With a paper published in the 19 February 2025 issue of Nature[1],Microsoft(Redmond,WA,USA)fanned the flames of its unique vision for quantum computing:a stable,error-resistant qubit based on the Majorana fermion,one ...With a paper published in the 19 February 2025 issue of Nature[1],Microsoft(Redmond,WA,USA)fanned the flames of its unique vision for quantum computing:a stable,error-resistant qubit based on the Majorana fermion,one of the strangest and most elusive particles in physics.The Microsoft Azure Quantum research team’s descriptions of a means to detect the as-yet theoretical particles[1]—called“an entirely new state of matter”by Microsoft’s chief executive officer[2]—and a design for a chip powered by them(Fig.1)[3]have refocused attention on the company’s ambition to build a topological quantum computer.The approach—if it works—could potentially leapfrog every other in the field.展开更多
The anomalous dimensions of the quantum fields are the Hausdorff dimensiongrad. The present candidate of the renormalization constant is the generalized Cantor discontinuum. The Hausdorff dimensiongrad of the Minkowsk...The anomalous dimensions of the quantum fields are the Hausdorff dimensiongrad. The present candidate of the renormalization constant is the generalized Cantor discontinuum. The Hausdorff dimensiongrad of the Minkowski space time is based upon the point set with σ-length on light cone.展开更多
We present a protocol to realize topological discrete-time quantum walks,which comprise a sequence of spindependent flipping displacement operations and quantum coin tossing operations,with a single trapped ion.It is ...We present a protocol to realize topological discrete-time quantum walks,which comprise a sequence of spindependent flipping displacement operations and quantum coin tossing operations,with a single trapped ion.It is demonstrated that the information of bulk topological invariants can be extracted by measuring the average projective phonon number when the walk takes place in coherent state space.Interestingly,the specific chiral symmetry owned by our discrete-time quantum walks simplifies the measuring process.Furthermore,we prove the robustness of such bulk topological invariants by introducing dynamical disorder and decoherence.Our work provides a simple method to measure bulk topological features in discrete-time quantum walks,which can be experimentally realized in the system of single trapped ions.展开更多
One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the...One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist.展开更多
In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental po...In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental polygons of the corresponding universal covering spaces. This is not the view from different perspectives of an observer who simply uses different coordinate systems to describe the same physical phenomenon but rather possible geometric and topological structures that quantum particles are endowed with when they are identified with differentiable manifolds that are embedded or immersed in Euclidean spaces of higher dimension. We present our discussions in the form of Bohr model in one, two and three dimensions using linear wave equations. In one dimension, the fundamental polygon is an interval and the universal covering space is the straight line and in this case the standing wave on a finite string is transformed into the standing wave on a circle which can be applied into the Bohr model of the hydrogen atom. In two dimensions, the fundamental polygon is a square and the universal covering space is the plane and in this case, the standing wave on the square is transformed into the standing wave on different surfaces that can be formed by gluing opposite sides of the square, which include a 2-sphere, a 2-torus, a Klein bottle and a projective plane. In three dimensions, the fundamental polygon is a cube and the universal covering space is the three-dimensional Euclidean space. It is shown that a 3-torus and the manifold K?× S1?defined as the product of a Klein bottle and a circle can be constructed by gluing opposite faces of a cube. Therefore, in three-dimensions, the standing wave on a cube is transformed into the standing wave on a 3-torus or on the manifold K?× S1. We also suggest that the mathematical degeneracy may play an important role in quantum dynamics and be associated with the concept of wavefunction collapse in quantum mechanics.展开更多
Since topological quantum materials may possess interesting properties and promote the application of electronic devices,the search for new topological quantum materials has become the focus and frontier of condensed ...Since topological quantum materials may possess interesting properties and promote the application of electronic devices,the search for new topological quantum materials has become the focus and frontier of condensed matter physics.Currently,it has been found that there are two interesting systems in topological quantum materials:topological superconducting materials and topological magnetic materials.Although research on these materials has made rapid progress,a systematic review of their synthesis,properties,and applications,particularly their synthesis,is still lacking.In this paper,we emphasize the experimental preparation of two typical topological quantum materials and then briefly introduce their potential physical properties and applications.Finally,we provide insights into current and future issues in the study of topological quantum material systems.展开更多
