Quantum mechanics (QM) is derived on the basis of a universe composed solely of events, for example, outcomes of observables. Such an event universe is represented by a dendrogram (a finite tree) and in the limit of infinitely many events by the p-adic tree. The trees are endowed with an ultrametric expressing hierarchical relationships between events. All events are coupled through the tree structure. Such a holistic picture of event-processes was formalized within the Dendrographic Hologram Theory (DHT). The present paper is devoted to the emergence of QM from DHT. We used the generalization of the QM-emergence scheme developed by Smolin. Following this scheme, we did not quantize events but rather the differences between them and through analytic derivation arrived at Bohmian mechanics. Previously, we were able to embed the basic elements of general relativity (GR) into DHT, and now after Smolin-like quantization of DHT, we can take a step toward quantization of GR. Finally, we remark that DHT is nonlocal in the treelike geometry, but this nonlocality refers to relational nonlocality in the space of events and not Einstein's spatial nonlocality.

Entanglement is one of the most fundamental features of quantum systems. In this work, we obtain the entanglement spectrum and entropy of Floquet noninteracting fermionic lattice models and build their connections with Floquet topological phases. Topological winding and Chern numbers are introduced to characterize the entanglement spectrum and eigenmodes. Correspondences between the spectrum and topology of entanglement Hamiltonians under periodic boundary conditions and topological edge states under open boundary conditions are further established. The theory is applied to Floquet topological insulators in different symmetry classes and spatial dimensions. Our work thus provides a useful framework for the study of rich entanglement patterns in Floquet topological matter.

Any physical system evolves at a finite speed that is constrained not only by the energetic cost but also by the topological structure of the underlying dynamics. In this Letter, by considering such structural information, we derive a unified topological speed limit for the evolution of physical states using an optimal transport approach. We prove that the minimum time required for changing states is lower bounded by the discrete Wasserstein distance, which encodes the topological information of the system, and the time-averaged velocity. The bound obtained is tight and applicable to a wide range of dynamics, from deterministic to stochastic, and classical to quantum systems. In addition, the bound provides insight into the design principles of the optimal process that attains the maximum speed. We demonstrate the application of our results to chemical reaction networks and interacting many-body quantum systems.

Author(s): Wojciech Górecki, Alberto Riccardi, and Lorenzo Maccone

We provide the optimal measurement strategy for a class of noisy channels that reduce to the identity channel for a specific value of a parameter (spreading channels). We provide an example that is physically relevant: the estimation of the absolute value of the displacement in the presence of phase…

[Phys. Rev. Lett. 129, 240503] Published Wed Dec 07, 2022

Author(s): Chao Fang, Ye Wang, Shilin Huang, Kenneth R. Brown, and Jungsang Kim

Crosstalk between target and neighboring spectator qubits due to spillover of control signals represents a major error source limiting the fidelity of two-qubit entangling gates in quantum computers. We show that in our laser-driven trapped-ion system coherent crosstalk error can be modeled as resid…

[Phys. Rev. Lett. 129, 240504] Published Wed Dec 07, 2022

Author(s): Samrat Sen, Edwin Peter Lobo, Ram Krishna Patra, Sahil Gopalkrishna Naik, Anandamay Das Bhowmik, Mir Alimuddin, and Manik Banik

The state-space structure for a composite quantum system is postulated among several mathematically consistent possibilities that are compatible with a local quantum description. For instance, the unentangled Gleason's theorem allows a state space that includes density operators as a proper subset a…

[Phys. Rev. A 106, 062406] Published Wed Dec 07, 2022

Author(s): F. S. Passos and A. R. C. Buarque

The dynamics of nonlinear flip-flop quantum walk with amplitude-dependent phase shifts with pertubing potential barrier is investigated. Through the adjustment between uniform local perturbations and a Kerr-like nonlinearity of the medium we find a rich set of dynamic profiles. We will show the exis…

[Phys. Rev. A 106, 062407] Published Wed Dec 07, 2022

We investigate a quantum-to-classical transition which arises naturally within the fuzzy sphere formalism for three-dimensional non-commutative quantum mechanics. We focus on treating a two-pinhole interference configuration within this formalism, as it provides an illustrative toy model for which this transition is readily observed and quantified. Specifically, we demonstrate a suppression of the quantum interference effects for objects passing through the pinholes with sufficiently-high energies or numbers of constituent particles.

Our work extends a similar treatment of the double slit experiment by Pittaway and Scholtz (2021) within the two-dimensional Moyal plane, only it addresses two key shortcomings that arise in that context. These are, firstly that the interference pattern in the Moyal plane lacks the expected reflection symmetry present in the pinhole setup, and secondly that the quantum-to-classical transition manifested in the Moyal plane occurs only at unrealistically high velocities and/or particle numbers. Both of these issues are solved in the fuzzy sphere framework.

