The Quantum State Preparation problem aims to prepare an n-qubit quantum state $|psi_vrangle=sum_{k=0}^{2^n-1}v_k|krangle$ from initial state $|0rangle^{otimes n}$, for a given vector $v=(v_0,ldots,v_{2^n-1})inmathbb{C}^{2^n}$ with $|v|_2=1$. The pro
blem is of fundamental importance in quantum algorithm design, Hamiltonian simulation and quantum machine learning, yet its circuit depth complexity remains open in the general case with ancillary qubits. In this paper, we study efficient constructions of quantum circuits for preparing a quantum state: Given $m=O(2^n/n^2)$ ancillary qubits, we construct a circuit to prepare $|psi_vrangle$ with depth $Theta(2^n/(m+n))$, which is optimal in this regime. In particular, when $m=Theta(2^n/n^2)$, the circuit depth is $Theta(n^2)$, which is an exponential improvement of the previous bound of $O(2^n)$. For $m=omega(2^n/n^2)$, we prove a lower bound of $Omega(n)$, an exponential improvement over the previous lower bound of $Omega(log n)$, leaving a polynomial gap between $Omega(n)$ and $O(n^2)$ for the depth complexity. These results also imply a tight bound of $Theta(4^n/(m+n))$ for depth of circuits implementing a general n-qubit unitary using $m=O(2^n/n)$ ancillary qubits. This closes a gap for circuits without ancillary qubits; for circuits with sufficiently many ancillary qubits, this gives a quadratic saving from $O(4^n)$ to $tildeTheta(2^n)$.Our circuits are deterministic, prepare the state and carry out the unitary precisely, utilize the ancillary qubits tightly and the depths are optimal in a wide range of parameter regime. The results can be viewed as (optimal) time-space tradeoff bounds, which is not only theoretically interesting, but also practically relevant in the current trend that the number of qubits starts to take off, by showing a way to use a large number of qubits to compensate the short qubit lifetime.
The belief function in Dempster Shafer evidence theory can express more information than the traditional Bayesian distribution. It is widely used in approximate reasoning, decision-making and information fusion. However, its power exponential explosi
on characteristics leads to the extremely high computational complexity when handling large amounts of elements in classic computers. In order to solve the problem, we encode the basic belief assignment (BBA) into quantum states, which makes each qubit correspond to control an element. Besides the high efficiency, this quantum expression is very conducive to measure the similarity between two BBAs, and the measuring quantum algorithm we come up with has exponential acceleration theoretically compared to the corresponding classical algorithm. In addition, we simulate our quantum version of BBA on Qiskit platform, which ensures the rationality of our algorithm experimentally. We believe our results will shed some light on utilizing the characteristic of quantum computation to handle belief function more conveniently.
Recently, Halder emph{et al.} [S. Halder emph{et al.}, Phys. Rev. Lett. textbf{122}, 040403 (2019)] present two sets of strong nonlocality of orthogonal product states based on the local irreducibility. However, for a set of locally indistinguishable
orthogonal entangled states, the remaining question is whether the states can reveal strong quantum nonlocality. Here we present a general definition of strong quantum nonlocality based on the local indistinguishability. Then, in $2 otimes 2 otimes 2$ quantum system, we show that a set of orthogonal entangled states is locally reducible but locally indistinguishable in all bipartitions, which means the states have strong nonlocality. Furthermore, we generalize the result in N-qubit quantum system, where $Ngeqslant 3$. Finally, we also construct a class of strong nonlocality of entangled states in $dotimes dotimes cdots otimes d, dgeqslant 3$. Our results extend the phenomenon of strong nonlocality for entangled states.
In this paper, we generalize the concept of strong quantum nonlocality from two aspects. Firstly in $mathbb{C}^dotimesmathbb{C}^dotimesmathbb{C}^d$ quantum system, we present a construction of strongly nonlocal quantum states containing $6(d-1)^2$ or
thogonal product states, which is one order of magnitude less than the number of basis states $d^3$. Secondly, we give the explicit form of strongly nonlocal orthogonal product basis in $mathbb{C}^3otimes mathbb{C}^3otimes mathbb{C}^3otimes mathbb{C}^3$ quantum system, where four is the largest known number of subsystems in which there exists strong quantum nonlocality up to now. Both the two results positively answer the open problems in [Halder, textit{et al.}, PRL, 122, 040403 (2019)], that is, there do exist and even smaller number of quantum states can demonstrate strong quantum nonlocality without entanglement.
