arXiv subjects

Le Luo

Publications and source records attributed to Le Luo.

At least 37 records · Page 2Linked to original sources

arXiv2024

Distributed exact multi-objective quantum search algorithm

Multi-objective search means searching for any one of several objectives in an unstructured database. Grover's algorithm has quadratic acceleration in multi-objection search than classical ones. Iterated operator in Grover's algorithm is a key element and plays an important role in amplitude amplification. In this paper, we design two distributed iterated operators and therefore two new distributed Grover's algorithms are obtained with the following advantages: (1) Compared to Grover's algorithm and the modified Grover's algorithm by Long, our distributed algorithms require fewer qubits; (2) Compared to the distributed Grover's algorithm proposed by Qiu et al., one of our distributed algorithms is exact. Of course, both our distributed algorithms require quite quantum communication and involve a number of more complicated unitary operators as cost, but there still may have certain advantage of physical realizability in the Noisy Intermediate-Scale Quantum (NISQ) era.

quant-ph↗

arXiv2024

Distributed Exact Generalized Grover's Algorithm

Distributed quantum computation has garnered immense attention in the noisy intermediate-scale quantum (NISQ) era, where each computational node necessitates fewer qubits and quantum gates. In this paper, we focus on a generalized search problem involving multiple targets within an unordered database and propose a Distributed Exact Generalized Grover's Algorithm (DEGGA) to address this challenge by decomposing it into arbitrary $t$ components, where $2 \leq t \leq n$. Specifically, (1) our algorithm ensures accuracy, with a theoretical probability of identifying the target states at $100\%$; (2) if the number of targets is fixed, the pivotal factor influencing the circuit depth of DEGGA is the partitioning strategy, rather than the magnitude of $n$; (3) our method requires a total of $n$ qubits, eliminating the need for auxiliary qubits; (4) we elucidate the resolutions (two-node and three-node) of a particular generalized search issue incorporating two goal strings (000000 and 111111) by applying DEGGA. The feasibility and effectiveness of our suggested approach is further demonstrated by executing the quantum circuits on MindSpore Quantum (a quantum simulation software). Eventually, through the decomposition of multi-qubit gates, DEGGA diminishes the utilization of quantum gates by $90.7\%$ and decreases the circuit depth by $91.3\%$ in comparison to the modified Grover's algorithm by Long. It is increasingly evident that distributed quantum algorithms offer augmented practicality.

quant-ph↗

arXiv2024

Implementation of a scalable universal two-qubit quantum processor with electron and nuclear spins in a trapped ion

Increasing the quantum information processing power with limited number of hosts is vital for achieving quantum advantage. Here we propose a novel scheme that achieves a scalable n-ion-2n-qubit quantum processor utilizing four internal levels of each ion, and experimentally implement a 1-ion-2-qubit universal processor using the valence electron spin and nuclear spin of a single 171Yb+ ion. Fidelities of single-qubit and two-qubit gates are around 0.98 obtained by quantum process tomography. Additionally, the Grover's algorithm is implemented with a successful rate exceeding 0.99. We provide explicit scaling-up protocols based on standard laser-less and laser-based frameworks, and further demonstrate that the electron/nuclear-spin scheme allows less demanding two-qubit entangling gates between different ions. The replacement of some inter-atomic gates by intra-atomic gates could increase the fidelity of some quantum circuits. Our work paves the way towards achieving 2n-times increase in the size of quantum computational Hilbert space with n ions.

quant-ph↗

arXiv2024

Dynamical topology of chiral and nonreciprocal state transfers in a non-Hermitian quantum system

The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological phenomenon, known as topological dynamics, where the evolution process allows a hidden topological invariant associated with continuous flows. To validate this conjecture, we study topological chiral and nonreciprocal dynamics by encircling the exceptional points (EPs) of non-Hermitian Hamiltonians in a trapped ion system. These dynamics are topologically robust against external perturbations even in the presence dissipation-induced nonadiabatic processes. Our findings indicate that they are protected by dynamical vorticity -- an emerging topological invariant associated with the energy dispersion of non-Hermitian band structures in a parallel transported eigenbasis. The symmetry breaking and other key features of topological dynamics are directly observed through quantum state tomography. Our results mark a significant step towards exploring topological properties of open quantum systems.

