Quantum Physics (quant-ph)

Abstract: Preparation of a target quantum many-body state on quantum simulators is one of the significant steps in quantum science and technology. With a small number of qubits, a few quantum states, such as the Greenberger-Horne-Zeilinger state, have been prepared, but fundamental difficulties in systems with many qubits remain, including the Lieb-Robinson bounds for the number of quantum operations. Here, we provide one algorithm with an implementation of a deep learning process and achieve to prepare the target ground states with many qubits. Our strategy is to train a machine-learning model and predict parameters with many qubits by utilizing a pattern of quantum states from the corresponding quantum states with small numbers of qubits. For example, we demonstrate that our algorithm with the Quantum Approximate Optimization Ansatz can effectively generate the ground state for a 1D XY model with 64 spins. We also demonstrate that the reduced density operator of two qubits can be utilized to capture the pattern of quantum many-body states such as correlation lengths even for quantum critical states.

Abstract: We develop the Euclidean time method of the variational quantum eigensolver for solving the generalized eigenvalue equation $A \ket{\phi_n} = \lambda_n B \ket{\phi_n}$. For the purpose we modify the usual Euclidean time formalism, which was developed for solving the time-independent Schr\"{o}dinger equation. We apply our formalism to two numerical examples for test, where $B$ is regular and singular respectively. It is shown that our formalism works very well in both examples. The future applications to the atomic problems are briefly discussed.

Abstract: The rotating-wave approximation to light-matter interactions is widely used in the quantum electrodynamics Hamiltonian; however, its validity has long been a matter of debate. In this article, we explore the impact of the rotating-wave approximation on the quantum dynamics of multiple molecules in complex dielectric environments within the framework of macroscopic quantum electrodynamics. In general, we find that the energy shifts of the molecules and the inter-molecule dipole-dipole interaction obtained in the weak coupling regime are correct only when the counter-rotating interactions are considered. Moreover, under the rotating-wave approximation, the energy shifts of the ground-state molecules and a portion of the inter-molecule interaction are discarded. Notably, in the near-field zone (short inter-molecular distance), the reduction of inter-molecule interaction can reach up to 50 percent. We also conduct a case study on the population dynamics of a pair of identical molecules above a plasmonic surface. Through analytical and numerical analysis, it is revealed that the rotating-wave approximation can profoundly affect the dynamics of the molecules in both strong and weak coupling regimes, emphasizing the need for careful consideration when making the rotating-wave approximation in a multiple-molecule system coupled with quantum light.

Abstract: Recent works have shown that collective single photon spontaneous emission from an ensemble of $N$ resonant two-level atoms is a rich field of study. Superradiance describes emission from a completely symmetric state of $N$ atoms, with a single excited atom prepared with a given phase, for instance imprinted by an external laser. Instead, subradiance is associated with the emission from the remaining $N-1$ asymmetric states, with a collective decay rate less than the single-atom value. Here, we discuss the properties of the orthonormal basis of symmetric and asymmetric states and the entanglement properties of superradiant and subradiant states.

Abstract: There is a Casimir force between two metal plates. It is generally believed that the Casimir force is mediated by virtual photons in a vacuum, which correspond to the massless intermediate particles used in our theoretical calculations. Studies have shown that not only virtual photons in a vacuum, but also other virtual particles that have masses. The lightest chargeless virtual particles with mass are positronium (1 MeV) and $\pi^{0}$ mesons (135 MeV). This paper primarily focuses on studying the corrections to the Casimir force caused by positronium and $\pi^{0}$ mesons. Especially when the distance between the two plates is on the order of $1/m_{positronium}$ , the contribution of positronium becomes significant, and on the order of $1/m_{\pi^0}$ , the contribution of the $\pi^{0}$ meson becomes significant. We hope that the calculation results can reduce the error in the theoretical calculation of the Casimir force when the distance between the plates is large and provide significant corrections when the distance is small.

