The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads ultimate lower bound of an error. We address here a question whether Gaussian scheme can achieve for phase single-mode metrology exploits probe states environment. identify three types setups yielding maximal Fisher information depending on displacement, squeezing, and thermalization state. show homodyne attains both displaced thermal squeezed vacuum states, whereas other optimized...

Cross-entropy (XE) measure is a widely used benchmark to demonstrate quantum computational advantage from sampling problems, such as random circuit using superconducting qubits and boson (BS). We present heuristic classical algorithm that attains better XE than the current BS experiments in verifiable regime likely attain score near-future reasonable running time. The key idea behind there exist distributions correlate with ideal probability distribution can be efficiently computed....

We find and investigate the optimal scheme of quantum distributed Gaussian sensing for estimation average independent phase shifts. show that ultimate sensitivity is achievable by using an entangled symmetric state, which can be generated a single-mode squeezed vacuum beam-splitter network, homodyne detection on each output mode in absence photon loss. Interestingly, maximal entanglement state not although presence advantageous as compared to case product state. It also demonstrated when...

Characterizing the computational advantage from noisy intermediate-scale quantum (NISQ) devices is an important task theoretical and practical perspectives. Here, we numerically investigate power of NISQ focusing on boson sampling, one well-known promising problems which can exhibit supremacy. We study hardness lossy sampling using matrix product operator (MPO) simulation to address effect photon-loss classical simulability MPO entanglement entropy (EE), characterizes a running time...

Boson sampling is a fundamentally and practically important task that can be used to demonstrate quantum supremacy using noisy intermediate-scale devices. In this Letter, we present classical algorithms for single-photon Gaussian input states take advantage of graph structure linear-optical circuit. The algorithms' complexity grows as so-called treewidth, which closely related the connectivity given Using algorithms, study approximated simulations local Haar-random circuits. For equally...

We analyze the ultimate quantum limit of resolving two identical sources in a noisy environment. prove that presence noise causing false excitation, such as thermal noise, Fisher information arbitrary states for separation objects, which quantifies resolution, always converges to zero goes zero. Noisy cases contrast with noiseless where has been shown be nonzero small distance various circumstances, revealing superresolution. In addition, we show excitation on an measurement, dark counts,...

Quantum entanglement is a crucial resource for learning properties from nature, but precise characterization of its advantage can be challenging.In this work, we consider algorithms without to those that only utilize states, measurements, and operations are separable between the main system interest an ancillary system.Interestingly, show these equivalent apply quantum circuits on interleaved with mid-circuit measurements classical feedforward.Within setting, prove tight lower bound Pauli...

Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and claimed surpass the classical simulation capabilities of even most powerful supercomputers today. However, whether current approach limited by photon loss noise in such experiments prescribes scalable path advantage an open question. To understand effect on scalability we analytically derive asymptotic operator entanglement entropy scaling, which...

Gaussian boson sampling is a promising candidate for showing experimental quantum advantage. While there evidence that noiseless hard to efficiently simulate using classical computer, the current experiments inevitably suffer from loss and other noise models. Despite high photon rate presence of noise, they are currently claimed be classically with best-known algorithm. In this work, we present tensor-network algorithm simulates whose complexity can significantly reduced when high. By...

We present a quantum-inspired classical algorithm that can be used for graph-theoretical problems, such as finding the densest <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>k</a:mi></a:math> subgraph and maximum weight clique, which are proposed applications of Gaussian boson sampler. The main observation from samplers is given graph’s adjacency matrix to encoded in sampler non-negative computing output probability sampling restricted thought...

We study the sensitivity of phase estimation in a lossy Mach-Zehnder interferometer (MZI) using two general, and practical, resources generated by laser nonlinear optical medium with passive optimal elements, which are readily available laboratory: One is two-mode separable coherent squeezed vacuum state at beam splitter other state. In view ultimate precision given quantum Fisher information, we show that can achieve lower bound error than under photon-loss channel. further consider...

