arXiv subjects

Youngrong Lim

Publications and source records attributed to Youngrong Lim.

At least 19 recordsLinked to original sources

arXiv2026

Local Gaussian bounds on the non-destructive discrimination of two-mode squeezed states

Typical measurement setups in quantum systems are destructive, meaning that states are irretrievably altered after measurement. In this work, we analyse non-destructive discrimination of two two-mode squeezed vacuum states using local Gaussian measurements. We investigate a tradeoff relation between the success probability of discrimination and the fidelity of the resulting state with the initial state, and construct a protocol given by local Gaussian measurements, which is optimal within our numerically explored class. We also extend to the case where we allow for additional pre-shared entanglement, and show that this regime allows us to exceed the standard local Gaussian bound for the fidelity-success probability tradeoff. Our work provides a natural extension of the tradeoff between information gain and disturbance in entangled-state discrimination, previously established for finite-dimensional quantum systems, to infinite-dimensional continuous-variable systems.

quant-ph↗

arXiv2026

Quantum Circuit Representation of Combinatorial Matrix Functions

Permanents, hafnians, and loop-hafnians are combinatorial matrix functions closely related to perfect matchings in graphs. These matrix functions arise in the quantum amplitudes of boson configurations in bosonic networks, and the classical hardness of computing them has been used to establish hardness arguments for boson sampling and Gaussian boson sampling. Remarkably, these matrix functions also appear in quantum spin systems. Previous work has shown that transition amplitudes in bipartite Ising and Heisenberg models are proportional to the permanent of the corresponding interaction matrix. Here, we extend the Ising interaction structure beyond the bipartite case to generate hafnians and loop-hafnians. This extension relies on the fact that the Ising model reflects the underlying graph structure and that each matrix function arises naturally from quantum superposition. In particular, since the graph corresponding to the loop-hafnian involves self-loops, we design the interaction structure to incorporate them while preserving the two-body XX form. Through this construction, we unify the three matrix functions within a single Ising-model framework, based on the nested inclusion relations among the corresponding classes of graphs. We further show that the quantum spin dynamics of our model, including the preparation of the nontrivial output state for the loop-hafnian case, can be simulated on a quantum circuit using only $\mathcal{O}(N^2)$ gates.

quant-ph↗

arXiv2025

Classical algorithms for measurement-adaptive Gaussian circuits

Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then provides a natural parameter for computational power. Rather than assessing power only through sampling problems -- the usual benchmark -- we follow the ongoing shift toward tasks of practical relevance and study the quantum mean-value problem, i.e., estimating observable expectation values that underpin simulation and variational algorithms. More specifically, we analyze bosonic circuits with adaptivity and prove that when the number of adaptive measurements is small, the mean-value problem admits efficient classical algorithms even if a large amount of non-Gaussian resources are present in the input state, whereas less constrained regimes are computationally hard. This yields a task-level contrast with sampling, where non-Gaussian ingredients alone often induce hardness, and provides a clean complexity boundary parameterized by the number of adaptive measurement-and-feedforward steps between classical simulability and quantum advantage. Beyond the main result, we introduce classical techniques -- including a generalization of Gurvits' second algorithm to arbitrary product inputs and Gaussian circuits -- for computing the marginal quantities needed by our estimators, which may be of independent interest.

quant-ph↗

arXiv2025

Formulas for Mutually Orthogonal Quantum States in Two-Qubit Systems: Orthogonal Schmidt Decompositions

We present Schmidt decomposition formulas for mutually orthogonal two-qubit pure states and classify orthonormal sets based on their entanglement structure. First, we derive explicit Schmidt decomposition formulas for any pure state and extend them to two orthogonal pure states. For three mutually orthogonal states, we provide formulas for specific cases and discuss the challenges of obtaining analytic expressions for the rest. Additionally, we derive explicit formulas for certain orthonormal bases and analyze those containing one or two maximally entangled states. Finally, we prove that no orthonormal basis can consist of three product states and one entangled state.

quant-ph↗

arXiv2025

Trade-off between Information Gain and Disturbance in Local Discrimination of Entangled Quantum States