Abstract: We demonstrate that the unitary dynamics of a multi-qubit system can display hypersensitivity to initial state perturbation. This contradicts the common belief that the classical approach based on the exponential divergence of initially neighboring trajectories cannot be applied to identify chaos in quantum systems. To observe hypersensitivity we use quantum state-metric, introduced by Girolami and Anza in [Phys. Rev. Lett. 126 (2021) 170502], which can be interpreted as a quantum Hamming distance. As an example of a quantum system, we take the multi-qubit implementation of the quantum kicked top, a paradigmatic system known to exhibit quantum chaotic behavior. Our findings confirm that the observed hypersensitivity corresponds to commonly used signatures of quantum chaos. Furthermore, we demonstrate that the proposed metric can detect quantum chaos in the same regime and under analogous initial conditions as in the corresponding classical case.

Abstract: In this article, we present a detailed analysis of two famous delayed choice experiments: Wheeler's classic gedanken-experiment and the delayed quantum eraser. It shows that the outcomes of both experiment can be fully explained on the basis of the information collected during the experiments using textbook quantum mechanics only. At no point in the analysis, information from the future is needed to explain what happens next. In fact more is true: for both experiments we show, in a strictly mathematical way, that a modified version in which the time-ordering of the steps is changed to avoid the delayed choice leads to exactly the same final state. In this operational sense, the scenarios are completely equivalent in terms of conclusions that can be drawn from their outcomes.

Abstract: We prove that any asymptotics of a finite-dimensional quantum Markov processes can be formulated in the form of a generalized Jaynes principle in the discrete as well as in the continuous case. Surprisingly, we find that the open system dynamics does not require maximization of von Neumannentropy. In fact, the natural functional to be extremized is the quantum relative entropy and the resulting asymptotic states or trajectories are always of the exponential Gibbs-like form. Three versions of the principle are presented for different settings, each treating different prior knowledge: for asymptotic trajectories of fully known initial states, for asymptotic trajectories incompletely determined by known expectation values of some constants of motion and for stationary states incompletely determined by expectation values of some integrals of motion. All versions are based on the knowledge of the underlying dynamics. Hence our principle is primarily rooted in the inherent physics and it is not solely an information construct. The found principle coincides with the MaxEnt principle in the special case of unital quantum Markov processes. We discuss how the generalized principle modifies fundamental relations of statistical physics.

Abstract: Engineering quantum devices requires reliable characterization of the quantum system including qubits, quantum operations (aka instruments) and the quantum noise. Recently, quantum gate set tomography (GST) has emerged as a promissing technique to self-consistently describe the quantum states, gates and measurements. However, non-Markovian correlations between the quantum system and environment cause the reliability regression of GST. It is essential to simultaneously describe the gate set and non-Markovian correlations. To this end, we first propose a self-consistent operational method, named instrument set tomography (IST), for non-Markovian GST. Based on the stochastic quantum process, the instrument set is defined to describe instruments, the initial state, and non-Markovian system-environment (SE) correlations. First, we propose a linear inversion IST (LIST) to detect and describe the disharmony of linear relationship of instruments and SE correlations with gauge freedom. However, LIST cannot always determine physical implementable instrument set because of the absence of constraints. Then, a physically constrained statistical method based on the miximum likelihood estimation for IST (MLE-IST) is proposed with polynomial number of parameters with respect to the Markovian order. It shows significant flexibility that suit for different types of device, e.g. noisy intermediate-scale quantum (NISQ) devices, by adjusting the model and constraints. The experimental results show the effectiveness of describing instruments and the non-Markovian quantum system. As a result, the IST provides an essential method for benchmarking and developing quantum devices in the aspect of instrument set.

Abstract: A software product line models the variability of highly configurable systems. Complete exploration of all valid configurations (the configuration space) is infeasible as it grows exponentially with the number of features in the worst case. In practice, few representative configurations are sampled instead, which may be used for software testing or hardware verification. Pseudo-randomness of modern computers introduces statistical bias into these samples. Quantum computing enables truly random, uniform configuration sampling based on inherently random quantum physical effects. We propose a method to encode the entire configuration space in a superposition and then measure one random sample. We show the method's uniformity over multiple samples and investigate its scale for different feature models. We discuss the possibilities and limitations of quantum computing for uniform random sampling regarding current and future quantum hardware.