quant-ph↗

arXiv2024

Observation of a broad state-to-state spin-exchange collision near a p-wave Feshbach resonances of $^6$Li atoms

The study of state-to-state spin-exchange collisions in the vicinity of $p$-wave Feshbach resonances offer great opportunities to explore many-body interactions and novel quantum phases. Here, we report the observation of a spin-exchange collision near a $p$-wave Feshbach resonance within a mixture of the lowest and third-lowest hyperfine states of $^6$Li atoms. The spin-exchange interaction is observed over a range of ten gausses and produces a pair of atoms in the second-lowest hyperfine states that are captured by a deep optical dipole trap. We apply a coupled-channel method to calculate the scattering properties of this system. We find that the $p$-wave resonance exhibits a low inelastic collision rate and a broad resonance profile, which is due to the modification by the accompanying spin-exchange collisions. These findings open up new possibilities for the creation of long-lived, strongly interacting $p$-wave Fermi gases.

cond-mat.quant-gas↗

arXiv2024

A Fourier Transform Framework for Domain Adaptation

By using unsupervised domain adaptation (UDA), knowledge can be transferred from a label-rich source domain to a target domain that contains relevant information but lacks labels. Many existing UDA algorithms suffer from directly using raw images as input, resulting in models that overly focus on redundant information and exhibit poor generalization capability. To address this issue, we attempt to improve the performance of unsupervised domain adaptation by employing the Fourier method (FTF).Specifically, FTF is inspired by the amplitude of Fourier spectra, which primarily preserves low-level statistical information. In FTF, we effectively incorporate low-level information from the target domain into the source domain by fusing the amplitudes of both domains in the Fourier domain. Additionally, we observe that extracting features from batches of images can eliminate redundant information while retaining class-specific features relevant to the task. Building upon this observation, we apply the Fourier Transform at the data stream level for the first time. To further align multiple sources of data, we introduce the concept of correlation alignment. To evaluate the effectiveness of our FTF method, we conducted evaluations on four benchmark datasets for domain adaptation, including Office-31, Office-Home, ImageCLEF-DA, and Office-Caltech. Our results demonstrate superior performance.

cs.CV↗

arXiv2024

Discrimination of Chiral Molecules through Holonomic Quantum Coherent Control

A novel optical method for distinguishing chiral molecules is proposed and validated within a quantum simulator employing a trapped-ion qudit. This approach correlates the sign disparity of the dipole moment of chiral molecules with distinct cyclic evolution trajectories, yielding the unity population contrast induced by the different non-Abelian holonomies corresponding to the chirality. Harnessing the principles of holonomic quantum computation (HQC), our method achieves highly efficient, non-adiabatic, and robust detection and separation of chiral molecules. Demonstrated in a trapped ion quantum simulator, this scheme achieves nearly 100% contrast between the two enantiomers in the population of a specific state, showcasing its resilience to the noise inherent in the driving field.

quant-ph↗

arXiv2023

Scaling law for three-body collisions near a narrow s-wave Feshbach resonance

Ultracold atomic gases provide a controllable system to study the inelastic processes for three-body systems, where the three-body recombination rate depends on the scattering length scaling. Such scalings have been confirmed in bosonic systems with various interaction strengths, but their existence with fermionic atoms remains elusive. In this work, we report on an experimental investigation of the scaling law for the three-body atomic loss rate $L_3$ in a two-component $^6$Li Fermi gas with the scattering length $a<0$. The scaling law is validated within a certain range of $a$ near the narrow $s$-wave Feshbach resonance, where $L_3\propto T|a|^{2.60(5)}$, and $T$ is the gas temperature. The scaling law is observed to have an upper and a lower bound in terms of the scattering length. For the upper bound, when $a\rightarrow \infty$, the power-law scaling is suppressed by the unitary behavior of the resonance caused by the strong three-body collisions. For the lower bound, $a\rightarrow 0$, the finite range effect modifies the scaling law by the effective scattering length $L_e$. These results indicate that the three-body recombination rate in a fermionic system could be characterized by the scaling law associated with the generalized Efimov physics.

