arXiv subjects

Hongye Yu

Publications and source records attributed to Hongye Yu.

12 recordsLinked to original sources

arXiv2026

Three-body scattering area of identical bosons in two dimensions

We study the wave function $\phi^{(3)}$ of three identical bosons scattering at zero energy, zero total momentum, and zero orbital angular momentum in two dimensions, interacting via short-range potentials with a finite two-body scattering length $a$. We derive asymptotic expansions of $\phi^{(3)}$ in two regimes: the 111-expansion, where all three pairwise distances are large, and the 21-expansion, where one particle is far from the other two. In the 111-expansion, the leading term grows as $\ln^3(B/a)$ at large hyperradius $B=\sqrt{(s_1^2+s_2^2+s_3^2)/2}$. At order $B^{-2}\ln^{-3}(B/a)$, we identify a three-body parameter $D$ with dimension of length squared, which we term the three-body scattering area. This quantity should be contrasted with the three-body scattering area previously studied for infinite or vanishing two-body scattering length. If the two-body interaction is attractive and supports bound states, $D$ acquires a negative imaginary part, and we derive its relation to the probability amplitudes for the production of two-body bound states in three-body collisions. Under weak modifications of the interaction potentials, we derive the corresponding shift of $D$ in terms of $\phi^{(3)}$ and the changes of the two-body and three-body potentials. We also study the effects of $D$ and $\phi^{(3)}$ on three-body and many-body physics, including the three-body ground-state energy in a large periodic volume, the many-body energy and the three-body correlation function of the dilute two-dimensional Bose gas, and the three-body recombination rates of two-dimensional ultracold atomic Bose gases.

cond-mat.quant-gas↗

arXiv2025

Universal energy-space localization and stable quantum phases against time-dependent perturbations

Stability against perturbations is a highly nontrivial property of quantum systems and is often a requirement to define new phases. In most systems where stability can be rigorously established, only static perturbations are considered; whether any system can remain stable against generic time-dependent perturbations is largely elusive. In this work, we identify a universal phenomenon in driving $q$-local Hamiltonians called energy-space localization and prove that it can survive under generic time-dependent perturbations, where the evolving state is exponentially localized in an energy window of the instantaneous spectrum. For spin glass models where the configuration spaces are separated by large energy barriers, the localization in energy spaces can induce a true localization in configuration spaces and robustly break ergodicity. We then demonstrate its applications in several systems with such barriers. For certain LDPC codes, we show that the system remains localized near the original codeword for an exponentially long time even under generic time-dependent perturbations. For classical optimization problems with clustered solution space, the stability becomes an obstacle for quantum Hamiltonian-based algorithms to escape local minima. Our work provides a new lens for analyzing non-equilibrium dynamics of generic quantum systems, and versatile mathematical tools for establishing stability and for designing quantum algorithms.

quant-ph↗

arXiv2024

The robustness condition for general disordered discrete time crystals, and subspace-thermal DTCs from phase transitions between different n-tuple DTCs

We propose a new Floquet time crystal model that responds in arbitrary multiples of the driving period. Such an $n$-tuple discrete time crystal is theoretically constructed by permuting spins in a disordered chain and is well suited for experimental implementations. Transitions between these time crystals with different periods give rise to a novel phase of matter that we call subspace-thermal discrete time crystals, where states within subspaces of definite charges are fully thermalized at an early time. However, the whole system still robustly responds to the periodic driving subharmonically, with a period being the greatest common divisor of the original two periods. Existing theoretical analysis from many-body localization cannot be used to understand the rigidity of such subspace-thermal time crystal phases. To resolve this, we develop a new theoretical framework for the robustness of DTCs from the perspective of the robust $2\pi/n$ quasi-energy gap. Its robustness is rigorously proved if the system satisfies a certain condition where the mixing length, defined by the Hamming distance of the symmetry charges, does not exceed a global threshold. The proof applies beyond the models considered here to other existing DTCs realized by kicking disordered systems, where conventional MBL-DTCs can be regarded as a special case of the subspace-thermal DTC with the subspace dimension being one, thus offering a systematic way to construct new discrete time crystal models. We also introduce the notion of DTC-charges that allow us to probe the observables that spontaneously break the time-translation symmetry in both the regular discrete time crystals and subspace-thermal discrete time crystals. Moreover, our discrete time crystal models can be generalized to systems with higher spin magnitudes or qudits, as well as to higher spatial dimensions.

quant-ph↗

arXiv2024

Feedback-based Quantum Algorithm Inspired by Counterdiabatic Driving

In recent quantum algorithmic developments, a feedback-based approach has shown promise for preparing quantum many-body system ground states and solving combinatorial optimization problems. This method utilizes quantum Lyapunov control to iteratively construct quantum circuits. Here, we propose a substantial enhancement by implementing a protocol that uses ideas from quantum Lyapunov control and the counterdiabatic driving protocol, a key concept from quantum adiabaticity. Our approach introduces an additional control field inspired by counterdiabatic driving. We apply our algorithm to prepare ground states in one-dimensional quantum Ising spin chains. Comprehensive simulations demonstrate a remarkable acceleration in population transfer to low-energy states within a significantly reduced time frame compared to conventional feedback-based quantum algorithms. This acceleration translates to a reduced quantum circuit depth, a critical metric for potential quantum computer implementation. We validate our algorithm on the IBM cloud computer, highlighting its efficacy in expediting quantum computations for many-body systems and combinatorial optimization problems.