We theoretically investigate the single- and few-electron states in deformed HgTe quantum dots （QDs） with an inverted band structure using the full configuration interaction method. For the circular and deformed QD,...We theoretically investigate the single- and few-electron states in deformed HgTe quantum dots （QDs） with an inverted band structure using the full configuration interaction method. For the circular and deformed QD, it is found that the energy of edge states is robust against the shape from the circular QD in various elliptic ones. For the few electron states, electrons will firstly fill the edge states localized at the short axis, then the states localized at the long axis of the QD before filling the bulk states. The filling of the edge states can be controlled by tuning the dot size or the deformation of the geometry of the HgTe QD, respectively.展开更多
Topological crystalline insulators （TCIs） have attracted worldwide interest since their theoretical predication and have created exciting opportunities for studying topological quantum physics and for exploring spin...Topological crystalline insulators （TCIs） have attracted worldwide interest since their theoretical predication and have created exciting opportunities for studying topological quantum physics and for exploring spintronic appli- cations. In this work, we successfully synthesize PbTe nanowires via the chemical vapor deposition method and demonstrate the existence of topological surface states by their 2D weak anti-localization effect and Shubnikov-de Haas oscillations. More importantly, the surface state contributes ~61% of the total conduction, suggesting dom- inant surface transport in PbTe nanowires at low temperatures. Our work provides an experimental groundwork for researching TCIs and is a step forward for the applications of PbTe nanowires in spintronic devices.展开更多
Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topologica...Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases.It is a fundamental challenge to realize quantum transition between Z_2 nontrivial topological insulator（TI） and topological crystalline insulator（TCI） in one material because Z_2 TI and TCI have different requirements on the number of band inversions. The Z_2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe_2 alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z_2 TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.展开更多
Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connectio...Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory and topological phases of matter, which distinguishes them from other classes of topological insulators. Here, we implement a model Hamiltonian for Hopf insulators in a solid-state quantum simulator and report the first experimental observation of their topological properties, including nontrivial topological links associated with the Hopf fibration and the integer-valued topological invariant obtained from a direct tomographic measurement. Our observation of topological links and Hopf fibration in a quantum simulator opens the door to probe rich topological properties of Hopf insulators in experiments. The quantum simulation and probing methods are also applicable to the study of other intricate three-dimensional topological model Hamiltonians.展开更多
Ferroelectric topological insulators realized in heterostructures of two topologically trivial two-dimensional materials have recently attracted significant interest. Using first-principles calculations combined with ...Ferroelectric topological insulators realized in heterostructures of two topologically trivial two-dimensional materials have recently attracted significant interest. Using first-principles calculations combined with topological quantum chemistry, we investigate bilayer α-In_(2) Se_(3)(2 L-In_(2) Se_(3)) in van der Waals heterostructures with XSe(X = Ga, In, Tl) substrates within space group P 3m1(No. 156). We show that the emergence of ferroelectricity-driven topological phase transitions in these systems is dictated by fundamental symmetry principles rather than material-specific effects. The band bending at the XSe/2 L-In_(2) Se_(3) interface enables topological band inversions, with higher-electron-affinity substrates such as GaSe and TlSe favoring the transition. Remarkably, GaSe/2 L-In_(2) Se_(3) exhibits a reversible transition between topological and trivial insulating phases upon polarization switching, while TlSe/2 L-In_(2) Se_(3) undergoes sequential transitions from a topological insulator to a trivial insulator and eventually to a metallic state. This multistate manipulation highlights a viable route for designing tunable, low-power, multi-functional electronic devices.展开更多