We establish an information gain-disturbance trade-off relation in local state discrimination. Our result demonstrates a fundamental limitation of local strategy to discriminate entangled quantum states without disturbance, which becomes more difficult as the entanglement of the states to be discriminated increases. For a set of maximally entangled states, the capability of local strategy is tightly suppressed, as random guessing without measurements saturates the bound provided by the trade-off relation. We also show that the trade-off can be circumvented when local operations are aided by pre-shared entanglement. To simultaneously achieve correct guessing of state and non-disturbance, an entirely different strategy from conventional state discrimination should be adopted to lower the cost of pre-shared entanglement. We explicitly propose an adaptive and non-destructive strategy based on the stabilizer formalism, which shows a strict advantage over conventional teleportation-based approaches in pre-shared entanglement cost for discriminating a set of maximally entangled states. As an application of the trade-off relation, we propose an entanglement certification protocol that is robust against depolarizing noise and generalize it to multipartite scenarios in a quantum network.

quant-ph↗

arXiv2025

Virtual purification complements quantum error correction in quantum metrology

Quantum resources enable one to achieve quantum-enhanced estimation sensitivity beyond its classical counterpart. Many studies mainly focus on reducing statistical error, under the assumption that one can always set an unbiased estimator. However, setting an unbiased estimator is not always feasible, especially when one cannot fully characterize noise. Such incomplete noise characterization induces a bias and eventually makes it impossible to attain the enhanced-estimation. In this work, we explore two systematic approaches; quantum error correction (QEC) and the virtual purification (VP) to reduce the bias, and compare their performance. First, we show that when the noise is indistinguishable from the signal, QEC cannot reduce the bias since it is impossible to construct a QEC code that corrects the noise while preserving the signal. We then show that VP can mitigate indistinguishable error that eventually enable a more accurate estimation compared to QEC. Our findings reveal that VP offers a robust alternative to QEC in scenarios where indistinguishable errors pose significant challenges. We then demonstrate that VP with a stabilizer state probe can efficiently suppress the bias under local depolarizing noise, thereby yielding a significant improvement in estimation performance compared to the QEC-based approach.

quant-ph↗

arXiv2025

Classical algorithms for estimating expectation values in linear-optical circuits

We present a classical algorithm for approximating the expectation values of observables in linear-optical circuits with arbitrary product input states, achieving additive-error accuracy. This result indicates that current applications of photonic systems aimed at demonstrating practical quantum supremacy through expectation value estimation, such as photonic variational algorithms, may face challenges in attaining the computational advantage. It also implies the output probabilities of boson sampling with arbitrary product input states can be efficiently approximated by our method, resulting that boson sampling becomes efficiently simulable when its output probability distribution is polynomially sparse. We also develop an efficient classical algorithm for estimating transition amplitudes of arbitrary product states in linear-optical circuits. This provides additive-error approximation algorithms for matrix functions associated with linear-optical circuits, such as the (loop-)hafnian, which are of independent interest. As an application, it solves the generalized molecular vibronic spectra problem (Oh et al., 2024), previously suggested as a candidate for practical quantum advantage. Finally, we extend our framework to near-Clifford circuits, enabling classical approximation of their expectation values.

quant-ph↗

arXiv2024

Nondestructive discrimination of Bell states between distant parties

Identifying Bell states without destroying it is frequently dealt with in nowadays quantum technologies such as quantum communication and quantum computing. In practice, quantum entangled states are often distributed among distant parties, and it might be required to determine them separately at each location, without inline communication between parties. We present a scheme for discriminating an arbitrary Bell state distributed to two distant parties without destroying it. The scheme requires two entangled states that are pre-shared between the parties, and we show that without these ancillary resources, the probability of non-destructively discriminating the Bell state is bounded by 1/4, which is the same as random guessing. Furthermore, we demonstrate a proof-of-principle experiment through an IonQ quantum computer that our scheme can surpass classical bounds when applied to practical quantum processor.

quant-ph↗

arXiv2023

Efficacy of virtual purification-based error mitigation on quantum metrology

Noise is the main source that hinders us from fully exploiting quantum advantages in various quantum informational tasks. However, characterizing and calibrating the effect of noise is not always feasible in practice. Especially for quantum parameter estimation, an estimator constructed without precise knowledge of noise entails an inevitable bias. Recently, virtual purification-based error mitigation (VPEM) has been proposed to apply for quantum metrology to reduce such a bias occurring from unknown noise. While it was demonstrated to work for particular cases, whether VPEM always reduces a bias for general estimation schemes is unclear yet. For more general applications of VPEM to quantum metrology, we study factors determining whether VPEM can reduce the bias. We find that the closeness between the dominant eigenvector of a noisy state and the ideal quantum probe (without noise) with respect to an observable determines the reducible amount of bias by VPEM. Next, we show that one should carefully choose the reference point of the target parameter, which gives a smaller bias than others because the bias depends on the reference point. Otherwise, even if the dominant eigenvector and the ideal quantum probe are close, the bias of the mitigated case could be larger than the non-mitigated one. Finally, we analyze the error mitigation for a phase estimation scheme under various noises. Based on our analysis, we predict whether VPEM can effectively reduce a bias and numerically verify our results.

