arXiv subjects

Liang Jiang

Publications and source records attributed to Liang Jiang.

At least 163 records · Page 9Linked to original sources

arXiv2023

On classical simulation algorithms for noisy Boson Sampling

We present a classical algorithm that approximately samples from the output distribution of certain noisy Boson Sampling experiments. This algorithm is inspired by a recent result of Aharonov, Gao, Landau, Liu and Vazirani and makes use of an observation originally due to Kalai and Kindler that the output probability of Boson Sampling experiments with a Gaussian noise model can be approximated by sparse low-degree polynomials. This observation alone does not suffice for classical sampling, because its marginal probabilities might not be approximated by sparse low-degree polynomials, and furthermore, the approximated probabilities might be negative. We solve this problem by employing the first quantization representation to give an algorithm for computing the marginal probabilities of these experiments. We prove that when the overall noise rate is constant, the algorithm runs in time quasi-polynomial in the number of input photons $N$ and accuracy. When the overall noise rate scales as $1-x_1^γ$ for constant $x_1$ and $γ=Ω(\log N)$, the running time becomes polynomial. Furthermore, we study noisy Boson Sampling with practically relevant noise models such as partial distinguishability and photon loss. We show that the same technique does not immediately apply in these settings, leaving open the possibility of a scalable demonstration of noisy quantum advantage for these noise models in certain parameter regimes.

quant-ph↗

arXiv2022

The learnability of Pauli noise

Recently, several quantum benchmarking algorithms have been developed to characterize noisy quantum gates on today's quantum devices. A well-known issue in benchmarking is that not everything about quantum noise is learnable due to the existence of gauge freedom, leaving open the question of what information about noise is learnable and what is not, which has been unclear even for a single CNOT gate. Here we give a precise characterization of the learnability of Pauli noise channels attached to Clifford gates, showing that learnable information corresponds to the cycle space of the pattern transfer graph of the gate set, while unlearnable information corresponds to the cut space. This implies the optimality of cycle benchmarking, in the sense that it can learn all learnable information about Pauli noise. We experimentally demonstrate noise characterization of IBM's CNOT gate up to 2 unlearnable degrees of freedom, for which we obtain bounds using physical constraints. In addition, we give an attempt to characterize the unlearnable information by assuming perfect initial state preparation. However, based on the experimental data, we conclude that this assumption is inaccurate as it yields unphysical estimates, and we obtain a lower bound on state preparation noise.

quant-ph↗

arXiv2022

Deterministic Grover search with a restricted oracle

Grover's quantum search algorithm provides a quadratic quantum advantage over classical algorithms across a broad class of unstructured search problems. The original protocol is probabilistic, returning the desired result with significant probability on each query, but in general, requiring several iterations of the algorithm. We present a modified version to return the correct result with certainty without having user control over the quantum search oracle. Our deterministic, two-parameter "D2p" protocol utilizes generalized phase rotations replacing the phase inversions after a standard oracle query. The D2p protocol achieves a 100% success rate in no more than one additional iteration compared to the optimal number of steps in the original Grover's search enabling the same quadratic speed up. We also provide a visualization using the Bloch sphere for enhanced geometric intuition.

quant-ph↗

arXiv2022

Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits

We propose an autonomous quantum error correction scheme using squeezed cat (SC) code against the dominant error source, excitation loss, in continuous-variable systems. Through reservoir engineering, we show that a structured dissipation can stabilize a two-component SC while autonomously correcting the errors. The implementation of such dissipation only requires low-order nonlinear couplings among three bosonic modes or between a bosonic mode and a qutrit. While our proposed scheme is device independent, it is readily implementable with current experimental platforms such as superconducting circuits and trapped-ion systems. Compared to the stabilized cat, the stabilized SC has a much lower dominant error rate and a significantly enhanced noise bias. Furthermore, the bias-preserving operations for the SC have much lower error rates. In combination, the stabilized SC leads to substantially better logical performance when concatenating with an outer discrete-variable code. The surface-SC scheme achieves more than one order of magnitude increase in the threshold ratio between the loss rate $κ_1$ and the engineered dissipation rate $κ_2$. Under a practical noise ratio $κ_1/κ_2 = 10^{-3}$, the repetition-SC scheme can reach a $10^{-15}$ logical error rate even with a small mean excitation number of 4, which already suffices for practically useful quantum algorithms.

