arXiv subjects

Tzu-Chieh Wei

Publications and source records attributed to Tzu-Chieh Wei.

At least 55 records · Page 3Linked to original sources

arXiv2024

Tensor Network Methods for Extracting CFT Data from Fixed-Point Tensors and Defect Coarse Graining

We present a comprehensive study on the extraction of CFT data using tensor network methods, specially, from the fixed-point tensor of the linearized tensor renormalization group (lTRG) for the 2D classical Ising model near the critical temperature. Utilizing two different methods, we extract operator scaling dimensions and operator-product-expansion (OPE) coefficients by introducing defects on the lattice and by employing the fixed-point tensor. We also explore the effects of point-like defects in the lattice on the coarse-graining process. We find that there is a correspondence between coarse-grained defect tensors and conformal states obtained from lTRG fixed-point equation. We also analyze the capabilities and limitations of our proposed coarse-graining scheme for tensor networks with point-like defects, which includes graph independent local truncation (GILT) and higher-order tensor renormalization group (HOTRG). Our results provide a better understanding of the capacity and limitations of the tenor renormalization group scheme in coarse-graining defect tensors, and we show that GILT+HOTRG can be used to give accurate two- and four-point functions under specific conditions. We also find that employing the minimal canonical form further improves the stability of the RG flow.

cond-mat.stat-mech↗

arXiv2023

An Improved Method for Quantum Matrix Multiplication

Following the celebrated quantum algorithm for solving linear equations (so-called HHL algorithm), Childs, Kothari and Somma [SIAM Journal on Computing, {\bf 46}: 1920, (2017)] provided an approach to solve a linear system of equations with exponentially improved dependence on precision. In this note, we aim to complement such a result for applying a matrix to some quantum state, based upon their Chebyshev polynomial approach. A few examples that motivate this application are included and we further discuss an application of this improved matrix application algorithm explicitly with an efficient quantum procedure.

quant-ph↗

arXiv2023

Measuring Topological Field Theories: Lattice Models and Field-Theoretic Description

Recent years have witnessed a surge of interest in performing measurements within topological phases of matter, e.g., symmetry-protected topological (SPT) phases and topological orders. Notably, measurements of certain SPT states have been known to be related to Kramers-Wannier duality and Jordan-Wigner transformations, giving rise to long-range entangled states and invertible phases, such as the Kitaev chain. Moreover, measurements of topologically ordered states correspond to charge condensations. In this work, we present a field-theoretic framework for describing measurements within topological field theories. We employ various lattice models as examples to illustrate the outcomes of measuring local symmetry operators within topological phases, demonstrating their agreement with the predictions from field-theoretic descriptions. We demonstrate that these measurements can lead to SPT, spontaneous symmetry-breaking, and topologically ordered phases. Specifically, when there is emergent symmetry after measurement, the remaining symmetry and emergent symmetry will have a mixed anomaly, which leads to long-ranged entanglement.

cond-mat.str-el↗

arXiv2023

Learning marginals suffices!

Beyond computer science, quantum complexity theory can potentially revolutionize multiple branches of physics, ranging from quantum many-body systems to quantum field theory. In this paper, we investigate the relationship between the sample complexity of learning a quantum state and the circuit complexity of the state. The circuit complexity of a quantum state refers to the minimum depth of the quantum circuit necessary to implement it. We show that learning its marginals for the quantum state with low circuit complexity suffices for state tomography, thus breaking the exponential barrier of the sample complexity for quantum state tomography. Our proof is elementary and overcomes difficulties characterizing short-range entanglement by bridging quantum circuit complexity and ground states of gapped local Hamiltonians. Our result, for example, settles the quantum circuit complexity of the multi-qubit GHZ state exactly.

quant-ph↗

arXiv2023

Quantum Algorithm For Estimating Eigenvalue

A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance these computational tasks, and in some cases, such as solving linear equations, can be shown to yield exponential speedup. Here, employing the techniques in the HHL algorithm and the ideas of the classical power method, we provide a simple quantum algorithm for estimating the largest eigenvalue in magnitude of a given Hermitian matrix. As in the case of the HHL algorithm, our quantum procedure can also yield exponential speedup compared to classical algorithms that solve the same problem. We also discuss a few possible extensions and applications of our quantum algorithm, such as a version of a hybrid quantum-classical Lanczos algorithm.

