Quantum Physics (quant-ph)

Abstract: We introduce and explicitly construct a quantum code we coin a "Pauli Manipulation Detection" code (or PMD), which detects every Pauli error with high probability. We apply them to construct the first near-optimal codes for two tasks in quantum communication over adversarial channels. Our main application is an approximate quantum code over qubits which can efficiently correct from a number of (worst-case) erasure errors approaching the quantum Singleton bound. Our construction is based on the composition of a PMD code with a stabilizer code which is list-decodable from erasures. Our second application is a quantum authentication code for "qubit-wise" channels, which does not require a secret key. Remarkably, this gives an example of a task in quantum communication which is provably impossible classically. Our construction is based on a combination of PMD codes, stabilizer codes, and classical non-malleable codes (Dziembowski et al., 2009), and achieves "minimal redundancy" (rate $1-o(1)$).

Abstract: Signing quantum messages has been shown to be impossible even under computational assumptions. We show that this result can be circumvented by relying on verification keys that change with time or that are large quantum states. Correspondingly, we give two new approaches to sign quantum information. The first approach assumes quantum-secure one-way functions (QOWF) to obtain a time-dependent signature scheme where the algorithms take into account time. The keys are classical but the verification key needs to be continually updated. The second construction uses fixed quantum verification keys and achieves information-theoretic secure signatures against adversaries with bounded quantum memory i.e. in the bounded quantum storage model. Furthermore, we apply our time-dependent signatures to authenticate keys in quantum public key encryption schemes and achieve indistinguishability under chosen quantum key and ciphertext attack (qCKCA).

Abstract: Quantum parameter estimation offers solid conceptual grounds for the design of sensors enjoying quantum advantage. This is realised not only by means of hardware supporting and exploiting quantum properties, but data analysis has its impact and relevance, too. In this respect, Bayesian methods have emerged as an effective and elegant solution, with the perk of incorporating naturally the availability of a priori information. In this article we present an evaluation of Bayesian methods for multiple phase estimation, assessed based on bounds that work beyond the usual limit of large samples assumed in parameter estimation. Importantly, such methods are applied to experimental data generated from the output statistics of a three-arm interferometer seeded by single photons. Our studies provide a blueprint for a more comprehensive data analysis in quantum metrology.

Abstract: Greenberger-Horne-Zeilinger (GHZ) states are quantum states involving at least three entangled particles. They are of fundamental interest in quantum information theory and have several applications in quantum communication and cryptography. Motivated by this, physicists have been designing various experiments to create high-dimensional GHZ states using multiple entangled particles. In 2017, Krenn, Gu and Zeilinger discovered a bridge between experimental quantum optics and graph theory. A large class of experiments to create a new GHZ state are associated with an edge-coloured edge-weighted graph having certain properties. Using this framework, Cervera-Lierta, Krenn, and Aspuru-Guzik proved using SAT solvers that through these experiments, the maximum dimension achieved is less than $3,4$ using $6,8$ particles, respectively. They further conjectured that using $n$ particles, the maximum dimension achievable is less than $\dfrac{n}{{2}}$ [Quantum 2022]. We make progress towards proving their conjecture by showing that the maximum dimension achieved is less than $\dfrac{n}{\sqrt{2}}$.

Abstract: We investigate the dynamical Casimir-Polder force between an atom and a conducting wall during the time evolution of the system from a partially dressed state. This state is obtained by a sudden change of the atomic position with respect to the plate. To evaluate the time-dependent atom-plate Casimir-Polder force we solve the Heisenberg equations for the field and atomic operators by an iterative technique. We find that the dynamical atom-plate Casimir-Polder interaction exhibits oscillation in time, and can be attractive or repulsive depending on time and the atom-wall distance. We also investigate the time dependence of global observables, such as the field and atomic Hamiltonians, and discuss some interesting features of the dynamical process bringing the interaction energy to the equilibrium configuration.