Quantum switches are envisioned to be an integral component of future entanglement distribution networks. They can provide high quality entanglement distribution service to end-users by performing quantum operations such as entanglement swapping and entanglement purification. In this work, we characterize the capacity region of such a quantum switch under noisy channel transmissions and imperfect quantum operations. We express the capacity region as a function of the channel and network parameters (link and entanglement swap success probability), entanglement purification yield and application level parameters (target fidelity threshold). In particular, we provide necessary conditions to verify if a set of request rates belong to the capacity region of the switch. We use these conditions to find the maximum achievable end-to-end user entanglement generation throughput by solving a set of linear optimization problems. We develop a max-weight scheduling policy and prove that the policy stabilizes the switch for all feasible request arrival rates. As we develop scheduling policies, we also generate new results for computing the conditional yield distribution of different classes of purification protocols. From numerical experiments, we discover that performing link-level entanglement purification followed by entanglement swaps provides a larger capacity region than doing entanglement swaps followed by end-to-end entanglement purification. The conclusions obtained in this work can yield useful guidelines for subsequent quantum switch designs.

Solid-state spin defects are promising quantum sensors for a large variety of sensing targets. Some of these defects couple appreciably to strain in the host material. We propose to use this strain coupling for mechanically-mediated dispersive single-shot spin readout by an optomechanically-induced transparency measurement. Surprisingly, the estimated measurement times for negatively-charged silicon-vacancy defects in diamond are an order of magnitude shorter than those for single-shot optical fluorescence readout.

We investigate coupled-qubit-based thermal machines powered by quantum measurements and feedback. We consider two different versions of the machine: 1) a quantum Maxwell's demon where the coupled-qubit system is connected to a detachable single shared bath, and 2) a measurement-assisted refrigerator where the coupled-qubit system is in contant with a hot and cold bath. In the quantum Maxwell's demon case we discuss both discrete and continuous measurements. We find that the power output from a single qubit-based device can be improved by coupling it to the second qubit. We further find that the simultaneous measurement of both qubits can produce higher net heat extraction compared to two setups operated in parallel where only single-qubit measurements are performed. In the refrigerator case, we use continuous measurement and unitary operations to power the coupled-qubit-based refrigerator. We find that the cooling power of a refrigerator operated with swap operations can be enhanced by performing suitable measurements.

The cosmological scalar perturbations should satisfy the thermal distribution at the beginning of inflation since the cosmic temperature is presumably very high. In this paper, we investigate, by the Fubini-study method, the effect of this thermal contribution, which is characterized by a parameter $\kappa_{0}$, on the evolution of the cosmological complexity $\mathcal{C}_{FS}$ . We find that when the thermal effect is considered, the Universe would ``decomplex" firstly with the cosmic expansion after the mode of the scalar perturbations exiting the horizon in the de Sitter (dS) phase and $\mathcal{C}_{FS}$ has a minimum about $\pi/4$. If $\mathcal{C}_{FS}$ can reach its minimum during the dS era, which requires a small $\kappa_0$ or a large e-folding number for a large $\kappa_0$, it will bounce back to increase, and after the Universe enters the radiation dominated (RD) phase from the dS one, $\mathcal{C}_{FS}$ will decrease, pass its minimum again, and then increase till the mode reenters the horizon. For the case of a large enough $\kappa_0$, $\mathcal{C}_{FS}$ decreases but does not reach its minimum during the dS era, and it begins to increase after the transition from the dS phase to the RD one. When the mode reenters the horizon during the RD era, the cosmological complexity will oscillate around about $\kappa_{0}$. These features are different from that of the initial zero-temperature case, i.e., the cosmological complexity increases during the dS phase and decreases in the RD era till the mode reenters the horizon. Our results therefore suggest that the thermal effect changes qualitatively the evolutionary behavior of the cosmological complexity.

We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), Ising spin glasses ($p$-spin model), and $k$-local constraint satisfaction problems ($k$-CSP). We show that either (a) the algorithm finds the optimal solution in time $O^*(2^{(0.5-c)n})$ for an $n$-independent constant $c$, a $2^{cn}$ advantage over Grover's algorithm; or (b) there are sufficiently many low-cost solutions such that classical random guessing produces a $(1-\eta)$ approximation to the optimal cost value in sub-exponential time for arbitrarily small choice of $\eta$. Additionally, we show that for a large fraction of random instances from the $k$-spin model and for any fully satisfiable or slightly frustrated $k$-CSP formula, statement (a) is the case. The algorithm and its analysis is largely inspired by Hastings' short-path algorithm [$\textit{Quantum}$ $\textbf{2}$ (2018) 78].

This is a review of recent work on quantum fluctuations of the electric field and of stress tensor operators and their physical effects. The probability distribution for vacuum fluctuations of the electric field is Gaussian, but that for quadratic operators, such as the energy density, can have a more slowly decreasing tail, leading to an enhanced probability of large fluctuations. This effect is very sensitive to the details of how the measurement is performed. Some possible physical effects of these large fluctuations will be discussed.