quant-ph↗

arXiv2023

In search of a many-body mobility edge with matrix product states in a Generalized Aubry-André model with interactions

We investigate the possibility of a many-body mobility edge in the generalized Aubry-André (GAA) model with interactions using the Shift-Invert Matrix Product States (SIMPS) algorithm [Phys. Rev. Lett. 118, 017201 (2017)]. The non-interacting GAA model is a one-dimensional quasiperiodic model with a self-duality-induced mobility edge. To search for a many-body mobility edge in the interacting case, we exploit the advantages of SIMPS that it targets many-body states in an energy-resolved fashion and does not require all many-body states to be localized for some to converge. Our analysis indicates that the targeted states in the presence of the single-particle mobility edge match neither `MBL-like' fully-converged localized states nor the fully delocalized case where SIMPS fails to converge. We benchmark the algorithm's output both for parameters that give fully converged, `MBL-like' localized states and for delocalized parameters where SIMPS fails to converge. In the intermediate cases, where the parameters produce a single-particle mobility edge, we find many-body states that develop entropy oscillations as a function of cut position at larger bond dimensions. These oscillations at larger bond dimensions, which are also found in the fully-localized benchmark but not the fully-delocalized benchmark, occur both at the band edge and center and may indicate convergence to a non-thermal state (either localized or critical).

cond-mat.dis-nn↗

arXiv2023

Symmetry-enriched topological order from partially gauging symmetry-protected topologically ordered states assisted by measurements

Symmetry protected topological phases exhibit nontrivial short-ranged entanglement protected by symmetry and cannot be adiabatically connected to trivial product states while preserving the symmetry. In contrast, intrinsic topological phases do not need ordinary symmetry to stabilize them and their ground states exhibit long-range entanglement. It is known that for a given symmetry group $G$, the 2D SPT phase protected by $G$ is dual to the 2D topological phase exemplified by the twisted quantum double model $D^ω(G)$ via gauging the global symmetry $G$. Recently it was realized that such a general gauging map can be implemented by some local unitaries and local measurements when $G$ is a finite, solvable group. Here, we review the general approach to gauging a $G$-SPT starting from a fixed-point ground-state wave function and applying a $N$-step gauging procedure. We provide an in-depth analysis of the intermediate states emerging during the N-step gauging and provide tools to measure and identify the emerging symmetry-enriched topological order of these states. We construct the generic lattice parent Hamiltonians for these intermediate states, and show that they form an entangled superposition of a twisted quantum double with an SPT ordered state. Notably, we show that they can be connected to the TQD through a finite-depth, local quantum circuit which does not respect the global symmetry of the SET order. We introduce the so-called symmetry branch line operators and show that they can be used to extract the symmetry fractionalization classes and symmetry defectification classes of the SET phases with the input data $G$ and $[ω]\in H^3(G,U(1))$ of the pre-gauged SPT ordered state. We illustrate the procedure of preparing and characterizing the emerging SET ordered states for some Abelian and non-Abelian examples such as dihedral groups $D_n$ and the quaternion group $Q_8$.

quant-ph↗

arXiv2023

Broadcasting single-qubit and multi-qubit-entangled states: authentication, cryptography, and distributed quantum computation

Quantum entanglement assisted with measurements provides various pathways to communicate information to parties within a network. In this work, we generalize a previous broadcasting protocol and present schemes to broadcast product and multi-partite entangled quantum states, where in the latter case the sender can remotely add phase gates or abort distributing the states. We first focus on the broadcasting of product quantum states in a network, and generalize the basic protocol to include an arbitrary basis rotation and allow for multiple receivers and senders. We show how to add and delete senders from the network. The generalization also includes the case where a phase to be applied to the broadcast states is not known in advance but is provided to a sender encoded in another quantum state. Applications of broadcasting product states include authentication and three-state quantum cryptography. In the second part, we study the distribution of a single multi-qubit state shared among several receivers entangled with multi-qubit phase gates, which includes the graph states as an example. We show that by coordinating with the sender, the receivers can assist in performing remote, distributed measurement-based quantum computation with the Pauli X basis measurement alone. As another application of this, we discuss the distribution of the multi-qubit Greenberger-Horne-Zeilinger state.