Abstract: In pursuit of enhancing the predication capabilities of the neural network, it has been a longstanding objective to create dataset encompassing a diverse array of samples. The purpose is to broaden the horizons of neural network and continually strive for improved prediction accuracy during training process, which serves as the ultimate evaluation metric. In this paper, we explore an intriguing avenue for enhancing algorithm effectiveness through exploiting the knowledge blindness of neural network. Our approach centers around a machine learning algorithm utilized for preparing arbitrary quantum states in a semiconductor double quantum dot system, a system characterized by highly constrained control degrees of freedom. By leveraging stochastic prediction generated by the neural network, we are able to guide the optimization process to escape local optima. Notably, unlike previous methodologies that employ reinforcement learning to identify pulse patterns, we adopt a training approach akin to supervised learning, ultimately using it to dynamically design the pulse sequence. This approach not only streamlines the learning process but also constrains the size of neural network, thereby improving the efficiency of algorithm.

Abstract: We study the dynamics of a single-photon pulse traveling through a linear qubit chain coupled to continuum modes in a one-dimensional (1D) photonic waveguide. We derive a time-dependent dynamical theory for qubits' amplitudes and for transmitted and reflected spectra. We show that the requirement for the photon-qubit coupling to exist only for positive frequencies can significantly change the dynamics of the system. First, it leads to the additional photon-mediated dipole-dipole interaction between qubits which results in the violation of the phase coherence between them. Second, the spectral lines of transmitted and reflected spectra crucially depend on the shape of the incident pulse. We apply our theory to one-qubit and two-qubit systems. For these two cases, we obtain the explicit expressions for the qubits' amplitudes and for the photon radiation spectra as time tends to infinity. For the incident Gaussian wave packet we calculate the line shapes of transmitted and reflected photons.

Abstract: We develop a photonic description of short, one-dimensional electromagnetic pulses, specifically in the language of electrical transmission lines. Current practice in quantum technology, using arbitrary waveform generators, can readily produce very short, few-cycle pulses in microwave TEM guided structures (coaxial cables or coplanar waveguides) in a very low noise, low temperature setting. We argue that these systems attain the limit of producing pure coherent quantum states, in which the vacuum has been displaced for a short time, and therefore short spatial extent. When the pulse is bipolar, that is, the integrated voltage of the pulse is zero, then the state can be described by the finite displacement of a single mode. Therefore there is a definite mean number of photons, but which have neither a well defined frequency nor position. Due to the Paley-Wiener theorem, the two-component photon 'wavefunction' of this mode is not strictly bounded in space even if the vacuum displacement that defines it is bounded. This wavefunction's components are, for the case of pulses moving in a specific direction, complex valued, with the real and imaginary parts related by a Hilbert transform. They are thus akin to the 'analytic signals' of communication theory. When the pulse is unipolar no photonic description is possible -- the photon number can be considered to be divergent. We consider properties that photon counters and quantum non-demolition detectors must have to optimally convert and detect the photons in several example pulses, and we discuss some consequence of this optimization for the application of very short pulses in quantum cryptography.

Abstract: The interaction energy between two atoms is crucially dependent on the quantum state of the two-atom system. In this paper, it is demonstrated that a steady resonance interaction energy between two atoms exists when the atoms are in a certain type of coherent superposition of single-excitation states. The interaction is tree-level classical in the sense of the Feynman diagrams. A quantity called quantum classicality is defined in the present paper, whose nonzero-ness ensures the existence of this interaction. The dependence of the interatomic interaction on the quantum nature of the state of the two-atom system may potentially be tested with Rydberg atoms.

