Quantum Physics (quant-ph)

Abstract: In quantum information technology, crucial information is regularly encoded in different quantum states. To extract information, the identification of one state from the others is inevitable. However, if the states are non-orthogonal and unknown, this task will become awesomely tricky, especially when our resources are also limited. Here, we introduce the quantum stochastic neural network (QSNN), and show its capability to accomplish the binary discrimination of quantum states. After a handful of optimizing iterations, the QSNN achieves a success probability close to the theoretical optimum, no matter whether the states are pure or mixed. Other than binary discrimination, the QSNN is also applied to classify an unknown set of states into two types: entangled ones and separable ones. After training with four samples, it can classify a number of states with acceptable accuracy. Our results suggest that the QSNN has the great potential to process unknown quantum states in quantum information.

Abstract: The quantum circuit model is the most commonly used model for implementing quantum computers and quantum neural networks whose essential tasks are to realize certain unitary operations. The circuit model usually implements a desired unitary operation by a sequence of single-qubit and two-qubit unitary gates from a universal set. Although this certainly facilitates the experimentalists as they only need to prepare several different kinds of universal gates, the number of gates required to implement an arbitrary desired unitary operation is usually large. Hence the efficiency in terms of the circuit depth or running time is not guaranteed. Here we propose an alternative approach; we use a simple discrete-time quantum walk (DTQW) on a cycle graph to model an arbitrary unitary operation without the need to decompose it into a sequence of gates of smaller sizes. Our model is essentially a quantum neural network based on DTQW. Firstly, it is universal as we show that any unitary operation can be realized via an appropriate choice of coin operators. Secondly, our DTQW-based neural network can be updated efficiently via a learning algorithm, i.e., a modified stochastic gradient descent algorithm adapted to our network. By training this network, one can promisingly find approximations to arbitrary desired unitary operations. With an additional measurement on the output, the DTQW-based neural network can also implement general measurements described by positive-operator-valued measures (POVMs). We show its capacity in implementing arbitrary 2-outcome POVM measurements via numeric simulation. We further demonstrate that the network can be simplified and can overcome device noises during the training so that it becomes more friendly for laboratory implementations. Our work shows the capability of the DTQW-based neural network in quantum computation and its potential in laboratory implementations.

Abstract: Multipartite entanglement is a critical resource in quantum information processing that exhibits much richer phenomenon and stronger correlations than in bipartite systems. This advantage is also reflected in its multi-user applications. Although many demonstrations have used photonic polarization qubits, polarization-mode dispersion confines the transmission of photonic polarization qubits through an optical fiber. Consequently, time-bin qubits have a particularly important role to play in quantum communication systems. Here, we generate a three-photon time-bin Greenberger-Horne-Zeilinger (GHZ) state using a 2 x 2 optical switch as a time-dependent beam splitter to entangle time-bin Bell states from a spontaneous parametric down-conversion source and a weak coherent pulse. To characterize the three-photon time-bin GHZ state, we performed measurement estimation, showed a violation of the Mermin inequality, and used quantum state tomography to fully reconstruct a density matrix, which shows a state fidelity exceeding 70%. We expect that our three-photon time-bin GHZ state can be used for long-distance multi-user quantum communication.

Abstract: We point out that, when the dimension of the Hilbert space is greater than two, Bell's operators entering the Bell-CHSH inequality do exhibit inequivalent unitary matrix representations. Although the Bell-CHSH inequality turns out to be violated, the size of the violation is different for different representations, the maximum violation being given by Tsirelson's bound. The feature relies on a pairing mechanism between the modes of the entangled state employed to test the Bell-CHSH inequality.

Abstract: It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is discussed, with the quantum contribution specified by a measure of the noncommutativity of a given set of operators relative to the quantum state, and the classical contribution generated by the mixedness of the state. Suitable measures of noncommutativity or `quantumness' include quantum Fisher information and the asymmetry of a given set, group or algebra of operators, and are generalised to nonprojective observables and quantum channels. Strong entropic uncertainty relations and lower bounds for R\'enyi entropies are obtained, valid for both projective and nonprojective observables, that take the mixedness of the state into account via a classical contribution to the lower bound. These relations can also be interpreted without reference to quantum-classical decompositions, as tradeoff relations that bound the asymmetry of one observable in terms of the entropy of another.