Solid-state quantum computation station belongs to the group 2 of manipulation of quantum state in the Synergetic Extreme Condition User Facility. Here we will first outline the research background, aspects, and objec...Solid-state quantum computation station belongs to the group 2 of manipulation of quantum state in the Synergetic Extreme Condition User Facility. Here we will first outline the research background, aspects, and objectives of the station, followed by a discussion of the recent scientific as well as technological progress in this field based on similar experimental facilities to be constructed in the station. Finally, a brief summary and research perspective will be presented.展开更多
Topological quantum states have attracted great attention both theoretically and experimentally.Here,we show that the momentum-space lattice allows us to couple two Su-Schrieffer-Heeger(SSH)chains with opposite dimeri...Topological quantum states have attracted great attention both theoretically and experimentally.Here,we show that the momentum-space lattice allows us to couple two Su-Schrieffer-Heeger(SSH)chains with opposite dimerizations and staggered interleg hoppings.The coupled SSH chain is a four-band model which has sublattice symmetry similar to the SSH4.Interestingly,the topological edge states occupy two sublattices at the same time,which can be regarded as a one-dimension analogue of the type-II corner state.The analytical expressions of the edge states are also obtained by solving the eigenequations.Finally,we provide a possible experimental scheme to detect the topological winding number and corresponding edge states.展开更多
Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum co...Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum computer. For this new topological stabilizer code-XYZ^(2) code defined on the cellular lattice, it is implemented on a hexagonal lattice of qubits and it encodes the logical qubits with the help of stabilizer measurements of weight six and weight two. However topological stabilizer codes in cellular lattice quantum systems suffer from the detrimental effects of noise due to interaction with the environment. Several decoding approaches have been proposed to address this problem. Here, we propose the use of a state-attention based reinforcement learning decoder to decode XYZ^(2) codes, which enables the decoder to more accurately focus on the information related to the current decoding position, and the error correction accuracy of our reinforcement learning decoder model under the optimisation conditions can reach 83.27% under the depolarizing noise model, and we have measured thresholds of 0.18856 and 0.19043 for XYZ^(2) codes at code spacing of 3–7 and 7–11, respectively. our study provides directions and ideas for applications of decoding schemes combining reinforcement learning attention mechanisms to other topological quantum error-correcting codes.展开更多
Two-dimensional topological insulators(2DTIs)have attracted increasing attention during the past few years.New 2DTIs with increasing larger spin-orbit coupling(SOC)gaps have been predicted by theoretical calculations ...Two-dimensional topological insulators(2DTIs)have attracted increasing attention during the past few years.New 2DTIs with increasing larger spin-orbit coupling(SOC)gaps have been predicted by theoretical calculations and some of them have been synthesized experimentally.In this review,the 2DTIs,ranging from single element graphene-like materials to bi-elemental transition metal chalcogenides(TMDs)and to multi-elemental materials,with different thicknesses,structures,and phases,have been summarized and discussed.The topological properties(especially the quantum spin Hall effect and Dirac fermion feature)and potential applications have been summarized.This review also points out the challenge and opportunities for future 2DTI study,especially on the device applications based on the topological properties.展开更多
A recent research reports on chip-fiber-chip quantum teleportation of time-bin-encoded qubits over a 12.3 km optical fiber link within a star-topology quantum network,composed of an on-chip accommodated user node,rela...A recent research reports on chip-fiber-chip quantum teleportation of time-bin-encoded qubits over a 12.3 km optical fiber link within a star-topology quantum network,composed of an on-chip accommodated user node,relay node and a central node.An active feedback optimization scheme is embedded to ensure highly stable Bell state measurements.展开更多
Kitaev model has both Abelian and non-Abelian anyonic excitations. It can act as a starting point for topological quantum compu- tation. However, this model Hamiltonian is difficult to implement in natural condensed m...Kitaev model has both Abelian and non-Abelian anyonic excitations. It can act as a starting point for topological quantum compu- tation. However, this model Hamiltonian is difficult to implement in natural condensed matter systems. Here we propose a quantum simulation scheme by constructing the Kitaev model Hamiltonian in a lattice of coupled cavities with embedded A-type three-level atoms. In this scheme, several parameters are tunable, for example, via external laser fields. Importantly, our scheme is based on currently existing technologies and it provides a feasible way of realizing the Kitaev model to explore topological excitations.展开更多