Abstract: Parametrized quantum circuits (PQC) are quantum circuits which consist of both fixed and parametrized gates. In recent approaches to quantum machine learning (QML), PQCs are essentially ubiquitous and play the role analogous to classical neural networks. They are used to learn various types of data, with an underlying expectation that if the PQC is made sufficiently deep, and the data plentiful, the generalisation error will vanish, and the model will capture the essential features of the distribution. While there exist results proving the approximability of square-integrable functions by PQCs under the $L^2$ distance, the approximation for other function spaces and under other distances has been less explored. In this work we show that PQCs can approximate the space of continuous functions, $p$-integrable functions and the $H^k$ Sobolev spaces under specific distances. Moreover, we develop generalisation bounds that connect different function spaces and distances. These results provide a rigorous basis for the theory of explored classes of uses of PQCs. Such as for solving new potential uses of PQCs such as solving differential equations. Further, they provide us with new insight on how to design PQCs and loss functions which better suit the specific needs of the users.

Abstract: In order to achieve fault-tolerant quantum computation, we need to repeat the following sequence of four steps: First, perform 1 or 2 qubit quantum gates (in parallel if possible). Second, do a syndrome measurement on a subset of the qubits. Third, perform a fast classical computation to establish which errors have occurred (if any). Fourth, depending on the errors, we apply a correction step. Then the procedure repeats with the next sequence of gates. In order for these four steps to succeed, we need the error rate of the gates to be below a certain threshold. Unfortunately, the error rates of current quantum hardware are still too high. On the other hand, current quantum hardware platforms are designed with these four steps in mind. In this work we make use of this four-step scheme not to carry out fault-tolerant computations, but to enhance short, constant-depth, quantum circuits that perform 1 qubit gates and nearest-neighbor 2 qubit gates. To explore how this can be useful, we study a computational model which we call Local Alternating Quantum Classical Computations (LAQCC). In this model, qubits are placed in a grid allowing nearest neighbor interactions; the quantum circuits are of constant depth with intermediate measurements; a classical controller can perform log-depth computations on these intermediate measurement outcomes to control future quantum operations. This model fits naturally between quantum algorithms in the NISQ era and full fledged fault-tolerant quantum computation. We show that LAQCC circuits can create long-ranged interactions, which constant-depth quantum circuits cannot achieve, and use it to construct a range of useful multi-qubit gates. With these gates, we create three new state preparation protocols for a uniform superposition over an arbitrary number of states, W-states and Dicke states.

Abstract: We propose a hybrid quantum-classical approximate optimization algorithm for photonic quantum computing, specifically tailored for addressing continuous-variable optimization problems. Inspired by counterdiabatic protocols, our algorithm significantly reduces the required quantum operations for optimization as compared to adiabatic protocols. This reduction enables us to tackle non-convex continuous optimization and countably infinite integer programming within the near-term era of quantum computing. Through comprehensive benchmarking, we demonstrate that our approach outperforms existing state-of-the-art hybrid adiabatic quantum algorithms in terms of convergence and implementability. Remarkably, our algorithm offers a practical and accessible experimental realization, bypassing the need for high-order operations and overcoming experimental constraints. We conduct proof-of-principle experiments on an eight-mode nanophotonic quantum chip, successfully showcasing the feasibility and potential impact of the algorithm.

Abstract: We propose a minimal setup for a quantum heat pump, consisting of two tunnel-coupled quantum dots, each hosting a single level and each being coupled to a different fermionic reservoir. The working principle relies on both non-Markovian system-bath coupling and driving induced resonant coupling. We describe the system using a reaction-coordinate mapping in combination with Floquet-Born-Markov theory and characterize its performance.

Abstract: Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. In this paper, we present a natural analogue to this technique, for simulating Markovian dynamics governed by the well known Lindblad master equation. For this purpose, we first propose an input model in which a Lindblad operator $L$ is encoded into a quantum state $\psi$. Then, given access to $n$ copies of the state $\psi$, the task is to simulate the corresponding Markovian dynamics for time $t$. We propose a quantum algorithm for this task, called Wave Matrix Lindbladization, and we also investigate its sample complexity. We show that our algorithm uses $n = O(t^2/\varepsilon)$ samples of $\psi$ to achieve the target dynamics, with an approximation error of $O(\varepsilon)$.

