Quantum Physics (quant-ph)

Abstract: Transform-limited photon emission from quantum emitters is essential for high-fidelity entanglement generation. In this study, we report the coherent optical property of a single negatively-charged lead-vacancy (PbV) center in diamond. Photoluminescence excitation measurements reveal stable fluorescence with a linewidth of 39 MHz at 6 K, close to the transform-limit estimated from the lifetime measurement. We observe four orders of magnitude different linewidths of the two zero-phonon-lines, and find that that the phonon-induced relaxation in the ground state contributes to this huge difference in the linewidth. Due to the suppressed phonon absorption in the PbV center, we observe nearly transform-limited photon emission up to 16 K, demonstrating its high temperature robustness compared to other color centers in diamond.

Abstract: We analyse a nonlinear QW model which can be experimentally implemented using the components of the electric field on an optical nonlinear Kerr medium, which translates into a rotation in the coin operator, with an angle which depends (in a nonlinear fashion) on the state of the walker. This simple dependence makes it easy to consider the space-time continuum limit of the evolution equation, which takes the form of a nonlinear Dirac equation. The analysis of this continuum limit allows us, under some approximations, to gain some insight into the nature of soliton structures, which is illustrated by our numerical calculations. These solitons are stable structures whose trajectories can be modulated by choosing the appropriate initial conditions. We have also studied the stability of solitons when they are subject to an additional phase that simulates an external electric field, and also explored if they are formed in higher dimensional spaces.

Abstract: Quantum Key Distribution is a key distribution method that uses the qubits to safely distribute one-time use encryption keys between two or more authorised participants in a way that ensures the identification of any eavesdropper. In this paper, we have done a comparison between the BB84 and B92 protocols and BBM92 and E91 entanglement based protocols for satellite based uplink and downlink in low Earth orbit. The expressions for the quantum bit error rate and the keyrate are given for all four protocols. The results indicate that, when compared to the B92 protocol, the BB84 protocol guarantees the distribution of a higher secure keyrate for a specific distance. Similarly, it is observed that BBM92 ensures higher keyrate in comparison with E91 protocol.

Abstract: We introduce a general framework called neural network (NN) encoded variational quantum algorithms (VQAs), or NN-VQA for short, to address the challenges of implementing VQAs on noisy intermediate-scale quantum (NISQ) computers. Specifically, NN-VQA feeds input (such as parameters of a Hamiltonian) from a given problem to a neural network and uses its outputs to parameterize an ansatz circuit for the standard VQA. Combining the strengths of NN and parameterized quantum circuits, NN-VQA can dramatically accelerate the training process of VQAs and handle a broad family of related problems with varying input parameters with the pre-trained NN. To concretely illustrate the merits of NN-VQA, we present results on NN-variational quantum eigensolver (VQE) for solving the ground state of parameterized XXZ spin models. Our results demonstrate that NN-VQE is able to estimate the ground-state energies of parameterized Hamiltonians with high precision without fine-tuning, and significantly reduce the overall training cost to estimate ground-state properties across the phases of XXZ Hamiltonian. We also employ an active-learning strategy to further increase the training efficiency while maintaining prediction accuracy. These encouraging results demonstrate that NN-VQAs offer a new hybrid quantum-classical paradigm to utilize NISQ resources for solving more realistic and challenging computational problems.

Abstract: Cavity optomechanical systems in the quantum regime consist of a cavity mode and mechanical element coupled together through radiation pressure. In the nonlinear optomechanical regime, open-system dynamics is generally challenging to treat analytically, since the noise terms do not commute with the optomechanical interaction term. Specifically, a general treatment of both Markovian and non-Markovian mechanical noise in the nonlinear optomechanical regime is still outstanding. Here we address this question by solving the full dynamics of an optomechanical system in the nonlinear regime where the mechanical element interacts with a bath of harmonic oscillators, representing full quantum Brownian motion. The solutions, which are exact and analytic, allow us to consider the strength of the optomechanical nonlinearity in the presence of both Markovian (Ohmic) and non-Markovian (sub-Ohmic and super-Ohmic) baths. We show that that while the strength of the nonlinearity is generally reduced by a Markovian bath spectrum, it can be enhanced by constructing a bath with a highly non-Markovian structure. The results have potential implications for future optomechanical experiments which seek to achieve a strong optomechanical nonlinearity.