In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small fixed-width arrays, we deliberately engineer an error bias at the lowest level of encoding using the surface code. We then address this engineered bias at a higher level of encoding using a lattice-surgery surface code bus that exploits this bias, or a repetition code to make logical qubits with unbiased errors out of biased surface code qubits. Arbitrarily low error rates can then be reached by further concatenating with other codes, such as Steane [[7,1,3]] code and the [[15,7,3]] CSS code. This enables a scalable fixed-width quantum computing architecture on a square qubit lattice that is only 19 qubits wide, given physical qubits with an error rate of $8.0\times 10^{-4}$. This potentially eases engineering issues in systems with fine qubit pitches, such as quantum dots in silicon or gallium arsenide.

We report on experimental studies of the distribution of the reflection coefficients, and the imaginary and real parts of Wigner's reaction (K) matrix employing open microwave networks with symplectic symmetry and varying size of absorption. The results are compared to analytical predictions derived for the single-channel scattering case within the framework of random matrix theory (RMT). Furthermore, we performed Monte Carlo simulations based on the Heidelberg approach for the scattering (S) and K matrix of open quantum-chaotic systems and the two-point correlation function of the S-matrix elements. The analytical results and the Monte Carlo simulations depend on the size of absorption. To verify them, we performed experiments with microwave networks for various absorption strengths. We show that deviations from RMT predictions observed in the spectral properties of the corresponding closed quantum graph, and attributed to the presence of nonuniversal short periodic orbits, does not have any visible effects on the distributions of the reflection coefficients and the K and S matrices associated with the corresponding open quantum graph.

Estimating statistical properties is fundamental in statistics and computer science. In this paper, we propose a unified quantum algorithm framework for estimating properties of discrete probability distributions, with estimating R\'enyi entropies as specific examples. In particular, given a quantum oracle that prepares an $n$-dimensional quantum state $\sum_{i=1}^{n}\sqrt{p_{i}}|i\rangle$, for $\alpha>1$ and $0<\alpha<1$, our algorithm framework estimates $\alpha$-R\'enyi entropy $H_{\alpha}(p)$ to within additive error $\epsilon$ with probability at least $2/3$ using $\widetilde{\mathcal{O}}(n^{1-\frac{1}{2\alpha}}/\epsilon + \sqrt{n}/\epsilon^{1+\frac{1}{2\alpha}})$ and $\widetilde{\mathcal{O}}(n^{\frac{1}{2\alpha}}/\epsilon^{1+\frac{1}{2\alpha}})$ queries, respectively. This improves the best known dependence in $\epsilon$ as well as the joint dependence between $n$ and $1/\epsilon$. Technically, our quantum algorithms combine quantum singular value transformation, quantum annealing, and variable-time amplitude estimation. We believe that our algorithm framework is of general interest and has wide applications.

Non-orthogonal multiple access (NOMA) technique is important for achieving a high data rate in next-generation wireless communications. A key challenge to fully utilizing the effectiveness of the NOMA technique is the optimization of the resource allocation (RA), e.g., channel and power. However, this RA optimization problem is NP-hard, and obtaining a good approximation of a solution with a low computational complexity algorithm is not easy. To overcome this problem, we propose the coherent Ising machine (CIM) based optimization method for channel allocation in NOMA systems. The CIM is an Ising system that can deliver fair approximate solutions to combinatorial optimization problems at high speed (millisecond order) by operating optimization algorithms based on mutually connected photonic neural networks. The performance of our proposed method was evaluated using a simulation model of the CIM. We compared the performance of our proposed method to simulated annealing, a conventional-NOMA pairing scheme, deep Q learning based scheme, and an exhaustive search scheme. Simulation results indicate that our proposed method is superior in terms of speed and the attained optimal solutions.

We study observation entropy (OE) for the Quantum kicked top (QKT) model, whose classical counterpart possesses different phases: regular, mixed, or chaotic, depending on the strength of the kicking parameter. We show that OE grows logarithmically with coarse-graining length beyond a critical value in the regular phase, while OE growth is much faster in the chaotic regime. In the dynamics, we demonstrate that the short-time growth rate of OE acts as a measure of the chaoticity in the system, and we compare our results with out-of-time-ordered correlators (OTOC). Moreover, we show that in the deep quantum regime, the results obtained from OE are much more robust compared to OTOC results. Finally, we also investigate the long-time behaviour of OE to distinguish between saddle-point scrambling and true chaos, where the former shows large persistent fluctuations compared to the latter.

We address a modified uncertainty principle interpreted in terms of the Planck length $l_P$ and a dimensionless constant $\alpha$. We set up a consistent scheme derived from the scalar Helmholtz equation that allows estimating $\alpha$ by providing a lower bound on it. Subsequently we turn to the issue of a $\mathcal{PT}$ optical structure where the Helmholtz equation could be mapped to the Sch\"{r}odinger form with the refractive index distribution $n$ admitting variation in the longitudinal direction only. Interpreting the Sch\"{r}odinger equation in terms of a superpotential we determine partners for $n$ in the supersymmetry context. New analytical solutions for the refractive index profiles are presented which are graphically illustrated.