Abstract: We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing problems and put forward the usage of sequential strategies where the signal is analyzed in real time, allowing the experiment to be concluded as soon as the underlying hypothesis can be identified with a certified prescribed success probability. We analyze the performance of sequential tests by studying the stopping-time behavior, showing a considerable advantage over currently-used strategies based on a fixed predetermined measurement time.

Abstract: Based on a previously proposed unitary transformation for cavity quantum electrodynamics, we investigate the spectral shift of an atom induced by quantum fluctuations in a chiral vacuum cavity. Remarkably, we find an intriguing angular momentum-dependent shift in the spectra of bound states. Our approach surpasses conventional perturbative calculations and remains valid even in the strong-coupling limit. In addition, we establish a cavity-interaction picture for calculating the chiral vacuum Rabi oscillation in the strong-coupling limit for a generic central potential, without using the rotating wave approximation. The anomalous spectral shift revealed in this study possesses both fundamental and practical significance and could be readily observed in experiments.

Abstract: A quantum spin-$\frac{1}{2}$ chain with an axial symmetry is normally described by quasiparticles associated with the spins oriented along the axis of rotation. Kinetic constraints can enrich such a description by setting apart different species of quasiparticles, which can get stuck at high enough density, realising the quantum analogue of jamming. We identify a family of interactions satisfying simple kinetic constraints and consider generic translationally invariant models built up from them. We study dynamics following a local unjamming perturbation in a jammed state. We show that they can be mapped into dynamics of ordinary unconstrained systems, but the nonlocality of the mapping changes the scales at which the phenomena manifest themselves. Scattering of quasiparticles, formation of bound states, eigenstate localisation become all visible at macroscopic scales. Depending on whether a symmetry is present or not, the microscopic details of the jammed state turn out to have either a marginal or a strong effect. In the former case or when the initial state is almost homogeneous, we show that even a product state is turned into a macroscopic quantum state.

Abstract: Quantum technologies have the potential to solve computationally hard problems that are intractable via classical means. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolerant quantum computing. Surface codes currently stand as the most promising candidates to build error corrected qubits given their two-dimensional architecture, a requirement of only local operations, and high tolerance to quantum noise. Decoding algorithms are an integral component of any error correction scheme, as they are tasked with producing accurate estimates of the errors that affect quantum information, so that it can subsequently be corrected. A critical aspect of decoding algorithms is their speed, since the quantum state will suffer additional errors with the passage of time. This poses a connundrum-like tradeoff, where decoding performance is improved at the expense of complexity and viceversa. In this review, a thorough discussion of state-of-the-art surface code decoding algorithms is provided. The core operation of these methods is described along with existing variants that show promise for improved results. In addition, both the decoding performance, in terms of error correction capability, and decoding complexity, are compared. A review of the existing software tools regarding surface code decoding is also provided.

Abstract: Quantum computing is in an era defined by rapidly evolving quantum hardware technologies, combined with persisting high gate error rates, large amounts of noise, and short coherence times. Overcoming these limitations requires systems-level approaches that account for the strengths and weaknesses of the underlying hardware technology. Yet few hardware-aware compiler techniques exist for neutral atom devices, with no prior work on compiling to the neutral atom native gate set. In particular, current neutral atom hardware does not support certain single-qubit rotations via local addressing, which often requires the circuit to be decomposed into a large number of gates, leading to long circuit durations and low overall fidelities. We propose the first compiler designed to overcome the challenges of limited local addressibility in neutral atom quantum computers. We present algorithms to decompose circuits into the neutral atom native gate set, with emphasis on optimizing total pulse area of global gates, which dominate gate execution costs in several current architectures. Furthermore, we explore atom movement as an alternative to expensive gate decompositions, gaining immense speedup with routing, which remains a huge overhead for many quantum circuits. Our decomposition optimizations result in up to ~3.5x and ~2.9x speedup in time spent executing global gates and time spent executing single-qubit gates, respectively. When combined with our atom movement routing algorithms, our compiler achieves up to ~10x reduction in circuit duration, with over ~2x improvement in fidelity. We show that our compiler strategies can be adapted for a variety of hardware-level parameters as neutral atom technology continues to develop.