quant-ph↗

arXiv2023

Approximating outcome probabilities of linear optical circuits

Quasiprobability representation is an important tool for analyzing a quantum system, such as a quantum state or a quantum circuit. In this work, we propose classical algorithms specialized for approximating outcome probabilities of a linear optical circuit using $s$-parameterized quasiprobability distributions. Notably, we can reduce the negativity bound of a circuit from exponential to at most polynomial for specific cases by modulating the shapes of quasiprobability distributions thanks to the norm-preserving property of a linear optical transformation. Consequently, our scheme renders an efficient estimation of outcome probabilities with precision depending on the classicality of the circuit. Surprisingly, when the classicality is high enough, we reach a polynomial-time estimation algorithm within a multiplicative error. Our results provide quantum-inspired algorithms for approximating various matrix functions beating best-known results. Moreover, we give sufficient conditions for the classical simulability of Gaussian boson sampling using the approximating algorithm for any (marginal) outcome probability under the poly-sparse condition. Our study sheds light on the power of linear optics, providing plenty of quantum-inspired algorithms for problems in computational complexity.

quant-ph↗

arXiv2023

Quantum-inspired classical algorithm for molecular vibronic spectra

We have recently seen the first plausible claims for quantum advantage using sampling problems such as random circuit sampling and Gaussian boson sampling. The obvious next step is to channel the potential quantum advantage to solving practical applications rather than proof-of-principle experiments. Recently, a quantum simulator, specifically a Gaussian boson sampler, has been proposed to generate molecular vibronic spectra efficiently, which is an essential property of molecules and an important tool for analyzing chemical components and studying molecular structures. Computing molecular vibronic spectra has been a challenging task, and its best-known classical algorithm scales combinatorially in the system size. Thus, it is a candidate of tasks for which quantum devices provide computational advantages. In this work, we propose a quantum-inspired classical algorithm for molecular vibronic spectra for harmonic potential. We first show that the molecular vibronic spectra problem corresponding to Fock-state boson sampling can be efficiently solved using a classical algorithm as accurately as running a boson sampler. In particular, we generalize Gurvits's algorithm to approximate Fourier components of the spectra of Fock-state boson sampling and prove using Parseval's relation that the error of the spectra can be suppressed as long as that of the Fourier components are small. We also show that the molecular vibronic spectra problems of Gaussian boson sampling, which corresponds to the actual molecular vibronic spectra problem in chemistry, can be exactly solved even without Gurvits-type algorithms. Consequently, we demonstrate that those problems are not candidates of quantum advantage. We then provide a more general molecular vibronic spectra problem, which is also chemically well-motivated, for which we might be able to take advantage of a boson sampler.

quant-ph↗

arXiv2022

Classical simulation of bosonic linear-optical random circuits beyond linear light cone

Sampling from probability distributions of quantum circuits is a fundamentally and practically important task which can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In the present work, we examine classical simulability of sampling from the output photon-number distribution of linear-optical circuits composed of random beam splitters with equally distributed squeezed vacuum states and single-photon states input. We provide efficient classical algorithms to simulate linear-optical random circuits and show that the algorithms' error is exponentially small up to a depth less than quadratic in the distance between sources using a classical random walk behavior of random linear-optical circuits. Notably, the average-case depth allowing an efficient classical simulation is larger than the worst-case depth limit, which is linear in the distance. Besides, our results together with the hardness of boson sampling give a lower-bound on the depth for constituting global Haar-random unitary circuits.

quant-ph↗

arXiv2022

Polynomial T-depth Quantum Solvability of Noisy Binary Linear Problem: From Quantum-Sample Preparation to Main Computation

The noisy binary linear problem (NBLP) is known as a computationally hard problem, and therefore, it offers primitives for post-quantum cryptography. An efficient quantum NBLP algorithm that exhibits a polynomial quantum sample and time complexities has recently been proposed. However, the algorithm requires a large number of samples to be loaded in a highly entangled state and it is unclear whether such a precondition on the quantum speedup can be obtained efficiently. Here, we present a complete analysis of the quantum solvability of the NBLP by considering the entire algorithm process, namely from the preparation of the quantum sample to the main computation. By assuming that the algorithm runs on "fault-tolerant" quantum circuitry, we introduce a reasonable measure of the computational time cost. The measure is defined in terms of the overall number of T gate layers, referred to as T-depth complexity. We show that the cost of solving the NBLP can be polynomial in the problem size, at the expense of an exponentially increasing logical qubits.