Abstract: Entanglement and uncertainty relation are two focuses of quantum theory. We relate entanglement sharing to entropic uncertainty relation in a $(d\times d)$-dimensional system via weak measurements with different pointers. We consider both the scenarios of one-sided sequential measurements in which the entangled pair is distributed to multiple Alices and one Bob and two-sided sequential measurements in which the entangled pair is distributed to multiple Alices and Bobs. It is found that the maximum number of observers sharing the entanglement strongly depends on the measurement scenarios, the pointer states of the apparatus, and the local dimension $d$ of each subsystem, while the required minimum measurement precision to achieve entanglement sharing decreases to its asymptotic value with the increase of $d$. The maximum number of observers remain unaltered even when the state is not maximally entangled but has strong enough entanglement.

Abstract: The Liouvillian exceptional points for a quantum Markovian master equation of an oscillator in a generic environment are obtained. They occur at the points when the modified frequency of the oscillator vanishes, whereby the eigenvalues of the Liouvillian become real. In a generic system there are two parameters that modify the oscillator's natural frequency. One of the parameters can be the damping rate. The exceptional point then corresponds to critical damping of the oscillator. This situation is illustrated by the Caldeira--Leggett (CL) equation and the Markovian limit of the Hu--Paz--Zhang (HPZ) equation. The other parameter changes the oscillator's effective mass whereby the exceptional point is reached in the limit of extremely heavy oscillator. This situation is illustrated by a modified form of the Kossakowski--Lindblad (KL) equation. The eigenfunctions coalesce at the exceptional points and break into subspaces labelled by a natural number $N$. In each of the $N$-subspace, there is a $(N+1)$-fold degeneracy and the Liouvillian has a Jordan block structure of order-$(N+1)$. We obtain the explicit form of the generalized eigenvectors for a few Liouvillians. Because of the degeneracies, there is a freedom of choice in the generalized eigenfunctions. This freedom manifests itself as an invariance in the Jordan block structure under a similarity transformation whose form is obtained. We compare the relaxation of the first excited state of an oscillator in the underdamped region, critically damped region which corresponds to the exceptional point, and overdamped region using the generalized eigenvectors of the CL equation.

Abstract: Although quantum mechanics applies to many macroscopic superconducting devices, one basic prediction remained controversial for decades. Namely, a Josephson junction connected to a resistor must undergo a dissipation-induced quantum phase transition from superconductor to insulator once the resistor's value exceeds $h/4e^2 \approx 6.5~\textrm{k}\Omega$ ($h$ is Planck's constant, $e$ is the electron charge). Here we finally demonstrate this transition by observing the resistor's internal dynamics. Implementing our resistor as a long transmission line section, we find that a junction scatters electromagnetic excitations in the line as either inductance (superconductor) or capacitance (insulator), depending solely on the line's wave impedance. At the phase boundary, the junction itself acts as ideal resistance: in addition to elastic scattering, incident photons can spontaneously down-convert with a frequency-independent probability, which provides a novel marker of quantum-critical behavior.

Abstract: This paper explores the effect of three-dimensional rotations on two-qubit Bell states and proposes a Bayesian method for the estimation of the parameters of the rotation. We use a particle filter to estimate the parameters of the rotation from a sequence of Bell state measurements and we demonstrate that the resultant improvement over the optimal single qubit case approaches the $\sqrt{2}$ factor that is consistent with the Heisenberg limit. We also demonstrate how the accuracy of the estimation method is a function of the purity of mixed states.

Abstract: The challenge of pattern recognition is to invoke a strategy that can accurately extract features of a dataset and classify its samples. In realistic scenarios this dataset may be a physical system from which we want to retrieve information, such as in the readout of optical classical memories. The theoretical and experimental development of quantum reading has demonstrated that the readout of optical memories can be dramatically enhanced through the use of quantum resources (namely entangled input-states) over that of the best classical strategies. However, the practicality of this quantum advantage hinges upon the scalability of quantum reading, and up to now its experimental demonstration has been limited to individual cells. In this work, we demonstrate for the first time quantum advantage in the multi-cell problem of pattern recognition. Through experimental realizations of digits from the MNIST handwritten digit dataset, and the application of advanced classical post-processing, we report the use of entangled probe states and photon-counting to achieve quantum advantage in classification error over that achieved with classical resources, confirming that the advantage gained through quantum sensors can be sustained throughout pattern recognition and complex post-processing. This motivates future developments of quantum-enhanced pattern recognition of bosonic-loss within complex domains.

