arXiv subjects

Hefeng Wang

Publications and source records attributed to Hefeng Wang.

At least 19 recordsLinked to original sources

arXiv2026

Quantum algorithm for PageRank computation through multistep quantum resonant transitions

We present a quantum algorithm for obtaining a quantum state that encodes the PageRank vector of the Google matrix through multistep quantum resonant transition (mQRT). In the algorithm, the PageRank vector is encoded in the ground state of a problem Hamiltonian associated with the Google matrix. By dividing the web graph corresponding to the Google matrix into a series of subgraphs with nested structure, we construct a sequence of Hamiltonians based on the subgraphs to form a Hamiltonian evolution path from a simple initial Hamiltonian to the problem Hamiltonian. The ground state of the problem Hamiltonian is obtained by going through ground states of the intermediate Hamiltonians via QRT step by step. This algorithm requires only one ancillary qubit, and the runtime of the algorithm is proportional to the number of steps. It provides a new way for efficiently obtaining the quantum state of the PageRank vector of large-scale networks.

quant-ph↗

arXiv2026

Saving resources through repeat-until-success positive-operator-valued-measure measurements in quantum computation

We present a quantum computation approach in which computation is guided by positive-operator-valuedmeasure (POVM) measurements following a given computation path in multisteps. In this approach, one ancillary qubit is coupled to a register of working qubits, and a POVM measurement is implemented effectively on the working qubits by applying a unitary operation on the whole system followed by a projective measurement performed on the ancillary qubit. Each step of the computation is a repeat-until-success procedure such that the desired state of the step is obtained deterministically on the working qubits via POVM measurements. The principle of deferred measurement states that measurements can always be moved from an intermediate stage of a quantum circuit to the end of the circuit without affecting the efficiency of the computation.We demonstrate that in our approach, by introducing intermediate measurements on the ancillary qubit in the computation process, both the number of qubits and unitary operations can be reduced polynomially, compared to the case where the intermediate measurements are deferred to the end of the computation. We also provide a method for implementation of the approach.

quant-ph↗

arXiv2025

Generalized quantum singular value transformation with application in quantum conjugate gradient least squares algorithm

Quantum signal processing (QSP) and generalized quantum signal processing (GQSP) are essential tools for implementing the block encoding of matrix functions. The achievable polynomials of QSP have restrictions on parity, while GQSP eliminates these restrictions. But GQSP only constructs functions of unitary matrices. In this paper, we further investigate GQSP and extend it to general matrices. Compared with the quantum singular value transformation (QSVT), our proposed method relaxes the requirements on the parity of polynomials. We refer to this extension as generalized quantum singular value transformation (GQSVT). Subsequently, by utilizing the relationship between generalized matrix functions and standard matrix functions, we propose a classical-quantum hybrid quantum conjugate gradient least squares (CGLS) algorithm using GQSVT.

math.NA↗

arXiv2024

Implicit and Explicit Language Guidance for Diffusion-based Visual Perception

Text-to-image diffusion models have shown powerful ability on conditional image synthesis. With large-scale vision-language pre-training, diffusion models are able to generate high-quality images with rich texture and reasonable structure under different text prompts. However, it is an open problem to adapt the pre-trained diffusion model for visual perception. In this paper, we propose an implicit and explicit language guidance framework for diffusion-based perception, named IEDP. Our IEDP comprises an implicit language guidance branch and an explicit language guidance branch. The implicit branch employs frozen CLIP image encoder to directly generate implicit text embeddings that are fed to diffusion model, without using explicit text prompts. The explicit branch utilizes the ground-truth labels of corresponding images as text prompts to condition feature extraction of diffusion model. During training, we jointly train diffusion model by sharing the model weights of these two branches. As a result, implicit and explicit branches can jointly guide feature learning. During inference, we only employ implicit branch for final prediction, which does not require any ground-truth labels. Experiments are performed on two typical perception tasks, including semantic segmentation and depth estimation. Our IEDP achieves promising performance on both tasks. For semantic segmentation, our IEDP has the mIoU$^\text{ss}$ score of 55.9% on AD20K validation set, which outperforms the baseline method VPD by 2.2%. For depth estimation, our IEDP outperforms the baseline method VPD with a relative gain of 11.0%.