Abstract: We approach two interconnected problems of quantum information processing in networks: Conference key agreement and entanglement distillation, both in the so-called source model where the given resource is a multipartite quantum state and the players interact over public classical channels to generate the desired correlation. The first problem is the distillation of a conference key when the source state is shared between a number of legal players and an eavesdropper; the eavesdropper, apart from starting off with this quantum side information, also observes the public communication between the players. The second is the distillation of Greenberger-Horne-Zeilinger (GHZ) states by means of local operations and classical communication (LOCC) from the given mixed state. These problem settings extend our previous paper [IEEE Trans. Inf. Theory 68(2):976-988, 2022], and we generalise its results: using a quantum version of the task of communication for omniscience, we derive novel lower bounds on the distillable conference key from any multipartite quantum state by means of non-interacting communication protocols. Secondly, we establish novel lower bounds on the yield of GHZ states from multipartite mixed states. Namely, we present two methods to produce bipartite entanglement between sufficiently many nodes so as to produce GHZ states. Next, we show that the conference key agreement protocol can be made coherent under certain conditions, enabling the direct generation of multipartite GHZ states.

Abstract: We give a rigorous proof of Conjecture 3.1 by Prosen [Prosen T 2010 J. Stat. Mech. $\textbf{2010}$ P07020] on the nilpotent part of the Jordan decomposition of a quadratic fermionic Liouvillian. We also show that the number of the Jordan blocks of each size can be expressed in terms of the coefficients of a polynomial called the $q$-binomial coefficient and describe the procedure to obtain the Jordan canonical form of the nilpotent part.

Abstract: Quantum battery (QB) is the energy storage and extraction device that is governed by the principles of quantum mechanics. Here we propose a three-level Dicke QB and investigate its charging process by considering three quantum optical states: a Fock state, a coherent state, and a squeezed state. The performance of the QB in a coherent state is substantially improved compared to a Fock and squeezed states. We find that the locked energy is positively related to the entanglement between the charger and the battery, and diminishing the entanglement leads to the enhancement of the ergotropy. We demonstrate the QB system is asymptotically free as $N \rightarrow \infty$. The stored energy becomes fully extractable when $N=10$, and the charging power follows the consistent behavior as the stored energy, independent of the initial state of the charger.

Abstract: Checking whether two quantum circuits are equivalent is important for the design and optimization of quantum-computer applications with real-world devices. We consider quantum circuits consisting of Clifford gates, a practically-relevant subset of all quantum operations which is large enough to exhibit quantum features such as entanglement and forms the basis of, for example, quantum-error correction and many quantum-network applications. We present a deterministic algorithm that is based on a folklore mathematical result and demonstrate that it is capable of outperforming previously considered state-of-the-art method. In particular, given two Clifford circuits as sequences of single- and two-qubit Clifford gates, the algorithm checks their equivalence in $O(n \cdot m)$ time in the number of qubits $n$ and number of elementary Clifford gates $m$. Using the performant Stim simulator as backend, our implementation checks equivalence of quantum circuits with 1000 qubits (and a circuit depth of 10.000 gates) in $\sim$22 seconds and circuits with 100.000 qubits (depth 10) in $\sim$15 minutes, outperforming the existing SAT-based and path-integral based approaches by orders of magnitude. This approach shows that the correctness of application-relevant subsets of quantum operations can be verified up to large circuits in practice.

Abstract: Full-counting statistics (FCS) provides a powerful framework to access the statistical information of a system from the characteristic function. However, applications of FCS for generic interacting quantum systems often be hindered by the intrinsic difficulty of classical simulation of quantum many-body problems. Here, we propose a quantum algorithm for FCS that can obtain both the particle distribution and cumulants of interacting systems. The algorithm evaluates the characteristic functions by quantum computing and then extracts the distribution and cumulants with classical post-processing. With digital signal processing theory, we analyze the dependency of accuracy with the number of sampling points for the characteristic functions. We show that the desired number of sampling points for accurate FCS can be reduced by filtering some components of the quantum state that are not of interest. By numeral simulation, we demonstrate FCS of domain walls for the mixed Ising model. The algorithm suggests an avenue for studying full-counting statistics on quantum computers.