quant-ph↗

arXiv2023

Constant-time Quantum Algorithm for Homology Detection in Closed Curves

Given a loop or more generally 1-cycle $r$ of size L on a closed two-dimensional manifold or surface, represented by a triangulated mesh, a question in computational topology asks whether or not it is homologous to zero. We frame and tackle this problem in the quantum setting. Given an oracle that one can use to query the inclusion of edges on a closed curve, we design a quantum algorithm for such a homology detection with a constant running time, with respect to the size or the number of edges on the loop $r$, requiring only a single usage of oracle. In contrast, classical algorithm requires $Ω(L)$ oracle usage, followed by a linear time processing and can be improved to logarithmic by using a parallel algorithm. Our quantum algorithm can be extended to check whether two closed loops belong to the same homology class. Furthermore, it can be applied to a specific problem in the homotopy detection, namely, checking whether two curves are \textit{not} homotopically equivalent on a closed two-dimensional manifold.

quant-ph↗

arXiv2022

Simulating large-size quantum spin chains on cloud-based superconducting quantum computers

Quantum computers have the potential to efficiently simulate large-scale quantum systems for which classical approaches are bound to fail. Even though several existing quantum devices now feature total qubit numbers of more than one hundred, their applicability remains plagued by the presence of noise and errors. Thus, the degree to which large quantum systems can successfully be simulated on these devices remains unclear. Here, we report on cloud simulations performed on several of IBM's superconducting quantum computers to simulate ground states of spin chains having a wide range of system sizes up to one hundred and two qubits. We find that the ground-state energies extracted from realizations across different quantum computers and system sizes reach the expected values to within errors that are small (i.e. on the percent level), including the inference of the energy density in the thermodynamic limit from these values. We achieve this accuracy through a combination of physics-motivated variational Ansatzes, and efficient, scalable energy-measurement and error-mitigation protocols, including the use of a reference state in the zero-noise extrapolation. By using a 102-qubit system, we have been able to successfully apply up to 3186 CNOT gates in a single circuit when performing gate-error mitigation. Our accurate, error-mitigated results for random parameters in the Ansatz states suggest that a standalone hybrid quantum-classical variational approach for large-scale XXZ models is feasible.

quant-ph↗

arXiv2022

Quantum State Transfer: Interplay between Gate and Readout Errors

Quantum networks consist of quantum nodes that are linked by entanglement and quantum information can be transferred from one node to another. Operations can be applied to qubits of local nodes coordinated by classical communication to manipulate quantum states and readout/measurement will be employed to obtain results. Here, we use quantum circuits to simulate quantum state transfer between two nodes connected in a linear geometry through other nodes. We explore the interplay between gate and readout errors on the performance of state transfer. We find that the nominal success probability is not necessarily a monotonic function of the two error rates and employ numerical simulations and analytic tools to understand their interplay.

quant-ph↗

arXiv2022

Broadcast of a restricted set of qubit and qutrit states

The no-cloning theorem forbids the distribution of an unknown state to more than one receiver. However, if the sender knows the state, and the state is chosen from a restricted set of possibilities, a procedure known as remote state preparation can be used to broadcast a state. Here we examine a remote state preparation protocol that can be used to send the state of a qubit, confined to the equator of the Bloch sphere, to an arbitrary number of receivers. The entanglement cost is less than that of using teleportation to accomplish the same task. We present a number of variations on this task, probabilistically sending an unknown qubit state to two receivers, sending different qubit states to two receivers, and sending qutrit states to two receivers. Finally, we discuss some applications of these protocols.

quant-ph↗

arXiv2022

Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors

Topological crystalline superconductors are known to have possible higher-order topology, which results in Majorana modes on $d-2$ or lower-dimensional boundaries. Given the rich possibilities of boundary signatures, it is desirable to have topological invariants that can predict the type of Majorana modes from band structures. Although symmetry indicators, a type of invariant that depends only on the band data at high-symmetry points, have been proposed for certain crystalline superconductors, there exist symmetry classes in which symmetry indicators fail to distinguish superconductors with different Majorana boundaries. Here, we systematically obtain topological invariants for an example of this kind, two-dimensional time-reversal symmetric superconductors with twofold rotational symmetry $C_2$. First, we show that the nontrivial topology is independent of band data on the high-symmetry points by conducting a momentum-space classification study. Then, from the resulting K groups, we derive calculable expressions for four $\mathbb{Z}_2$ invariants defined on high-symmetry lines or general points in the Brillouin zone. Finally, together with a real-space classification study, we establish the bulk-boundary correspondence and show that the four $\mathbb{Z}_2$ invariants can predict Majorana boundary types from band structures. Our proposed invariants can fuel practical material searches for $C_2$-symmetric topological superconductors featuring Majorana edge and corner modes.