In this contribution results from different disciplines of science were compared to show their intimate interweaving with each other having in common the golden ratio <span style="font-family:Verdana;">...In this contribution results from different disciplines of science were compared to show their intimate interweaving with each other having in common the golden ratio <span style="font-family:Verdana;">φ<span style="font-family:Verdana;"> respectively its fifth power <span style="font-family:Verdana;">φ<sup><span style="font-family:Verdana;">5</sup><span style="font-family:Verdana;">. The research fields cover model calculations of statistical physics associated with phase transitions, the quantum probability of two particles, new physics of everything suggested by the information relativity theory (<span style="font-family:Verdana;">IRT<span style="font-family:Verdana;">) including explanations of cosmological relevance, the <span style="font-family:Verdana;">ε<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-<span style="font-family:;" "=""><span style="font-family:Verdana;">infinity theory, superconductivity, and the <span style="font-family:Verdana;">Tammes<span style="font-family:Verdana;"> problem of the largest diameter of <span style="font-family:Verdana;">N<span style="font-family:Verdana;"> non-overlapping circles on the surface of a sphere with its connection to viral morphology and crystallography. Finally, <span style="font-family:Verdana;">Fibo<span style="font-family:Verdana;">nacci<span style="font-family:Verdana;"> anyons proposed for topological quantum<span style="font-family:Verdana;"> computation (<span style="font-family:Verdana;">TQC<span style="font-family:Verdana;">) were briefly described in comparison to the recently formulated reverse <span style="font-family:Verdana;">Fibonacci<span style="font-family:Verdana;"> approach using the <span style="font-family:Verdana;">Jani<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="white-space:nowrap;">čko<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> number sequence. An architecture applicable for a quantum computer is proposed consisting of 13-step twisted microtubules similar to tubulin microtubules of living matter. Most topics point to the omnipresence of the golden mean as the numerical dominator of our world.展开更多
Majorana quantum computation offers a potential approach to securely manipulating and storing quantum data in a topological manner that may effectively resist the decoherence induced by local noise. However, actual Ma...Majorana quantum computation offers a potential approach to securely manipulating and storing quantum data in a topological manner that may effectively resist the decoherence induced by local noise. However, actual Majorana qubit setups are susceptible to noise. In this study, from a quantum dynamics perspective, we develop a noise model for Majorana qubits that accounts for quasi-particle poisoning and Majorana overlapping with fluctuation. Furthermore, we focus on Majorana parity readout methodologies, specifically those leveraging an ancillary quantum dot, and carry out an indepth exploration of continuous measurement techniques founded on the quantum jump model of a quantum point contact.Utilizing these methodologies, we proceed to analyze the influence of noise on the afore-mentioned noise model, employing numerical computation to evaluate the power spectrum and frequency curve. In the culmination of our study, we put forward a strategy to benchmark the presence and detailed properties of noise in Majorana qubits.展开更多
We study the possibility to realize a Majorana zero mode that is robust and may be easily manipulated for braiding in quantum computing in the ground state of the Kitaev model in this work.To achieve this we first app...We study the possibility to realize a Majorana zero mode that is robust and may be easily manipulated for braiding in quantum computing in the ground state of the Kitaev model in this work.To achieve this we first apply a uniform[111]magnetic field to the gapless Kitaev model and turn the Kitaev model to an effective p+ip topological superconductor of spinons.We then study possible vortex binding in such system to a topologically trivial spot in the ground state.We consider two cases in the system:one is a vacancy and the other is a fully polarized spin.We show that in both cases,the system binds a vortex with the defect and a robust Majorana zero mode in the ground state at a weak uniform[111]magnetic field.The distribution and asymptotic behavior of these Majorana zero modes are studied.The Majorana zero modes in both cases decay exponentially in space,and are robust against local perturbations and other Majorana zero modes far away,which makes them promising candidates for braiding in topological quantum computing.展开更多
文摘With a paper published in the 19 February 2025 issue of Nature[1],Microsoft(Redmond,WA,USA)fanned the flames of its unique vision for quantum computing:a stable,error-resistant qubit based on the Majorana fermion,one of the strangest and most elusive particles in physics.The Microsoft Azure Quantum research team’s descriptions of a means to detect the as-yet theoretical particles[1]—called“an entirely new state of matter”by Microsoft’s chief executive officer[2]—and a design for a chip powered by them(Fig.1)[3]have refocused attention on the company’s ambition to build a topological quantum computer.The approach—if it works—could potentially leapfrog every other in the field.