Abstract: Developing protocols for preserving information in quantum systems is a central quest for implementing realistic quantum computation. However, many of the most promising approaches to this problem rely on hypotheses that may not reflect practical physical scenarios, like knowing the exact dynamics of the qubit-environment system or being able to store an informational qubit in multiple physical qubits. Here, we step away from these usual assumptions and analyze the probability of successfully storing a classical bit of information on a physical qubit during a single computational step, both for the case in which the qubit evolves freely and also when it is subject to a sequence of repeated measurements. The setup consists of a qubit coupled to a heat bath at finite temperature, whose dynamics is given by a generalized amplitude damping channel in a pointer basis that does not necessarily coincide with the computational basis of the qubit. We first show that requiring the dynamics to be Markovian implies an exponential decay of the pointer basis' populations. Then, we obtain the success probability as function of time and angle $\theta_0$ between the initial state of the qubit and the ground state of the pointer basis. Finally, we calculate these probabilities for the Zeno effective dynamics and show that they are never larger than those for the free evolution, implying that a repeated measurements protocol cannot improve the probability of a successful storage in our model. This last result indicates that to perform realistic quantum computation, when information is being continuously lost to the environment, the information must be somehow driven back into the system, highlighting this as the core feature of any technique that aims at reducing noise in open quantum systems.

Abstract: A nonclassical light source is essential for implementing a wide range of quantum information processing protocols, including quantum computing, networking, communication, and metrology. In the microwave regime, propagating photonic qubits that transfer quantum information between multiple superconducting quantum chips serve as building blocks of large-scale quantum computers. In this context, spectral control of propagating single photons is crucial for interfacing different quantum nodes with varied frequencies and bandwidth. Here we demonstrate a microwave quantum light source based on superconducting quantum circuits that can generate propagating single photons, time-bin encoded photonic qubits and qudits. In particular, the frequency of the emitted photons can be tuned in situ as large as 200 MHz. Even though the internal quantum efficiency of the light source is sensitive to the working frequency, we show that the fidelity of the propagating photonic qubit can be well preserved with the time-bin encoding scheme. Our work thus demonstrates a versatile approach to realizing a practical quantum light source for future distributed quantum computing.

Abstract: We have studied the performance of a measurement-based quantum Otto engine (QOE) in a working system of two spins coupled by Heisenberg anisotropic interaction. A non-selective quantum measurement fuels the engine. We have calculated thermodynamic quantities of the cycle in terms of the transition probabilities between the instantaneous energy eigenstates, and also between the instantaneous energy eigenstates and the basis states of the measurement, when the unitary stages of the cycle operate for a finite time $\tau$. The efficiency attains a large value in the limit of $\tau \rightarrow 0$ and then gradually reaches the adiabatic value in a long time limit $\tau \rightarrow \infty$. For finite values of $\tau$ and for anisotropic interaction, an oscillatory behaviour of the efficiency of the engine is observed. This oscillation can be interpreted in terms of interference between the relevant transition amplitudes in the unitary stages of the engine cycle. Therefore, for a suitable choice of timing of the unitary processes in the short time regime, the engine can have a higher work output and less heat absorption, such that it works more efficiently than a quasi-static engine. In the case of an always-on heat bath, in a very short time the bath has a negligible effect on its performance.

Abstract: The study of quantum information processing seeks to characterize the resources that enable quantum information processing to perform tasks that are unfeasible or inefficient for classical information processing. Quantum cryptography is one such task, and researchers have identified entanglement as a sufficient resource for secure key generation. However, quantum discord, another type of quantum correlation beyond entanglement, has been found to be necessary for guaranteeing secure communication due to its direct relation to information leakage. Despite this, it is a long-standing problem how to make use of discord to analyze security in a specific quantum cryptography protocol. Here, based on our proposed quantum discord witness recently, we successfully address this issue by considering a BB84-like quantum key distribution protocol and its equivalent entanglement-based version. Our method is robust against imperfections in qubit sources and qubit measurements as well as basis misalignment due to quantum channels, which results in a better key rate than standard BB84 protocol. Those advantages are experimentally demonstrated via photonic phase encoding systems, which shows the practicality of our results.

Abstract: We investigate a scheme for observing the third-order exceptional point (EP3) in an ion-cavity system. In the lambda-type level configuration, the ion is driven by a pump field, and the resonatoris probed with another weak laser field. We exploit the highly asymmetric branching ratio of an ion's excited state to satisfy the weak-excitation limit, which allows us to construct the non-Hermitian Hamiltonian $(H_{\textrm{nH}})$. Via fitting the cavity-transmission spectrum, the eigenvalues of $H_{\textrm{nH}}$ are obtained.The EP3 appears at a point where the Rabi frequency of the pump laser and the atom-cavity coupling constant balance the loss rates of the system. Feasible experimental parameters are provided.