cs.CV↗

arXiv2023

Quantum optimization algorithm based on multistep quantum computation

We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the state space of the problem. Usually the cost for solving the problem increases dramatically with the size of the problem. In this algorithm, the dimension of the search space of the problem can be reduced exponentially step by step. We construct a sequence of Hamiltonians such that the search space of a Hamiltonian is nested in that of the previous one. By applying a multistep quantum computation process, the optimal vector is finally located in a small state space and can be determined efficiently. One of the most difficult problems in optimization is that a trial vector is trapped in a deep local minimum while the global minimum is missed, this problem can be alleviated in our algorithm and the runtime is proportional to the number of the steps of the algorithm, provided certain conditions are satisfied. We have tested the algorithm for some continuous test functions.

quant-ph↗

arXiv2023

DFormer: Diffusion-guided Transformer for Universal Image Segmentation

This paper introduces an approach, named DFormer, for universal image segmentation. The proposed DFormer views universal image segmentation task as a denoising process using a diffusion model. DFormer first adds various levels of Gaussian noise to ground-truth masks, and then learns a model to predict denoising masks from corrupted masks. Specifically, we take deep pixel-level features along with the noisy masks as inputs to generate mask features and attention masks, employing diffusion-based decoder to perform mask prediction gradually. At inference, our DFormer directly predicts the masks and corresponding categories from a set of randomly-generated masks. Extensive experiments reveal the merits of our proposed contributions on different image segmentation tasks: panoptic segmentation, instance segmentation, and semantic segmentation. Our DFormer outperforms the recent diffusion-based panoptic segmentation method Pix2Seq-D with a gain of 3.6% on MS COCO val2017 set. Further, DFormer achieves promising semantic segmentation performance outperforming the recent diffusion-based method by 2.2% on ADE20K val set. Our source code and models will be publicly on https://github.com/cp3wan/DFormer

cs.CV↗

arXiv2023

Polynomial-time quantum algorithm for solving the hidden subgroup problem

The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP. However, there is no efficient quantum algorithm for solving the non-Abelian HSP. We find that the HSP can be reduced to a nested structured search problem that is solved efficiently by using a quantum algorithm via multistep quantum computation. Then we solve the HSP and problems that can be reduced to both the Abelian and the non-Abelian HSP in polynomial time by using this algorithm.

quant-ph↗

arXiv2023

Efficient quantum algorithms for solving quantum linear system problems

We transform the problem of solving linear system of equations $A\mathbf{x}=\mathbf{b}$ to a problem of finding the right singular vector with singular value zero of an augmented matrix $C$, and present two quantum algorithms for solving this problem. The first algorithm solves the problem directly by applying the quantum eigenstate filtering algorithm with query complexity of $O\left( sκ\log \left( 1/ε\right) \right) $ for a $s$-sparse matrix $C$, where $κ$ is the condition number of the matrix $A$, and $ε$ is the desired precision. The second algorithm uses the quantum resonant transition approach, the query complexity scales as $O\left[sκ+ \log\left( 1/ε\right)/\log \log \left( 1/ε\right) \right] $. Both algorithms meet the optimal query complexity in $κ$, and are simpler than previous algorithms.

quant-ph↗

arXiv2022

Efficient quantum algorithm for solving structured problems via multi-step quantum computation

In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process because the no-cloning theorem forbids making copies of an unknown quantum state perfectly. We find a method based on quantum resonant transition to protect and reuse an unknown quantum state that encodes calculated results of an intermediate step without making copies of the state, and present a quantum algorithm that solves a problem via a multi-step quantum computation process. This algorithm can achieve an exponential speedup over classical algorithms in solving a type of structured search problems.

quant-ph↗

arXiv2019

Quantum algorithm for total least squares data fitting

The total least squares~(TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the variables. In this work, the TLS problem is transformed to finding the ground state of a Hamiltonian matrix. We propose quantum algorithms for solving this problem based on quantum simulation of resonant transitions. Our algorithms can achieve at least polynomial speedup over the known classical algorithms.

quant-ph↗

arXiv2019

Quantum Simulation of Resonant Transitions for Solving the Eigen-problem of an Effective Water Hamiltonian

It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum algorithm which could solve this problem via simulated resonant transitions. Using a four-qubit quantum simulator in which two qubits are used as ancillas for control and measurement, we obtain the energy spectrum of a 2-qubit low-energy effective Hamiltonian of the water molecule. The simulated transitions allow the state of the quantum simulator to transform and access large regions of the Hilbert space, including states that have no overlap with the initial state. Furthermore, we make use of this algorithm to efficiently prepare specific eigenstates on the simulator according to the measured eigenenergies.