Early and accurately detecting faults in rotating machinery is crucial for operation safety of the modern manufacturing system. In this paper, we proposed a novel Deep fault diagnosis (DFD) method for rotating machinery with scarce labeled samples. D
FD tackles the challenging problem by transferring knowledge from shallow models, which is based on the idea that shallow models trained with different hand-crafted features can reveal the latent prior knowledge and diagnostic expertise and have good generalization ability even with scarce labeled samples. DFD can be divided into three phases. First, a spectrogram of the raw vibration signal is calculated by applying a Short-time Fourier transform (STFT). From those spectrograms, discriminative time-frequency domain features can be extracted and used to form a feature pool. Then, several candidate Support vector machine (SVM) models are trained with different combinations of features in the feature pool with scarce labeled samples. By evaluating the pretrained SVM models on the validation set, the most discriminative features and best-performed SVM models can be selected, which are used to make predictions on the unlabeled samples. The predicted labels reserve the expert knowledge originally carried by the SVM model. They are combined together with the scarce fine labeled samples to form an Augmented training set (ATS). Finally, a novel 2D deep Convolutional neural network (CNN) model is trained on the ATS to learn more discriminative features and a better classifier. Experimental results on two fault diagnosis datasets demonstrate the effectiveness of the proposed DFD, which achieves better performance than SVM models and the vanilla deep CNN model trained on scarce labeled samples. Moreover, it is computationally efficient and is promising for real-time rotating machinery fault diagnosis.
A protocol for two-party secure function evaluation (2P-SFE) aims to allow the parties to learn the output of function $f$ of their private inputs, while leaking nothing more. In a sense, such a protocol realizes a trusted oracle that computes $f$ an
d returns the result to both parties. There have been tremendous strides in efficiency over the past ten years, yet 2P-SFE protocols remain impractical for most real-time, online computations, particularly on modestly provisioned devices. Intels Software Guard Extensions (SGX) provides hardware-protected execution environments, called enclaves, that may be viewed as trusted computation oracles. While SGX provides native CPU speed for secure computation, previous side-channel and micro-architecture attacks have demonstrated how security guarantees of enclaves can be compromised. In this paper, we explore a balanced approach to 2P-SFE on SGX-enabled processors by constructing a protocol for evaluating $f$ relative to a partitioning of $f$. This approach alleviates the burden of trust on the enclave by allowing the protocol designer to choose which components should be evaluated within the enclave, and which via standard cryptographic techniques. We describe SGX-enabled SFE protocols (modeling the enclave as an oracle), and formalize the strongest-possible notion of 2P-SFE for our setting. We prove our protocol meets this notion when properly realized. We implement the protocol and apply it to two practical problems: privacy-preserving queries to a database, and a version of Dijkstras algorithm for privacy-preserving navigation. Our evaluation shows that our SGX-enabled SFE scheme enjoys a 38x increase in performance over garbled-circuit-based SFE. Finally, we justify modeling of the enclave as an oracle by implementing protections against known side-channels.
With the emerging of touch-less human-computer interaction techniques and gadgets, mid-air hand gestures have been widely used for authentication. Much literature examined either the usability or security of a handful of gestures. This paper aims at
quantifying usability and security of gestures as well as understanding their relationship across multiple gestures. To study gesture-based authentication, we design an authentication method that combines Dynamic Time Warping (DTW) and Support Vector Machine (SVM), and conducted a user study with 42 participants over a period of 6 weeks. We objectively quantify the usability of a gesture by the number of corners and the frame length of all gesture samples, quantify the security using the equal error rate (EER), and the consistency by EER over a period of time. Meanwhile, we obtain subjective evaluation of usability and security by conducting a survey. By examining the responses, we found that the subjective evaluation confirms with the objective ones, and usability is in inverse relationship with security. We studied the consistency of gestures and found that most participants forgot gestures to some degree and reinforcing the memorization of gestures is necessary to improve the authentication performance. Finally, we performed a study with another 17 participants on shoulder surfing attacks, where attackers can observe the victims multiple times. The results show that shoulder surfing does not help to boost the attacks.
Measure synchronization (MS) in a two-species bosonic Josephson junction (BJJ) is studied based on semi-classical theory. Six different scenarios for MS, including two in the Josephson oscillation regime (0 phase mode) and four in the self-trapping r
egime ($pi$ phase mode), have been clearly shown. Systematic investigations of the common features behind these different scenarios have been performed. We show that the average energies of the two species merge at the MS transition point. The scaling of the power law near the MS transition has been verified, and the critical exponent is 1/2 for all of the different scenarios for MS. We also illustrate MS in a three-dimensional phase space; from this illustration, more detailed information on the dynamical process can be obtained. Particularly, by analyzing the Poincare sections with changing interspecies interactions, we find that the two-species BJJ exhibits separatrix crossing behavior at MS transition point, and such behavior depicts the general mechanism behind the different scenarios for the MS transitions. The new critical behavior found in a two-species BJJ is expected to be found in real systems of atomic Bose gases.