quant-ph↗

arXiv2022

Quantum capacity and codes for the bosonic loss-dephasing channel

Bosonic qubits encoded in continuous-variable systems provide a promising alternative to two-level qubits for quantum computation and communication. So far, photon loss has been the dominant source of errors in bosonic qubits, but the significant reduction of photon loss in recent bosonic qubit experiments suggests that dephasing errors should also be considered. However, a detailed understanding of the combined photon loss and dephasing channel is lacking. Here, we show that, unlike its constituent parts, the combined loss-dephasing channel is non-degradable, pointing towards a richer structure of this channel. We provide bounds for the capacity of the loss-dephasing channel and use numerical optimization to find optimal single-mode codes for a wide range of error rates.

quant-ph↗

arXiv2022

Robust Domain Adaptation for Machine Reading Comprehension

Most domain adaptation methods for machine reading comprehension (MRC) use a pre-trained question-answer (QA) construction model to generate pseudo QA pairs for MRC transfer. Such a process will inevitably introduce mismatched pairs (i.e., noisy correspondence) due to i) the unavailable QA pairs in target documents, and ii) the domain shift during applying the QA construction model to the target domain. Undoubtedly, the noisy correspondence will degenerate the performance of MRC, which however is neglected by existing works. To solve such an untouched problem, we propose to construct QA pairs by additionally using the dialogue related to the documents, as well as a new domain adaptation method for MRC. Specifically, we propose Robust Domain Adaptation for Machine Reading Comprehension (RMRC) method which consists of an answer extractor (AE), a question selector (QS), and an MRC model. Specifically, RMRC filters out the irrelevant answers by estimating the correlation to the document via the AE, and extracts the questions by fusing the candidate questions in multiple rounds of dialogue chats via the QS. With the extracted QA pairs, MRC is fine-tuned and provides the feedback to optimize the QS through a novel reinforced self-training method. Thanks to the optimization of the QS, our method will greatly alleviate the noisy correspondence problem caused by the domain shift. To the best of our knowledge, this could be the first study to reveal the influence of noisy correspondence in domain adaptation MRC models and show a feasible way to achieve robustness to mismatched pairs. Extensive experiments on three datasets demonstrate the effectiveness of our method.

cs.LG↗

arXiv2022

Experimental Realization and Characterization of Stabilized Pair Coherent States

The pair coherent state (PCS) is a theoretical extension of the Glauber coherent state to two harmonic oscillators. It is an interesting class of non-Gaussian continuous-variable entangled state and is also at the heart of a promising quantum error correction code: the pair cat code. Here we report an experimental demonstration of the pair coherent state of microwave photons in two superconducting cavities. We implement a cross-cavity pair-photon driven dissipation process, which conserves the photon number difference between cavities and stabilizes the state to a specific complex amplitude. We further introduce a technique of quantum subspace tomography, which enables direct measurements of individual coherence elements of a high-dimensional quantum state without global tomographic reconstruction. We characterize our two-mode quantum state with up to 4 photons in each cavity using this subspace tomography together with direct measurements of the photon number difference and the joint Wigner function. We identify the spurious cross-Kerr interaction between the cavities and our dissipative reservoir mode as a prominent dephasing channel that limits the steady-state coherence in our current scheme. Our experiment provides a set of reservoir engineering and state characterization tools to study quantum optics and implement multi-mode bosonic codes in superconducting circuits.

quant-ph↗

arXiv2022

Regression-Adjusted Estimation of Quantile Treatment Effects under Covariate-Adaptive Randomizations