cond-mat.supr-con↗

arXiv2022

Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation

Affleck, Kennedy, Lieb, and Tasaki constructed a spin-1 model that is isotropic in spins and possesses a provable finite gap above the ground state more than three decades ago. They also constructed models in two dimensions. Their construction has impacted subsequent research that is still active. In this review article, we review some selected the progresses, such as magnetic ordering of the AKLT models, emerging phases under deforming the AKLT Hamiltonians, symmetry-protected topological order in several AKLT models, their spectral gap, and applications for quantum computation.

cond-mat.str-el↗

arXiv2022

Two-particle States in One-dimensional Coupled Bose-Hubbard Models

We study dynamically coupled one-dimensional Bose-Hubbard models and solve for the wave functions and energies of two-particle eigenstates. Even though the wave functions do not directly follow the form of a Bethe Ansatz, we describe an intuitive construction to express them as combinations of Choy-Haldane states for models with intra- and inter-species interaction. We find that the two-particle spectrum of the system with generic interactions comprises in general four different continua and three doublon dispersions. The existence of doublons depends on the coupling strength $Ω$ between two species of bosons, and their energies vary with $Ω$ and interaction strengths. We give details on one specific limit, i.e., with infinite interaction, and derive the spectrum for all types of two-particle states and their spatial and entanglement properties. We demonstrate the difference in time evolution under different coupling strengths, and examine the relation between the long-time behavior of the system and the doublon dispersion. These dynamics can in principle be observed in cold atoms and might also be simulated by digital quantum computers.

quant-ph↗

arXiv2021

Geometric quantum adiabatic methods for quantum chemistry

Existing quantum algorithms for quantum chemistry work well near the equilibrium geometry of molecules, but the results can become unstable when the chemical bonds are broken at large atomic distances. For any adiabatic approach, this usually leads to serious problems, such as level crossing and/or energy gap closing along the adiabatic evolution path. In this work, we propose a quantum algorithm based on adiabatic evolution to obtain molecular eigenstates and eigenenergies in quantum chemistry, which exploits a smooth geometric deformation by changing bond lengths and bond angles. Even with a simple uniform stretching of chemical bonds, this algorithm performs more stably and achieves better accuracy than our previous adiabatic method [Phys. Rev. Research 3, 013104 (2021)]. It solves the problems related to energy gap closing and level crossing along the adiabatic evolution path at large atomic distances. We demonstrate its utility in several examples, including H${}_2$O, CH${}_2$, and a chemical reaction of H${}_2$+D${}_2\rightarrow$ 2HD. Furthermore, our fidelity analysis demonstrates that even with finite bond length changes, our algorithm still achieves high fidelity with the ground state.

physics.chem-ph↗

arXiv2021

Quantum spin systems for measurement-based quantum computation

Measurement-based quantum computation is different from other approaches for quantum computation, in that everything needs to be done is only local measurement on a certain entangled state. It thus uses entanglement as the resource that drives computation. We give a pedagogical treatment on the basics, and then review some selected developments beyond graph states, including Affleck-Kennedy-Lieb-Tasaki states and more recent 2D symmetry-protected topological states.

quant-ph↗

arXiv2021

Measurement-Based Quantum Computation

Measurement-based quantum computation is a framework of quantum computation, where entanglement is used as a resource and local measurements on qubits are used to drive the computation. It originates from the one-way quantum computer of Raussendorf and Briegel, who introduced the so-called cluster state as the underlying entangled resource state and showed that any quantum circuit could be executed by performing only local measurement on individual qubits. The randomness in the measurement outcomes can be dealt with by adapting future measurement axes so that computation is deterministic. Subsequent works have expanded the discussions of the measurement-based quantum computation to various subjects, including the quantification of entanglement for such a measurement-based scheme, the search for other resource states beyond cluster states and computational phases of matter. In addition, the measurement-based framework also provides useful connections to the emergence of time ordering, computational complexity and classical spin models, blind quantum computation, etc. and has given an alternative, resource-efficient approach to implement the original linear-optic quantum computation of Knill, Laflamme and Milburn. Cluster states and a few other resource states have been created experimentally in various physical systems and the measurement-based approach offers a potential alternative to the standard circuit approach to realize a practical quantum computer.

quant-ph↗