文摘The anomalous dimensions of the quantum fields are the Hausdorff dimensiongrad. The present candidate of the renormalization constant is the generalized Cantor discontinuum. The Hausdorff dimensiongrad of the Minkowski space time is based upon the point set with σ-length on light cone.
基金Project supported by the National Key R&D Program of China(Grant No.2017YFA0304203)the National Natural National Science Foundation of China(Grant Nos.11604392 and 11674200)+1 种基金the Changjiang Scholars and Innovative Research Team in Universities of Ministry of Education of China(Grant No.IRT 17R70)the Fund for Shanxi“1331 Project”Key Subjects Construction,and the 111 Project,China(Grant No.D18001).
文摘We present a protocol to realize topological discrete-time quantum walks,which comprise a sequence of spindependent flipping displacement operations and quantum coin tossing operations,with a single trapped ion.It is demonstrated that the information of bulk topological invariants can be extracted by measuring the average projective phonon number when the walk takes place in coherent state space.Interestingly,the specific chiral symmetry owned by our discrete-time quantum walks simplifies the measuring process.Furthermore,we prove the robustness of such bulk topological invariants by introducing dynamical disorder and decoherence.Our work provides a simple method to measure bulk topological features in discrete-time quantum walks,which can be experimentally realized in the system of single trapped ions.
基金the Natural Science Foundation of Anhui Province,China(Grant No.2208085MA11)the National Natural Science Foundation of China(Grants Nos.11974356,12274414,and U1832209)。
文摘One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist.
文摘In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental polygons of the corresponding universal covering spaces. This is not the view from different perspectives of an observer who simply uses different coordinate systems to describe the same physical phenomenon but rather possible geometric and topological structures that quantum particles are endowed with when they are identified with differentiable manifolds that are embedded or immersed in Euclidean spaces of higher dimension. We present our discussions in the form of Bohr model in one, two and three dimensions using linear wave equations. In one dimension, the fundamental polygon is an interval and the universal covering space is the straight line and in this case the standing wave on a finite string is transformed into the standing wave on a circle which can be applied into the Bohr model of the hydrogen atom. In two dimensions, the fundamental polygon is a square and the universal covering space is the plane and in this case, the standing wave on the square is transformed into the standing wave on different surfaces that can be formed by gluing opposite sides of the square, which include a 2-sphere, a 2-torus, a Klein bottle and a projective plane. In three dimensions, the fundamental polygon is a cube and the universal covering space is the three-dimensional Euclidean space. It is shown that a 3-torus and the manifold K?× S1?defined as the product of a Klein bottle and a circle can be constructed by gluing opposite faces of a cube. Therefore, in three-dimensions, the standing wave on a cube is transformed into the standing wave on a 3-torus or on the manifold K?× S1. We also suggest that the mathematical degeneracy may play an important role in quantum dynamics and be associated with the concept of wavefunction collapse in quantum mechanics.
基金supported by National Natural Science Foundation of China(52373309).
文摘Since topological quantum materials may possess interesting properties and promote the application of electronic devices,the search for new topological quantum materials has become the focus and frontier of condensed matter physics.Currently,it has been found that there are two interesting systems in topological quantum materials:topological superconducting materials and topological magnetic materials.Although research on these materials has made rapid progress,a systematic review of their synthesis,properties,and applications,particularly their synthesis,is still lacking.In this paper,we emphasize the experimental preparation of two typical topological quantum materials and then briefly introduce their potential physical properties and applications.Finally,we provide insights into current and future issues in the study of topological quantum material systems.