Abstract: Monitored quantum dynamics -- unitary evolution interspersed with measurements -- has recently emerged as a rich domain for phase structure in quantum many-body systems away from equilibrium. Here we study monitored dynamics from the point of view of an eavesdropper who has access to the classical measurement outcomes, but not to the quantum many-body system. We show that a measure of information flow from the quantum system to the classical measurement record -- the informational power -- undergoes a phase transition in correspondence with the measurement-induced phase transition (MIPT). This transition determines the eavesdropper's (in)ability to learn properties of an unknown initial quantum state of the system, given a complete classical description of the monitored dynamics and arbitrary classical computational resources. We make this learnability transition concrete by defining classical shadows protocols that the eavesdropper may apply to this problem, and show that the MIPT manifests as a transition in the sample complexity of various shadow estimation tasks, which become harder in the low-measurement phase. We focus on three applications of interest: Pauli expectation values (where we find the MIPT appears as a point of optimal learnability for typical Pauli operators), many-body fidelity, and global charge in $U(1)$-symmetric dynamics. Our work unifies different manifestations of the MIPT under the umbrella of learnability and gives this notion a general operational meaning via classical shadows.

Abstract: Reliable quantum technology requires knowledge of the dynamics governing the underlying system. This problem of characterizing and benchmarking quantum devices or experiments in continuous time is referred to as the Hamiltonian learning problem. In contrast to multi-qubit systems, learning guarantees for the dynamics of bosonic systems have hitherto remained mostly unexplored. For $m$-mode Hamiltonians given as polynomials in annihilation and creation operators with modes arranged on a lattice, we establish a simple moment criterion in terms of the particle number operator which ensures that learning strategies from the finite-dimensional setting extend to the bosonic setting, requiring only coherent states and heterodyne detection on the experimental side. We then propose an enhanced procedure based on added dissipation that even works if the Hamiltonian time evolution violates this moment criterion: With high success probability it learns all coefficients of the Hamiltonian to accuracy $\varepsilon$ using a total evolution time of $\mathcal{O}(\varepsilon^{-2}\log(m))$. Our protocol involves the experimentally reachable resources of projected coherent state preparation, dissipative regularization akin to recent quantum error correction schemes involving cat qubits stabilized by a nonlinear multi-photon driven dissipation process, and heterodyne measurements. As a crucial step in our analysis, we establish our moment criterion and a new Lieb-Robinson type bound for the evolution generated by an arbitrary bosonic Hamiltonian of bounded degree in the annihilation and creation operators combined with photon-driven dissipation. Our work demonstrates that a broad class of bosonic Hamiltonians can be efficiently learned from simple quantum experiments, and our bosonic Lieb-Robinson bound may independently serve as a versatile tool for studying evolutions on continuous variable systems.

Abstract: The generation and control of entanglement in a quantum mechanical system is a critical element of nearly all quantum applications. Molecular systems are a promising candidate, with numerous degrees of freedom able to be targeted. However, knowledge of inter-system entanglement mechanisms in such systems is limited. In this work, we demonstrate the generation of entanglement between vibrational degrees of freedom in molecules via strong coupling to a cavity mode driven by a weak coherent field. In a bi-molecular system, we show entanglement can not only be generated between the cavity and molecular system, but also between molecules. This process also results in the generation of non-classical states of light, providing potential pathways for harnessing entanglement in molecular systems.

Abstract: There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman. We show how to generalize this to a large class of hierarchical graphs in which the vertices are grouped into ``supervertices'' which are arranged according to a $d$-dimensional lattice. Supervertices can have different sizes, and edges between supervertices correspond to random connections between their constituent vertices. The hitting times of quantum walks on these graphs are related to the localization properties of zero modes in certain disordered tight binding Hamiltonians. The speedups range from superpolynomial to exponential, depending on the underlying dimension and the random graph model. We also provide concrete realizations of these hierarchical graphs, and introduce a general method for constructing graphs with efficient quantum traversal times using graph sparsification.