quant-ph↗

arXiv2023

Efficient separate quantification of state preparation errors and measurement errors on quantum computers and their mitigation

Current noisy quantum computers have multiple types of errors, which can occur in the state preparation, measurement/readout, and gate operation, as well as intrinsic decoherence and relaxation. Partly motivated by the booming of intermediate-scale quantum processors, measurement and gate errors have been recently extensively studied, and several methods of mitigating them have been proposed and formulated in software packages (e.g., in IBM Qiskit). Despite this, the state preparation error and the procedure to quantify it have not yet been standardized, as state preparation and measurement errors are usually considered not directly separable. Inspired by a recent work of Laflamme, Lin, and Mor [Phys. Rev. A 106, 012439 (2022)], we propose a simple and resource-efficient approach to quantify separately the state preparation and readout error rates. With these two errors separately quantified, we also propose methods to mitigate them separately, especially mitigating state preparation errors with linear (with the number of qubits) complexity. As a result of the separate mitigation, we show that the fidelity of the outcome can be improved by an order of magnitude compared to the standard measurement error mitigation scheme. We also show that the quantification and mitigation scheme is resilient against gate noise and can be immediately applied to current noisy quantum computers. To demonstrate this, we present results from cloud experiments on IBM's superconducting quantum computers. The results indicate that the state preparation error rate is also an important metric for qubit metrology that can be efficiently obtained.

quant-ph↗

arXiv2023

Quantum Hamiltonian Algorithms for Maximum Independent Sets

With qubits encoded into atomic ground and Rydberg states and situated on the vertexes of a graph, the conditional quantum dynamics of Rydberg blockade, which inhibits simultaneous excitation of nearby atoms, has been employed recently to find maximum independent sets following an adiabatic evolution algorithm hereafter denoted by HV [Science 376, 1209 (2022)]. An alternative algorithm, short named the PK algorithm, reveals that the independent sets diffuse over a media graph governed by a non-abelian gauge matrix of an emergent PXP model. This work shows the above two algorithms are mathematically equivalent, despite of their seemingly different physical implementations. More importantly, we demonstrated that although the two are mathematically equivalent, the PK algorithm exhibits more efficient and resource-saving performance. Within the same range of experimental parameters, our numerical studies suggest that the PK algorithm performs at least 25% better on average and saves at least $6\times10^6$ measurements ($\sim 900$ hours of continuous operation) for each graph when compared to the HV algorithm. We further consider the measurement error and point out that this may cause the oscillations in the performance of the HV's optimization process.

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↗

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↗

arXiv2020

Quantum Zeno approach for molecular energies with maximum commuting initialHamiltonians

We propose to use a quantum adiabatic and simulated-annealing framework to compute theground state of small molecules. The initial Hamiltonian of our algorithms is taken to be themaximum commuting Hamiltonian that consists of a maximal set of commuting terms in the fullHamiltonian of molecules in the Pauli basis. We consider two variants. In the first method, weperform the adiabatic evolution on the obtained time- or path-dependent Hamiltonian with theinitial state as the ground state of the maximum commuting Hamiltonian. However, this methoddoes suffer from the usual problems of adiabatic quantum computation due to degeneracy andenergy-level crossings along the Hamiltonian path. This problem is mitigated by a Zeno method,i.e., via a series of eigenstate projections used in the quantum simulated annealing, with the path-dependent Hamiltonian augmented by a sum of Pauli X terms, whose contribution vanishes at thebeginning and the end of the path. In addition to the ground state, the low lying excited states canbe obtained using this quantum Zeno approach with equal accuracy to that of the ground state.

quant-ph↗

arXiv2020

Quantum Algorithm for Approximating Maximum Independent Sets

We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary Hamiltonian. For both sparse and dense graphs, our quantum algorithm on average can find an independent set of size very close to $\alpha(G)$, which is the size of the maximum independent set of a given graph $G$. Numerical results indicate that an $O(n^2)$ time complexity quantum algorithm is sufficient for finding an independent set of size $(1-\epsilon)\alpha(G)$. The best classical approximation algorithm can produce in polynomial time an independent set of size about half of $\alpha(G)$.

quant-ph↗

arXiv2018

Quantum independent set problem and non-abelian adiabatic mixing

We present an efficient quantum algorithm for some independent set problems in graph theory, based on non-abelian adiabatic mixing. We illustrate the performance of our algorithm with analysis and numerical calculations for two different types of graphs, with the number of edges proportional to the number of vertices or its square. The theoretical advantages of our quantum algorithm over classical algorithms are discussed. Non-abelian adiabatic mixing can be a general technique to aid exploration in a landscape of near-degenerate ground states.

quant-ph↗

arXiv2017

Exact Equivalence between Quantum Adiabatic Algorithm and Quantum Circuit Algorithm

We present a rigorous proof that quantum circuit algorithm can be transformed into quantum adiabatic algorithm with the exact same time complexity. This means that from a quantum circuit algorithm of $L$ gates we can construct a quantum adiabatic algorithm with time complexity of $O(L)$. Additionally, our construction shows that one may exponentially speed up some quantum adiabatic algorithms by properly choosing an evolution path.

quant-ph↗