quant-ph↗

arXiv2018

Multi-step quantum algorithm for solving the 3-bit exact cover problem

We present a multi-step quantum algorithm for solving the $3$-bit exact cover problem, which is one of the NP-complete problems. Unlike the brute force methods have been tried before, in this algorithm, we showed that by applying the clauses of the Boolean formula sequentially and introducing non-unitary operations, the state that satisfies all of the clauses can be projected out from an equal superposition of all computational basis states step by step, and the search space is reduced exponentially. The runtime of the algorithm is proportional to the number of clauses, therefore scales polynomial to the size of the problem. Our results indicate that quantum computers may be able to outperform classical computers in solving NP-complete problems.

quant-ph↗

arXiv2018

Quantum algorithm for preparing the ground state of a system via resonance transition

Preparing the ground state of a system is an important task in physics. We propose a quantum algorithm for preparing the ground state of a physical system that can be simulated on a quantum computer. The system is coupled to an ancillary qubit, by introducing a resonance mechanism between the ancilla qubit and the system, and combined with measurements performed on the ancilla qubit, the system can be evolved to monotonically converge to its ground state through an iterative procedure. We have simulated the application of this algorithm for the Afflect-Kennedy-Lieb-Tasaki model, whose ground state can be used as resource state in one-way quantum computation.

quant-ph↗

arXiv2015

Determine Ramsey numbers on a quantum computer

We present a quantum algorithm for computing the Ramsey numbers whose computational complexity grows super-exponentially with the number of vertices of a graph on a classical computer. The problem is mapped to a decision problem on a quantum computer, a probe qubit is coupled to a register that represents the problem and detects the energy levels of the problem Hamiltonian. The decision problem is solved by determining whether the probe qubit exhibits resonance dynamics. The algorithm shows a quadratic speedup over its classical counterparts, and the degenerate ground state problem in the adiabatic quantum evolution algorithm for this problem is avoided.

quant-ph↗

arXiv2015

Quantum algorithm for obtaining the eigenstates of a physical system

We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a probe qubit coupled to a quantum system, the system exhibits a resonance dynamics when the frequency of the probe qubit matches a transition frequency in the system. Therefore the system can be guided to evolve to the eigenstate with known eigenvalue by inducing resonance between the probe qubit and a designed transition in the system. This algorithm can also be used to obtain the energy spectrum of a physical system and can achieve even a quadratic speedup over the phase estimation algorithm.

quant-ph↗

arXiv2014

Fast quantum algorithm for EC3 problem with trapped ions

Adiabatic quantum computing~(AQC) is based on the adiabatic principle, where a quantum system remains in an instantaneous eigenstate of the driving Hamiltonian. The final state of the Hamiltonian encodes solution to the problem of interest. While AQC has distinct advantages, recent researches have shown that quantumness such as quantum coherence in adiabatic processes may be lost entirely due to the system-bath interaction when the evolution time is long, and consequently the expected quantum speedup dose not show up. Here we propose a fast-signal assisted adiabatic quantum algorithm. We find that by applying a sequence of fast random or regular signals during the evolution process, the runtime can be reduced greatly, yet advantages of the adiabatic algorithm remain intact. Significantly, we present a \emph{randomized} Trotter formula and show that the driving Hamiltonian and the sequence of fast signals can be implemented simultaneously. We apply the algorithm for solving the $3$-bit exact cover problem~(EC$3$) and put forward an approach for implementing the problem with trapped ions.

quant-ph↗

arXiv2014

A quantum algorithm for obtaining the energy spectrum of a physical system without guessing its eigenstates

We present a quantum algorithm that provides a general approach for obtaining the energy spectrum of a physical system without making a guess on its eigenstates. In this algorithm, a probe qubit is coupled to a quantum register $R$ which consists of one ancilla qubit and a $n$-qubit register that represents the system. $R$ is prepared in a general reference state, and a general excitation operator acts on $R$ is constructed. The probe exhibits a dynamical response only when it is resonant with a transition from the reference state to an excited state of $R$ which contains the eigenstates of the system. By varying the probe's frequency, the energy spectrum and the eigenstates of the system can be obtained.

quant-ph↗

arXiv2014

A quantum algorithm for solving some discrete mathematical problems by probing their energy spectra

When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum algorithm for solving discrete mathematical problems based on the circuit model. Our algorithm has favorable scaling properties in solving some discrete mathematical problems.

quant-ph↗