic candidates ranging from insulators and metals to a parent crystal of cuprate superconductor. Our results underpin emerging research of quantum phases and spintronics in high-temperature magnets with light elements, vanishing net magnetization, and strong spin-coherence.