Datasets from field experiments with covariate-adaptive randomizations (CARs) usually contain extra covariates in addition to the strata indicators. We propose to incorporate these additional covariates via auxiliary regressions in the estimation and inference of unconditional quantile treatment effects (QTEs) under CARs. We establish the consistency and limit distribution of the regression-adjusted QTE estimator and prove that the use of multiplier bootstrap inference is non-conservative under CARs. The auxiliary regression may be estimated parametrically, nonparametrically, or via regularization when the data are high-dimensional. Even when the auxiliary regression is misspecified, the proposed bootstrap inferential procedure still achieves the nominal rejection probability in the limit under the null. When the auxiliary regression is correctly specified, the regression-adjusted estimator achieves the minimum asymptotic variance. We also discuss forms of adjustments that can improve the efficiency of the QTE estimators. The finite sample performance of the new estimation and inferential methods is studied in simulations and an empirical application to a well-known dataset concerned with expanding access to basic bank accounts on savings is reported.

econ.EM↗

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

Failure behaviors and processing maps with failure domains for hot compression of a powder metallurgy Ni-based superalloy

Processing maps are key to guiding the thermo-mechanical processing (TMP) of superalloys. However, traditional processing maps are incapable of delimiting failure, which is an essential factor to be concerned about during the TMP of superalloys. Employing isothermal hot compression experiments and finite element analysis (FEA), the present study examined the failure behaviors of a powder metallurgy (P/M) Ni-based superalloy and constructed processing maps with failure domains based on the predicted failure threshold. The micromechanical Gurson-Tvergaard-Needleman (GTN) damage model was employed in the FEA to model the cavity-driven intergranular fracture of the superalloy. Deformation temperature and strain rate were considered in the range of 1050 ~ 1150 C and 0.001 ~ 1 s-1, respectively. The FEA results reveal that the maximum tensile stress locates at the outer budging surfaces of the samples, which causes failure initiation and subsequent propagation into longitudinal cracks, being consistent with the experiments. It is further demonstrated that the failure is strain-controlled and the critical failure strain remains nearly insensitive to the range of strain rates considered while increasing with the increase of temperature in a third-order polynomial. Finally, an optimized processing window for hot deformation of the superalloy is formulated to warrant good hot workability while avoiding flow instability and failure. The present study offers direct insights into the failure behaviors of P/M Ni-based superalloys and details a modeling strategy to delineate optimized parametric spaces for the TMP of superalloys.

cond-mat.mtrl-sci↗

arXiv2022

Construction of Bias-preserving Operations for Pair-cat Code

Fault-tolerant quantum computation with depolarization error often requires demanding error threshold and resource overhead. If the operations can maintain high noise bias -- dominated by dephasing error with small bit-flip error -- we can achieve hardware-efficient fault-tolerant quantum computation with a more favorable error threshold. Distinct from two-level physical systems, multi-level systems (such as harmonic oscillators) can achieve a desirable set of bias-preserving quantum operations while using continuous engineered dissipation or Hamiltonian protection to stabilize to the encoding subspace. For example, cat codes stabilized with driven-dissipation or Kerr nonlinearity can possess a set of biased-preserving gates while continuously correcting bosonic dephasing error. However, cat codes are not compatible with continuous quantum error correction against excitation loss error, because it is challenging to continuously monitor the parity to correct photon loss errors. In this work, we generalize the bias-preserving operations to pair-cat codes, which can be regarded as a multimode generalization of cat codes, to be compatible with continuous quantum error correction against both bosonic loss and dephasing errors. Our results open the door towards hardware-efficient robust quantum information processing with both bias-preserving operations and continuous quantum error correction simultaneously correcting bosonic loss and dephasing errors.