Quantum fidelity is a measure to quantify the closeness between two quantum states. In an operational sense, it defined as minimal overlap probability distributions of measurement outcomes and minimum taken over all possible positive-operator valued measures (POVMs). has been investigated in various scientific fields, but identification associated optimal measurements often overlooked despite its great importance both for fundamental interest practical purposes. We find here POVMs multimode...

Boson sampling stands out as a promising approach toward experimental demonstration of quantum computational advantage. However, the presence physical noise in near-term experiments hinders realization advantage with boson sampling. Since devices is inevitable, precise characterization boundary rates where classical intractability maintained crucial for using devices. In this work, we identify level partial distinguishability that upholds We find on average $O(\log N)$ number distinguishable...

We quantify performance of quantum imaging by modeling it as a learning task and calculating the Resolvable Expressive Capacity (REC). Compared to traditionally applied Fisher information matrix approach, REC provides single-parameter interpretation overall quality for specific measurements that applies in regime finite samples. first examine two-point sources generally distributed sources, referred compact both which have intensity distributions confined within Rayleigh limit system. Our...

We consider the task of learning quantum states in bosonic continuous-variable (CV) systems. present a concrete experimentally feasible protocol that utilizes entangled measurements and reflected to enable efficient characteristic function CV with sample complexity independent number modes $n$. then prove any general adaptive scheme without requires is exponential $n$ accomplish same task, demonstrating an advantage provided by measurements. Remarkably, we also entanglement-assisted if...

Recent advancements in quantum technologies have opened new horizons for exploring the physical world ways once deemed impossible. Central to these breakthroughs is concept of advantage, where systems outperform their classical counterparts solving specific tasks. While much attention has been devoted computational speedups, advantage learning remains a largely untapped frontier. Here, we present photonic implementation quantum-enhanced protocol probability distribution multimode bosonic...

We present efficient classical algorithms to approximate expectation values and probability amplitudes in linear optical circuits. Specifically, our algorithm efficiently approximates the of observables circuits for arbitrary product input states within an additive error under a mild condition. This result suggests that certain applications relying on value estimation, such as photonic variational algorithms, may face challenges achieving quantum advantage. In addition, (marginal) output...

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

Noise is the main source that hinders us from fully exploiting quantum advantages in various informational tasks. However, characterizing and calibrating effect of noise not always feasible practice. Especially for parameter estimation, an estimator constructed without precise knowledge entails inevitable bias. Recently, virtual purification-based error mitigation (VPEM) has been proposed to apply metrology reduce such a bias occurring unknown noise. While it was demonstrated work particular...

We present a classical algorithm that approximately samples from the output distribution of certain noisy Boson Sampling experiments. This is inspired by recent result Aharonov, Gao, Landau, Liu and Vazirani makes use an observation originally due to Kalai Kindler probability experiments with Gaussian noise model can be approximated sparse low-degree polynomials. alone does not suffice for sampling, because its marginal probabilities might polynomials, furthermore, negative. solve this...

We study the evolution of conditional mutual information (CMI) in generic open quantum systems, focusing on one-dimensional random circuits with interspersed local noise. Unlike noiseless circuits, where CMI spreads linearly while being bounded by light cone, we find that noisy an error rate p exhibit superlinear propagation CMI, which diverges far beyond cone at a critical circuit depth t_{c}∝p^{-1}. demonstrate underlying mechanism for such rapid spreading is combined effect noise and...

Estimation of a global parameter defined as weighted linear combination unknown multiple parameters can be enhanced by using quantum resources. Advantageous strategies may vary depending on the weight distribution, requiring study an optimal scheme achieving maximal advantage for given sensing scenario. In this work, we propose Heisenberg-limited distributed phase Gaussian states arbitrary distribution weights with positive and negative signs. The proposed exploits entanglement only among...