基金Supported by the National Natural Science Foundation of China under Grant No 11434010the National Basic Research Program of China under Grant No 2011CB922204
文摘We theoretically investigate the single- and few-electron states in deformed HgTe quantum dots （QDs） with an inverted band structure using the full configuration interaction method. For the circular and deformed QD, it is found that the energy of edge states is robust against the shape from the circular QD in various elliptic ones. For the few electron states, electrons will firstly fill the edge states localized at the short axis, then the states localized at the long axis of the QD before filling the bulk states. The filling of the edge states can be controlled by tuning the dot size or the deformation of the geometry of the HgTe QD, respectively.
基金Supported by the National Key Research and Development Program of China under Grant No 2016YFA0300803the National Basic Research Program of China under Grant No 2014CB921101the National Natural Science Foundation of China under Grant Nos 61474061 and 61674079
文摘Topological crystalline insulators （TCIs） have attracted worldwide interest since their theoretical predication and have created exciting opportunities for studying topological quantum physics and for exploring spintronic appli- cations. In this work, we successfully synthesize PbTe nanowires via the chemical vapor deposition method and demonstrate the existence of topological surface states by their 2D weak anti-localization effect and Shubnikov-de Haas oscillations. More importantly, the surface state contributes ~61% of the total conduction, suggesting dom- inant surface transport in PbTe nanowires at low temperatures. Our work provides an experimental groundwork for researching TCIs and is a step forward for the applications of PbTe nanowires in spintronic devices.
基金Supported by the Major State Basic Research Development Program of China under Grant No 2016YFB0700700the National Natural Science Foundation of China(NSFC)under Grants Nos 11634003,11474273,61121491 and U1530401+1 种基金supported by the National Young 1000 Talents Plansupported by the Youth Innovation Promotion Association of CAS(2017154)
文摘Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases.It is a fundamental challenge to realize quantum transition between Z_2 nontrivial topological insulator（TI） and topological crystalline insulator（TCI） in one material because Z_2 TI and TCI have different requirements on the number of band inversions. The Z_2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe_2 alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z_2 TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.
基金supported by the grants from the Ministry of Science and Technology of Chinathe Ministry of Education+2 种基金support from the ARL and the AFOSR MURI programssupported by JQI-NSF-PFCLPS-MPO-CMTC
文摘Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory and topological phases of matter, which distinguishes them from other classes of topological insulators. Here, we implement a model Hamiltonian for Hopf insulators in a solid-state quantum simulator and report the first experimental observation of their topological properties, including nontrivial topological links associated with the Hopf fibration and the integer-valued topological invariant obtained from a direct tomographic measurement. Our observation of topological links and Hopf fibration in a quantum simulator opens the door to probe rich topological properties of Hopf insulators in experiments. The quantum simulation and probing methods are also applicable to the study of other intricate three-dimensional topological model Hamiltonians.
基金supported by the National Natural Science Foundation of China (Grant Nos.11874141,12174059,and 11604134)。
文摘Ferroelectric topological insulators realized in heterostructures of two topologically trivial two-dimensional materials have recently attracted significant interest. Using first-principles calculations combined with topological quantum chemistry, we investigate bilayer α-In_(2) Se_(3)(2 L-In_(2) Se_(3)) in van der Waals heterostructures with XSe(X = Ga, In, Tl) substrates within space group P 3m1(No. 156). We show that the emergence of ferroelectricity-driven topological phase transitions in these systems is dictated by fundamental symmetry principles rather than material-specific effects. The band bending at the XSe/2 L-In_(2) Se_(3) interface enables topological band inversions, with higher-electron-affinity substrates such as GaSe and TlSe favoring the transition. Remarkably, GaSe/2 L-In_(2) Se_(3) exhibits a reversible transition between topological and trivial insulating phases upon polarization switching, while TlSe/2 L-In_(2) Se_(3) undergoes sequential transitions from a topological insulator to a trivial insulator and eventually to a metallic state. This multistate manipulation highlights a viable route for designing tunable, low-power, multi-functional electronic devices.