Abstract: Recently, a variety of quantum algorithms have been devised to estimate thermal averages on a genuine quantum processor. In this paper, we consider the practical implementation of the so-called Quantum-Quantum Metropolis algorithm. As a testbed for this purpose, we simulate a basic system of three frustrated quantum spins and discuss its systematics, also in comparison with the Quantum Metropolis Sampling algorithm.

Abstract: p-Adic quantum mechanics is constructed from the Dirac-von Neumann axioms identifying quantum states with square-integrable functions on the N-dimensional p-adic space, Q_{p}^{N}. The time is assumed to be a real variable. The time evolution is controlled by a nonlocal Schr\"odinger equation obtained from a p-adic heat equation by a temporal Wick rotation. This p-adic heat equation describes a particle performing a random motion in Q_{p}^{N}. The Hamiltonian is a nonlocal operator; thus, the Schr\"odinger equation describes the evolution of a quantum state under nonlocal interactions. In this framework, the Schr\"odinger equation admits plane wave solutions, but the de Broglie wave-particle duality is ruled out since the time is real and the position is p-adic. Consequently, our model has no quantum waves. Using a suitable Cauchy problem for the p-adic Schr\"odinger equation, we construct a mathematical model for the two-slit and one-slit experiments. At the time zero, at each slit, there is a localized particle; these particles interact with each other in a nonlocal way to produce an interference pattern. The pattern created by two slits looks like the pattern produced by one slit if the distance to the slits is sufficiently large. Finally, we propose that the classical de Broglie wave-particle duality is just a manifestation of the discreteness of space-time.

Abstract: We consider the generic form of a two-mode bosonic state $|\Psi_n\rangle$ with finite Fock expansion and fixed mean photon number to an integer $n\geq1$. The upper and lower modes of the input state $|\Psi_n\rangle$ pick up a phase $\phi$ and $-\phi$ respectively and we study the form of the optimal input state, i.e., the form of the state's Fock coefficients, such that the mean square error (MSE) for estimating $\phi$ is minimized while the MSE is always attainable by a measurement. Our setting is Bayesian, meaning that we consider $\phi$ as a random variable that follows a prior probability distribution function (PDF). For the celebrated NOON state (equal superposition of $|n0\rangle$ and $|0n\rangle$), which is a special case of the input state we consider, and for a flat prior PDF we find that the Heisenberg scaling is lost and the attainable minimum mean square error (MMSE) is found to be $\pi^2/3-1/4n^2$, which is a manifestation of the fundamental difference between the Fisherian and Bayesian approaches. Then, our numerical analysis provides the optimal form of the generic input state for fixed values of $n$ and we provide evidence that a state $|\Psi_{\tau}\rangle$ produced by mixing a Fock state with vacuum in a beam-splitter of transmissivity $\tau$ (i.e. a special case of the state $|\Psi_n\rangle$), must correspond to $\tau=0.5$. Finally, we consider an example of an adaptive technique: We consider a state of the form of $|\Psi_n\rangle$ for $n=1$. We start with a flat prior PDF, and for each subsequent step we use as prior PDF the posterior probability of the previous step, while for each step we update the optimal state and optimal measurement. We show our analysis for up to five steps, but one can allow the algorithm to run further. Finally, we conjecture the form the of the prior PDF and the optimal state for the infinite step and we calculate the corresponding MMSE.

Abstract: A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is accrued through astute betting. As information is gained from the stream of particles, the measurement directions are progressively adjusted, and the portfolio growth rate is raised. The optimal quantum strategy is determined numerically and shown to differ from the classical strategy, which is associated with the Kelly criterion. The paper contributes to the development of quantum finance, as aspects of portfolio optimisation are extended to the quantum realm.