quant-ph↗

arXiv2022

Quantum solvability of noisy linear problems by divide-and-conquer strategy

Noisy linear problems have been studied in various science and engineering disciplines. A class of "hard" noisy linear problems can be formulated as follows: Given a matrix $\hat{A}$ and a vector $\mathbf{b}$ constructed using a finite set of samples, a hidden vector or structure involved in $\mathbf{b}$ is obtained by solving a noise-corrupted linear equation $\hat{A}\mathbf{x} \approx \mathbf{b} + \boldsymbolη$, where $\boldsymbolη$ is a noise vector that cannot be identified. For solving such a noisy linear problem, we consider a quantum algorithm based on a divide-and-conquer strategy, wherein a large core process is divided into smaller subprocesses. The algorithm appropriately reduces both the computational complexities and size of a quantum sample. More specifically, if a quantum computer can access a particular reduced form of the quantum samples, polynomial quantum-sample and time complexities are achieved in the main computation. The size of a quantum sample and its executing system can be reduced, e.g., from exponential to sub-exponential with respect to the problem length, which is better than other results we are aware. We analyse the noise model conditions for such a quantum advantage, and show when the divide-and-conquer strategy can be beneficial for quantum noisy linear problems.

quant-ph↗

arXiv2022

Quantum Metrological Power of Continuous-Variable Quantum Networks

We investigate the quantum metrological power of typical continuous-variable (CV) quantum networks. Particularly, we show that most CV quantum networks provide an entanglement to quantum states in distant nodes that enables one to achieve the Heisenberg scaling in the number of modes for distributed quantum displacement sensing, which cannot be attained using an unentangled probe state. Notably, our scheme only requires local operations and measurements after generating an entangled probe using the quantum network. In addition, we find a tolerable photon-loss rate that maintains the quantum enhancement. Finally, we numerically demonstrate that even when CV quantum networks are composed of local beam splitters, the quantum enhancement can be attained when the depth is sufficiently large.

quant-ph↗

arXiv2022

Classical simulation of boson sampling based on graph structure

Boson sampling is a fundamentally and practically important task that can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In this work, we present classical sampling algorithms for single-photon and Gaussian input states that take advantage of a graph structure of a linear-optical circuit. The algorithms' complexity grows as so-called treewidth, which is closely related to the connectivity of a given linear-optical circuit. Using the algorithms, we study approximated simulations for local Haar-random linear-optical circuits. For equally spaced initial sources, we show that when the circuit depth is less than the quadratic in the lattice spacing, the efficient simulation is possible with an exponentially small error. Notably, right after this depth, photons start to interfere each other and the algorithms' complexity becomes sub-exponential in the number of sources, implying that there is a sharp transition of its complexity. Finally, when a circuit is sufficiently deep enough for photons to typically propagate to all modes, the complexity becomes exponential as generic sampling algorithms. We numerically implement a likelihood test with a recent Gaussian boson sampling experiment and show that the treewidth-based algorithm with a limited treewidth renders a larger likelihood than the experimental data.

quant-ph↗

arXiv2021

Quantum secure learning with classical samples

Studies addressing the question "Can a learner complete the learning securely?" have recently been spurred from the standpoints of fundamental theory and potential applications. In the relevant context of this question, we present a classical-quantum hybrid sampling protocol and define a security condition that allows only legitimate learners to prepare a finite set of samples that guarantees the success of the learning; the security condition excludes intruders. We do this by combining our security concept with the bound of the so-called probably approximately correct (PAC) learning. We show that while the lower bound on the learning samples guarantees PAC learning, an upper bound can be derived to rule out adversarial learners. Such a secure learning condition is appealing, because it is defined only by the size of samples required for the successful learning and is independent of the algorithm employed. Notably, the security stems from the fundamental quantum no-broadcasting principle. No such condition can thus occur in any classical regime, where learning samples can be copied. Owing to the hybrid architecture, our scheme also offers a practical advantage for implementation in noisy intermediate-scale quantum devices.

quant-ph↗

arXiv2019

Upper bounds on the quantum capacity for general attenuator and amplifier

There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises, including squeezing or even non-Gaussian one. We derive new upper bounds on the energy-constrained quantum capacity of those channels by using the quantum conditional entropy power inequality. Also, we obtain lower bounds for the same channels by means of Gaussian optimizer with fixed input entropy. They give narrow bounds when the transmissivity is near unity and the energy of input state is low.

quant-ph↗