quant-ph↗

arXiv2022

Electron spin coherence on a solid neon surface

A single electron floating on the surface of a condensed noble-gas liquid or solid can act as a spin qubit with ultralong coherence time, thanks to the extraordinary purity of such systems. Previous studies suggest that the electron spin coherence time on a superfluid helium (He) surface can exceed 100 s. In this paper, we present theoretical studies of the electron spin coherence on a solid neon (Ne) surface, motivated by our recent experimental realization of single-electron charge qubit on solid Ne. The major spin decoherence mechanisms investigated include the fluctuating Ne diamagnetic susceptibility due to thermal phonons, the fluctuating thermal current in normal metal electrodes, and the quasi-statically fluctuating nuclear spins of the $^{21}$Ne ensemble. We find that at a typical experimental temperature about 10 mK in a fully superconducting device, the electron spin decoherence is dominated by the third mechanism via electron-nuclear spin-spin interaction. For natural Ne with 2700 ppm abundance of $^{21}$Ne, the estimated inhomogeneous dephasing time $T_{2}^{*}$ is around 0.16 ms, already better than most semiconductor quantum-dot spin qubits. For commercially available, isotopically purified Ne with 1 ppm of $^{21}$Ne, $T_{2}^{*}$ can be $0.43$ s. Under the application of Hahn echoes, the coherence time $T_{2}$ can be improved to $30$ ms for natural Ne and $81$ s for purified Ne. Therefore, the single-electron spin qubits on solid Ne can serve as promising new spin qubits.

cond-mat.mes-hall↗

arXiv2022

Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound

Quantum error correction has recently been shown to benefit greatly from specific physical encodings of the code qubits. In particular, several researchers have considered the individual code qubits being encoded with the continuous variable GottesmanKitaev-Preskill (GKP) code, and then imposed an outer discrete-variable code such as the surface code on these GKP qubits. Under such a concatenation scheme, the analog information from the inner GKP error correction improves the noise threshold of the outer code. However, the surface code has vanishing rate and demands a lot of resources with growing distance. In this work, we concatenate the GKP code with generic quantum low-density parity-check (QLDPC) codes and demonstrate a natural way to exploit the GKP analog information in iterative decoding algorithms. We first show the noise thresholds for two lifted product QLDPC code families, and then show the improvements of noise thresholds when the iterative decoder - a hardware-friendly min-sum algorithm (MSA) - utilizes the GKP analog information. We also show that, when the GKP analog information is combined with a sequential update schedule for MSA, the scheme surpasses the well-known CSS Hamming bound for these code families. Furthermore, we observe that the GKP analog information helps the iterative decoder in escaping harmful trapping sets in the Tanner graph of the QLDPC code, thereby eliminating or significantly lowering the error floor of the logical error rate curves. Finally, we discuss new fundamental and practical questions that arise from this work on channel capacity under GKP analog information, and on improving decoder design and analysis.

quant-ph↗

arXiv2022

Laziness, Barren Plateau, and Noise in Machine Learning

We define \emph{laziness} to describe a large suppression of variational parameter updates for neural networks, classical or quantum. In the quantum case, the suppression is exponential in the number of qubits for randomized variational quantum circuits. We discuss the difference between laziness and \emph{barren plateau} in quantum machine learning created by quantum physicists in \cite{mcclean2018barren} for the flatness of the loss function landscape during gradient descent. We address a novel theoretical understanding of those two phenomena in light of the theory of neural tangent kernels. For noiseless quantum circuits, without the measurement noise, the loss function landscape is complicated in the overparametrized regime with a large number of trainable variational angles. Instead, around a random starting point in optimization, there are large numbers of local minima that are good enough and could minimize the mean square loss function, where we still have quantum laziness, but we do not have barren plateaus. However, the complicated landscape is not visible within a limited number of iterations, and low precision in quantum control and quantum sensing. Moreover, we look at the effect of noises during optimization by assuming intuitive noise models, and show that variational quantum algorithms are noise-resilient in the overparametrization regime. Our work precisely reformulates the quantum barren plateau statement towards a precision statement and justifies the statement in certain noise models, injects new hope toward near-term variational quantum algorithms, and provides theoretical connections toward classical machine learning. Our paper provides conceptual perspectives about quantum barren plateaus, together with discussions about the gradient descent dynamics in \cite{together}.