cond-mat.quant-gas↗

arXiv2023

Experimental demonstration of enhanced violations of Leggett-Garg inequalities in a $\mathcal{PT}$-symmetric trapped-ion qubit

The Leggett-Garg inequality (LGI) places a bound for the distinction between quantum systems and classical systems. Despite that the tests of temporal quantum correlations on LGIs have been studied in Hermitian realm, there are still unknowns for LGIs in non-Hermitian conditions due to the interplay between dissipation and coherence. For example, a theoretical hypothesis to be experimentally validated, suggests that within non-Hermitian systems, the non-unitary evolution of the system dynamics allows the boundaries of the LGIs to surpass the constraints imposed by traditional quantum mechanics. Here, we demonstrate the experimental violation of LGIs in a parity-time ($\mathcal{PT}$)-symmetric trapped-ion qubit system by measuring the temporal correlation of the evolving states at different times. We find that the upper bounds of the three-time parameter $K_3$ and the four-time parameter $K_4$ show enhanced violations with the increasing dissipation, and can reach the upper limit by infinitely approaching exceptional point. We also observe the distinct behavior of the lower bounds for $K_3$ and $K_4$. While the lower bound for $K_3$ remains constant, the case for $K_4$ shows an upward trend with increasing dissipation. These results reveal a pronounced dependence of the system's temporal quantum correlations on its dissipation to the environment. This opens up a potential pathway for harnessing dissipation to modulate quantum correlations and entanglement.

quant-ph↗

arXiv2023

Exact distributed quantum algorithm for generalized Simon's problem

Simon's problem is one of the most important problems demonstrating the power of quantum algorithms, as it greatly inspired the proposal of Shor's algorithm. The generalized Simon's problem is a natural extension of Simon's problem, and also a special hidden subgroup problem. In this paper, we present two key contributions. Firstly, we characterize the structure of the generalized Simon's problem in distributed scenario and introduce a corresponding distributed quantum algorithm. Secondly, we refine the algorithm to ensure exactness due to the application of quantum amplitude amplification technique. Our algorithm offers exponential acceleration compared to the distributed classical algorithm. When contrasted with the centralized quantum algorithm for the generalized Simon's problem, our algorithm's oracle requires fewer qubits, thus making it easier to be physically implemented. Particularly, the exact distributed quantum algorithm we develop for the generalized Simon's problem outperforms the best previously proposed distributed quantum algorithm for Simon's problem in terms of generalizability and exactness.

quant-ph↗

arXiv2023

Implementation of electromagnetic analogy to gravity mediated entanglement

Recently, experiments aimed at measuring gravity mediated entanglement (GME) using quantum information techniques have been proposed, based on the assumption that if two systems get entangled through local interactions with gravitational field, then this field must be quantum. While there is a debate about what could be drawn from GME, quantum simulation might provide some clarification. Here, we present electromagnetic analogy of GME using magnetic-field mediated interaction between the electron and nucleus in a single atom. Our work successfully implements the general procedures of GME experiments and confirms that the mediating field does not support the mean-field description. It also clarifies that, without considering the light-crossing time, the GME experiment would not distinguish a quantum-field-theory description from a quantum-controlled classical field one. Furthermore, this work provides a novel method to construct two-qubit systems in a single atom, and providing the first quantum simulation of GME using material qubits. It helps to conceive the future GME experiments on the scale of light-crossing time.