文摘Solid-state quantum computation station belongs to the group 2 of manipulation of quantum state in the Synergetic Extreme Condition User Facility. Here we will first outline the research background, aspects, and objectives of the station, followed by a discussion of the recent scientific as well as technological progress in this field based on similar experimental facilities to be constructed in the station. Finally, a brief summary and research perspective will be presented.
基金Project partially supported by the National Natural Science Foundation of China (Grant Nos. 12034012, 12074232, and 11804204)1331KSC
文摘Topological quantum states have attracted great attention both theoretically and experimentally.Here,we show that the momentum-space lattice allows us to couple two Su-Schrieffer-Heeger(SSH)chains with opposite dimerizations and staggered interleg hoppings.The coupled SSH chain is a four-band model which has sublattice symmetry similar to the SSH4.Interestingly,the topological edge states occupy two sublattices at the same time,which can be regarded as a one-dimension analogue of the type-II corner state.The analytical expressions of the edge states are also obtained by solving the eigenequations.Finally,we provide a possible experimental scheme to detect the topological winding number and corresponding edge states.
基金supported by the Natural Science Foundation of Shandong Province,China (Grant No. ZR2021MF049)Joint Fund of Natural Science Foundation of Shandong Province (Grant Nos. ZR2022LLZ012 and ZR2021LLZ001)。
文摘Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum computer. For this new topological stabilizer code-XYZ^(2) code defined on the cellular lattice, it is implemented on a hexagonal lattice of qubits and it encodes the logical qubits with the help of stabilizer measurements of weight six and weight two. However topological stabilizer codes in cellular lattice quantum systems suffer from the detrimental effects of noise due to interaction with the environment. Several decoding approaches have been proposed to address this problem. Here, we propose the use of a state-attention based reinforcement learning decoder to decode XYZ^(2) codes, which enables the decoder to more accurately focus on the information related to the current decoding position, and the error correction accuracy of our reinforcement learning decoder model under the optimisation conditions can reach 83.27% under the depolarizing noise model, and we have measured thresholds of 0.18856 and 0.19043 for XYZ^(2) codes at code spacing of 3–7 and 7–11, respectively. our study provides directions and ideas for applications of decoding schemes combining reinforcement learning attention mechanisms to other topological quantum error-correcting codes.
基金Project supported by the Beijing Natural Science Foundation,China(Grant Nos.Z190006 and 4192054)the National Natural Science Foundation of China(Grant Nos.61971035,61901038,and 61725107)+1 种基金Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB30000000)Beijing Institute of Technology Research Fund Program for Young Scholars(Grant No.3050011181814).
文摘Two-dimensional topological insulators(2DTIs)have attracted increasing attention during the past few years.New 2DTIs with increasing larger spin-orbit coupling(SOC)gaps have been predicted by theoretical calculations and some of them have been synthesized experimentally.In this review,the 2DTIs,ranging from single element graphene-like materials to bi-elemental transition metal chalcogenides(TMDs)and to multi-elemental materials,with different thicknesses,structures,and phases,have been summarized and discussed.The topological properties(especially the quantum spin Hall effect and Dirac fermion feature)and potential applications have been summarized.This review also points out the challenge and opportunities for future 2DTI study,especially on the device applications based on the topological properties.
文摘A recent research reports on chip-fiber-chip quantum teleportation of time-bin-encoded qubits over a 12.3 km optical fiber link within a star-topology quantum network,composed of an on-chip accommodated user node,relay node and a central node.An active feedback optimization scheme is embedded to ensure highly stable Bell state measurements.
基金supported by the National Basic Research Program of China(Grant No. 2009CB929302)the National Natural Science Foundation of China (Grant No. 91121015)+1 种基金the Ministry of Education of China (GrantNo. B06011)the U.S. National Science Foundation (Grant No. PHY-0925174)
文摘Kitaev model has both Abelian and non-Abelian anyonic excitations. It can act as a starting point for topological quantum compu- tation. However, this model Hamiltonian is difficult to implement in natural condensed matter systems. Here we propose a quantum simulation scheme by constructing the Kitaev model Hamiltonian in a lattice of coupled cavities with embedded A-type three-level atoms. In this scheme, several parameters are tunable, for example, via external laser fields. Importantly, our scheme is based on currently existing technologies and it provides a feasible way of realizing the Kitaev model to explore topological excitations.