cs.LG↗

arXiv2022

Coherent manipulation of graph states composed of finite-energy Gottesman-Kitaev-Preskill-encoded qubits

Graph states are a central resource in measurement-based quantum information processing. In the photonic qubit architecture based on Gottesman-Kitaev-Preskill (GKP) encoding, the generation of high-fidelity graph states composed of realistic, finite-energy approximate GKP-encoded qubits thus constitutes a key task. We consider the finite-energy approximation of GKP qubit states given by a coherent superposition of shifted finite-squeezed vacuum states, where the displacements are Gaussian distributed. We present an exact description of graph states composed of such approximate GKP qubits as a coherent superposition of a Gaussian ensemble of randomly displaced ideal GKP-qubit graph states. We determine the transformation rules for the covariance matrix and the mean displacement vector of the Gaussian distribution of the ensemble under tools such as GKP-Steane error correction and fusion operations that can be used to grow large, high-fidelity GKP-qubit graph states. The former captures the noise in the graph state due to the finite-energy approximation of GKP qubits, while the latter relates to the possible absolute displacement errors on the individual qubits due to the homodyne measurements that are a part of these tools. The rules thus help in pinning down an exact coherent error model for graph states generated from truly finite-energy GKP qubits, which can shed light on their error correction properties.

quant-ph↗

arXiv2022

Distributed quantum phase sensing for arbitrary positive and negative weights

Estimation of a global parameter defined as a weighted linear combination of unknown multiple parameters can be enhanced by using quantum resources. Advantageous quantum strategies may vary depending on the weight distribution, requiring the study of optimal schemes achieving a maximal quantum advantage for a given sensing scenarios. In this work, we propose an optimal distributed quantum phase sensing scheme using Gaussian states with zero displacement for an arbitrary distribution of the weights with positive and negative signs. The estimation precision of the optimal scheme is derived, and shown to be achievable by using squeezed states injected into linear beam-splitter networks and performing homodyne detection on them in the absence of loss. Interestingly, the optimal scheme exploits entanglement of Gaussian states only among the modes assigned with equal signs of the weights, but separates the modes with opposite weight signs. We also provide a deeper understanding of our finding by focusing on the two-mode case, in comparison with the cases using non-Gaussian probe states. We expect this work to motivate further studies on quantum-enhanced distributed sensing schemes considering various types of physical parameters with an arbitrary weight distribution.

quant-ph↗

arXiv2022

Quantum transduction is enhanced by single mode squeezing operators

Quantum transduction is an essential ingredient in scaling up distributed quantum architecture and is actively pursued based on various physical platforms. However, demonstrating a transducer with positive quantum capacity is still practically challenging. In this work, we discuss a new approach to relax the impedance matching condition to half impedance matching condition, which is achieved by introducing two-photon drive in the electro-optic transducer. We show the quantum transduction capacity can be enhanced and can be understood in a simple interference picture with the help of Bloch-Messiah decomposition. The parameter regimes with positive quantum capacity is identified and compared with and without the drive, indicating that the parametric drive-induced enhancement is really promising in demonstrating quantum state conversion, and is expected to boost the performance of transduction with various physical platforms.

quant-ph↗

arXiv2022

Algebraic structure of path-independent quantum control

Path-independent (PI) quantum control has recently been proposed to integrate quantum error correction and quantum control [Phys. Rev. Lett. 125, 110503 (2020)], achieving fault-tolerant quantum gates against ancilla errors. Here we reveal the underlying algebraic structure of PI quantum control. The PI Hamiltonians and propagators turn out to lie in an algebra isomorphic to the ordinary matrix algebra, which we call the PI matrix algebra. The PI matrix algebra, defined on the Hilbert space of a composite system (including an ancilla system and a central system), is isomorphic to the matrix algebra defined on the Hilbert space of the ancilla system. By extending the PI matrix algebra to the Hilbert-Schmidt space of the composite system, we provide an exact and unifying condition for PI quantum control against ancilla noise.

quant-ph↗