quant-ph↗

arXiv2023

Distributed exact quantum algorithms for Deutsch-Jozsa problem

Deutsch-Jozsa (DJ) problem is one of the most important problems demonstrating the power of quantum algorithm. DJ problem can be described as a Boolean function $f$: $\{0,1\}^n\rightarrow \{0,1\}$ with promising it is either constant or balanced, and the purpose is to determine which type it is. DJ algorithm can solve it exactly with one query. In this paper, we first discover the inherent structure of DJ problem in distributed scenario by giving a number of equivalence characterizations between $f$ being constant (balanced) and some properties of $f$'s subfunctions, and then we propose three distributed exact quantum algorithms for solving DJ problem. Our algorithms have essential acceleration over distributed classical deterministic algorithm, and can be extended to the case of multiple computing nodes. Compared with DJ algorithm, our algorithms can reduce the number of qubits and the depth of circuit implementing a single query operator. Therefore, we find that the structure of problem should be clarified for designing distributed quantum algorithm to solve it.

quant-ph↗

arXiv2022

Distributed Grover's algorithm

Let Boolean function $f:\{0,1\}^n\longrightarrow \{0,1\}$ where $|\{x\in\{0,1\}^n| f(x)=1\}|=a\geq 1$. To search for an $x\in\{0,1\}^n$ with $f(x)=1$, by Grover's algorithm we can get the objective with query times $\lfloor \fracπ{4}\sqrt{\frac{2^n}{a}} \rfloor$. In this paper, we propose a distributed Grover's algorithm for computing $f$ with lower query times and smaller number of input bits. More exactly, for any $k$ with $n>k\geq 1$, we can decompose $f$ into $2^k$ subfunctions, each which has $n-k$ input bits, and then the objective can be found out by computing these subfunctions with query times at most $\sum_{i=1}^{r_i} \lfloor \fracπ{4}\sqrt{\frac{2^{n-k}}{b_i}} \rfloor+\lceil\sqrt{2^{n-k}}\rceil+2t_a+1$ for some $1\leq b_i\leq a$ and $r_i\leq 2t_a+1$, where $t_a=\lceil 2π\sqrt{a}+11\rceil$. In particular, if $a=1$, then our distributed Grover's algorithm only needs $\lfloor \fracπ{4}\sqrt{2^{n-k}} \rfloor$ queries, versus $\lfloor \fracπ{4}\sqrt{2^{n}} \rfloor$ queries of Grover's algorithm. %When $n$ qubits belong to middle scale but still are a bit difficult to be processed in practice, $n-k$ qubits are likely feasible for appropriate $k$ in physical realizability. Finally, we propose an efficient algorithm of constructing quantum circuits for realizing the oracle corresponding to any Boolean function with conjunctive normal form (CNF).

quant-ph↗

arXiv2022

Distributed Shor's algorithm

Shor's algorithm is one of the most important quantum algorithm proposed by Peter Shor [Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994, pp. 124--134]. Shor's algorithm can factor a large integer with certain probability and costs polynomial time in the length of the input integer. The key step of Shor's algorithm is the order-finding algorithm. Specifically, given an $L$-bit integer $N$, we first randomly pick an integer $a$ with $gcd(a,N)=1$, the order of $a$ modulo $N$ is the smallest positive integer $r$ such that $a^r\equiv 1 (\bmod N)$. The order-finding algorithm in Shor's algorithm first uses quantum operations to obtain an estimation of $\dfrac{s}{r}$ for some $s\in\{0, 1, \cdots, r-1\}$, then $r$ is obtained by means of classical algorithms. In this paper, we propose a distributed Shor's algorithm. The difference between our distributed algorithm and the traditional order-finding algorithm is that we use two quantum computers separately to estimate partial bits of $\dfrac{s}{r}$ for some $s\in\{0, 1, \cdots, r-1\}$. To ensure their measuring results correspond to the same $\dfrac{s}{r}$, we need employ quantum teleportation. We integrate the measuring results via classical post-processing. After that, we get an estimation of $\dfrac{s}{r}$ with high precision. Compared with the traditional Shor's algorithm that uses multiple controlling qubits, our algorithm reduces nearly $\dfrac{L}{2}$ qubits and reduces the circuit depth of each computer.