文摘In this contribution results from different disciplines of science were compared to show their intimate interweaving with each other having in common the golden ratio <span style="font-family:Verdana;">φ<span style="font-family:Verdana;"> respectively its fifth power <span style="font-family:Verdana;">φ<sup><span style="font-family:Verdana;">5</sup><span style="font-family:Verdana;">. The research fields cover model calculations of statistical physics associated with phase transitions, the quantum probability of two particles, new physics of everything suggested by the information relativity theory (<span style="font-family:Verdana;">IRT<span style="font-family:Verdana;">) including explanations of cosmological relevance, the <span style="font-family:Verdana;">ε<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-<span style="font-family:;" "=""><span style="font-family:Verdana;">infinity theory, superconductivity, and the <span style="font-family:Verdana;">Tammes<span style="font-family:Verdana;"> problem of the largest diameter of <span style="font-family:Verdana;">N<span style="font-family:Verdana;"> non-overlapping circles on the surface of a sphere with its connection to viral morphology and crystallography. Finally, <span style="font-family:Verdana;">Fibo<span style="font-family:Verdana;">nacci<span style="font-family:Verdana;"> anyons proposed for topological quantum<span style="font-family:Verdana;"> computation (<span style="font-family:Verdana;">TQC<span style="font-family:Verdana;">) were briefly described in comparison to the recently formulated reverse <span style="font-family:Verdana;">Fibonacci<span style="font-family:Verdana;"> approach using the <span style="font-family:Verdana;">Jani<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="white-space:nowrap;">čko<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> number sequence. An architecture applicable for a quantum computer is proposed consisting of 13-step twisted microtubules similar to tubulin microtubules of living matter. Most topics point to the omnipresence of the golden mean as the numerical dominator of our world.
基金supported by the Innovation Program for Quantum Science and Technology (Grant No.2021ZD0302400)the National Natural Science Foundation of China (Grants No.11974198)the Natural Science Foundation of Shandong Province of China (Grant No.ZR2021MA091)。
文摘Majorana quantum computation offers a potential approach to securely manipulating and storing quantum data in a topological manner that may effectively resist the decoherence induced by local noise. However, actual Majorana qubit setups are susceptible to noise. In this study, from a quantum dynamics perspective, we develop a noise model for Majorana qubits that accounts for quasi-particle poisoning and Majorana overlapping with fluctuation. Furthermore, we focus on Majorana parity readout methodologies, specifically those leveraging an ancillary quantum dot, and carry out an indepth exploration of continuous measurement techniques founded on the quantum jump model of a quantum point contact.Utilizing these methodologies, we proceed to analyze the influence of noise on the afore-mentioned noise model, employing numerical computation to evaluate the power spectrum and frequency curve. In the culmination of our study, we put forward a strategy to benchmark the presence and detailed properties of noise in Majorana qubits.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11974166 and 11574134).
文摘We study the possibility to realize a Majorana zero mode that is robust and may be easily manipulated for braiding in quantum computing in the ground state of the Kitaev model in this work.To achieve this we first apply a uniform[111]magnetic field to the gapless Kitaev model and turn the Kitaev model to an effective p+ip topological superconductor of spinons.We then study possible vortex binding in such system to a topologically trivial spot in the ground state.We consider two cases in the system:one is a vacancy and the other is a fully polarized spin.We show that in both cases,the system binds a vortex with the defect and a robust Majorana zero mode in the ground state at a weak uniform[111]magnetic field.The distribution and asymptotic behavior of these Majorana zero modes are studied.The Majorana zero modes in both cases decay exponentially in space,and are robust against local perturbations and other Majorana zero modes far away,which makes them promising candidates for braiding in topological quantum computing.