Abstract: We propose a quantum algorithm for solving physical problems represented by the lattice Boltzmann formulation. Specifically, we deal with the case of a single phase, incompressible fluid obeying the Bhatnagar-Gross-Krook model. We use the framework introduced by Kowalski that links the nonlinear dynamics of a system to the evolution of bosonic modes, assigning a Carleman linearization order to the truncation in the bosonic Fock space of the bosons. The streaming and collision steps are both achieved via unitary operators. A quantized version of the nonlinear collision term has been implemented, without introducing variables of discrete densities coupled from neighbouring sites, unlike the classical Carleman technique. We use the compact mapping of the bosonic modes to qubits that uses a number of qubits which scales logarithmically with the size of truncated bosonic Fock space. The work can be readily extended to the multitude of multiphysics problems which could adapt the lattice Boltzmann formulation.

Abstract: We present and discuss a master equation blueprint for a generic class of quantum measurement feedback based models of friction. A desired velocity-dependent friction force is realized on average by random repeated applications of unsharp momentum measurements followed by immediate outcome-dependent momentum displacements. The master equations can describe arbitrarily strong measurement-feedback processes as well as the weak continuous limit resembling diffusion master equations of Caldeira-Leggett type. We show that the special case of linear friction can be equivalently represented by an average over random position measurements with squeezing and position displacements as feedback. In fact, the dissipative continuous spontaneous localization model of objective wavefunction collapse realizes this representation for a single quantum particle. We reformulate a consistent many-particle generalization of this model and highlight the possibility of feedback-induced correlations between otherwise non-interacting particles.

Abstract: We propose a scheme for detecting and correcting faults in any Clifford circuit. The scheme is based on the observation that the set of all possible outcome bit-strings of a Clifford circuit is a linear code, which we call the outcome code. From the outcome code we construct a corresponding stabilizer code, the spacetime code. Our construction extends the circuit-to-code construction of Bacon, Flammia, Harrow and Shi [2], revisited recently by Gottesman [16], to include intermediate and multi-qubit measurements. With this correspondence, we reduce the problem of correcting faults in a circuit to the well-studied problem of correcting errors in a stabilizer code. More precisely, a most likely error decoder for the spacetime code can be transformed into a most likely fault decoder for the circuit. We give efficient algorithms to construct the outcome and spacetime codes. We also identify conditions under which these codes are LDPC, and give an algorithm to generate low-weight checks, which can then be combined with effcient LDPC code decoders.

Abstract: In this study, we introduce an autonomous method for addressing the detection and classification of quantum entanglement, a core element of quantum mechanics that has yet to be fully understood. We employ a multi-layer perceptron to effectively identify entanglement in both two- and three-qubit systems. Our technique yields impressive detection results, achieving nearly perfect accuracy for two-qubit systems and over $90\%$ accuracy for three-qubit systems. Additionally, our approach successfully categorizes three-qubit entangled states into distinct groups with a success rate of up to $77\%$. These findings indicate the potential for our method to be applied to larger systems, paving the way for advancements in quantum information processing applications.

Abstract: Quantum computation consists of a quantum state corresponding to a solution, and measurements with some observables. To obtain a solution with an accuracy $\epsilon$, measurements $O(n/\epsilon^2)$ are required, where $n$ is the size of a problem. The cost of these measurements requires a large computing time for an accurate solution. In this paper, we propose a quantum multi-resolution measurement (QMRM), which is a hybrid quantum-classical algorithm that gives a solution with an accuracy $\epsilon$ in $O(n\log(1/\epsilon))$ measurements using a pair of functions. The QMRM computational cost with an accuracy $\epsilon$ is smaller than $O(n/\epsilon^2)$. We also propose an algorithm entitled QMRM-QLS (quantum linear solver) for solving a linear system of equations using the Harrow-Hassidim-Lloyd (HHL) algorithm as one of the examples. We perform some numerical experiments that QMRM gives solutions to with an accuracy $\epsilon$ in $O(n\log(1/\epsilon))$ measurements.

Abstract: We review several aspects related to the confinement of a massless scalar field in a cavity with a movable conducting wall of finite mass, free to move around its equilibrium position to which it is bound by a harmonic potential, and whose mechanical degrees of freedom are described quantum mechanically. This system, for small displacements of the movable wall from its equilibrium position, can be described by an effective interaction Hamiltonian between the field and the mirror, quadratic in the field operators and linear in the mirror operators. In the interacting, i.e. dressed, ground state, we first consider local field observables such as the field energy density: we evaluate changes of the field energy density in the cavity with the movable wall with respect to the case of a fixed wall, and corrections to the usual Casimir forces between the two walls. We then investigate the case of two one-dimensional cavities separated by a movable wall of finite mass, with two massless scalar fields defined in the two cavities. We show that in this case correlations between the squared fields in the two cavities exist, mediated by the movable wall, at variance with the fixed-wall case.