quant-ph↗

arXiv2022

Realizing quantum speed limit in open system with a PT-symmetric trapped-ion qubit

Evolution time of a qubit under a Hamiltonian operation is one of the key issues in quantum control, quantum information processing and quantum computing. It has a lower bound in Hermitian system, which is limited by the coupling between two states of the qubit, while it is proposed that in a non-Hermitian system it can be made much smaller without violating the time-energy uncertainty principle. Here we have experimentally confirmed the proposal in a single dissipative qubit system and demonstrate that the evolution time of a qubit from an initial state to an arbitrary state can be controlled by tuning the dissipation intensity in a non-Hermitian Parity-Time-Symmetric ($\mathcal{P T}$-symmetric) quantum system. It decreases with increasing dissipation intensity and also gives a tighter bound for quantum speed limit (QSL). We also find that the evolution time of its reversal operation increases with the increasing dissipation intensity. These findings give us a well-controlled knob for speeding up the qubit operation, and pave the way towards fast and practical quantum computation, opening the door for solving sophisticated problems with only a few qubits.

physics.atom-ph↗

arXiv2022

Controllable Production of Degenerate Fermi Gases of $^6$Li Atoms in the 2D-3D Crossover

The many-body physics in the dimensional crossover regime attracts much attention in cold atom experiments, but yet to explore systematically. One of the technical difficulties existed in the experiments is the lack of the experimental technique to quantitatively tune the atom occupation ratio of the different lattice bands. In this letter, we report such techniques in a process of transferring a 3D Fermi gas into a 1D optical lattice, where the capability of tuning the occupation of the energy band is realized by varying the trapping potentials of the optical dipole trap (ODT) and the lattice, respectively. We could tune a Fermi gas with the occupation in the lowest band from unity to 50$\%$ quantitatively. This provides a route to experimentally study the dependence of many-body interaction on the dimensionality in a Fermi gas.

cond-mat.quant-gas↗

arXiv2022

Distributed quantum algorithm for Simon's problem

Limited by today's physical devices, quantum circuits are usually noisy and difficult to be designed deeply. The novel computing architecture of distributed quantum computing is expected to reduce the noise and depth of quantum circuits. In this paper, we study the Simon's problem in distributed scenarios and design a distributed quantum algorithm to solve the problem. The algorithm proposed by us has the advantage of exponential acceleration compared with the classical distributed computing, and has the advantage of square acceleration compared with the best distributed quantum algorithm proposed before. In particular, the previous distributed quantum algorithm for Simon's problem can not be extended to the case of more than {\it two computing nodes} (i.e. two subproblems), but our distributed quantum algorithm can be extended to the case of {\it multiple computing nodes} (i.e. multiple subproblems) as well.

quant-ph↗

arXiv2022

Protection of quantum evolutions under parity-time symmetric non-Hermitian Hamiltonians by dynamical decoupling

Parity-time (PT) symmetric non-Hermitian Hamiltonians bring about many novel features and interesting applications such as quantum gates faster than those in Hermitian systems, and topological state transfer. The performance of evolutions under $\mathcal{PT}$-symmetric Hamiltonians is degraded by the inevitable noise and errors due to system-environment interaction and experimental imperfections. In contrast to Hermitian Hamiltonians, the fluctuations in dissipative beams that are utilized to generate non-Hermitian contributions in the PT-symmetric Hamiltonians cause additional errors. Here we achieve the protection of PT-symmetric Hamiltonians against noise acting along the qubit's quantization axis by combining quantum evolutions with dynamical decoupling sequences. We demonstrate the performance of our method by numerical simulations. Realistic noise sources and parameters are chosen including: constant detuning error, time-varying detuning noise and dissipative-beam noise. The fidelities of the protected evolutions are well above the unprotected ones under all the above situations. Our work paves the way for further studies and applications of non-Hermitian $\mathcal{PT}$-symmetric physics in noisy quantum systems.

quant-ph↗