Abstract: Motion along semi-infinite straight line in a potential that is a combination of positive quadratic and inverse quadratic functions of the position is considered with the emphasis on the analysis of its quantum-information properties. Classical measure of symmetry of the potential is proposed and its dependence on the particle energy and the factor $\mathfrak{a}$ describing a relative strength of its constituents is described; in particular, it is shown that a variation of the parameter $\mathfrak{a}$ alters the shape from the half-harmonic oscillator (HHO) at $\mathfrak{a}=0$ to the perfectly symmetric one of the double frequency oscillator (DFO) in the limit of huge $\mathfrak{a}$. Quantum consideration focuses on the analysis of information-theoretical measures, such as standard deviations, Shannon, R\'{e}nyi and Tsallis entropies together with Fisher information, Onicescu energy and non--Gaussianity. For doing this, among others, a method of calculating momentum waveforms is proposed that results in their analytic expressions in form of the confluent hypergeometric functions. Increasing parameter $\mathfrak{a}$ modifies the measures in such a way that they gradually transform into those corresponding to the DFO what, in particular, means that the lowest orbital saturates Heisenberg, Shannon, R\'{e}nyi and Tsallis uncertainty relations with the corresponding position and momentum non--Gaussianities turning to zero. A simple expression is derived of the orbital-independent lower threshold of the semi-infinite range of the dimensionless R\'{e}nyi/Tsallis coefficient where momentum components of these one-parameter entropies exist which shows that it varies between $1/4$ at HHO and zero when $\mathfrak{a}$ tends to infinity. Physical interpretation of obtained mathematical results is provided.

Abstract: Focusing on a continuous-time quantum walk on $\mathbb{Z}=\left\{0,\pm 1,\pm 2,\ldots\right\}$, we analyze a probability distribution with which the quantum walker is observed at a position. The walker launches off at a localized state and its system is operated by a spatially periodic Hamiltonian. As a result, we see an asymmetry probability distribution. To catch a long-time behavior, we also try to find a long-time limit theorem and realize that the limit distribution holds a symmetry density function.

Abstract: Quantum Local Search (QLS) is a promising approach that employs small-scale quantum computers to tackle large combinatorial optimization problems through local search on quantum hardware, starting from an initial point. However, the random selection of the sub-problem to solve in QLS may not be efficient. In this study, we propose a reinforcement learning (RL) based approach to train an agent for improved subproblem selection in QLS, beyond random selection. Our results demonstrate that the RL agent effectively enhances the average approximation ratio of QLS on fully-connected random Ising problems, indicating the potential of combining RL techniques with Noisy Intermediate-scale Quantum (NISQ) algorithms. This research opens a promising direction for integrating RL into quantum computing to enhance the performance of optimization tasks.

Abstract: Multi-mode optical interferometers represent the most viable platforms for the successful implementation of several quantum information schemes that take advantage of optical processing. Examples range from quantum communication, sensing and computation, including optical neural networks, optical reservoir computing or simulation of complex physical systems. The realization of such routines requires high levels of control and tunability of the parameters that define the operations carried out by the device. This requirement becomes particularly crucial in light of recent technological improvements in integrated photonic technologies, which enable the implementation of progressively larger circuits embedding a considerable amount of tunable parameters. In this work, we formulate efficient procedures for the characterization of optical circuits in the presence of imperfections that typically occur in physical experiments, such as unbalanced losses and phase instabilities in the input and output collection stages. The algorithm aims at reconstructing the transfer matrix that represents the optical interferometer without making any strong assumptions about its internal structure and encoding. We show the viability of this approach in an experimentally relevant scenario, defined by a tunable integrated photonic circuit, and we demonstrate the effectiveness and robustness of our method. Our findings can find application in a wide range of optical setups, based both on bulk and integrated configurations.

Abstract: Solving the Anderson impurity model typically involves a two-step process, where one first calculates the ground state of the Hamiltonian, and then computes its dynamical properties to obtain the Green's function. Here we propose a hybrid classical/quantum algorithm where the first step is performed using a classical computer to obtain the tensor network ground state as well as its quantum circuit representation, and the second step is executed on the quantum computer to obtain the Green's function. Our algorithm exploits the efficiency of tensor networks for preparing ground states on classical computers, and takes advantage of quantum processors for the evaluation of the time evolution, which can become intractable on classical computers. We demonstrate the algorithm using 20 qubits on a quantum computing emulator for SrVO3 with a multi-orbital Anderson impurity model within the dynamical mean field theory. The tensor network based ground state quantum circuit preparation algorithm can also be performed for up to 40 qubits with our available computing resources, while the state vector emulation of the quantum algorithm for time evolution is beyond what is accessible with such resources. We show that, provided the tensor network calculation is able to accurately obtain the ground state energy, this scheme does not require a perfect reproduction of the ground state wave function on the quantum circuit to give an accurate Green's function. This hybrid approach may lead to quantum advantage in materials simulations where the ground state can be computed classically, but where the dynamical properties cannot.

Abstract: Quantum correlations, both spatial and temporal, are the central pillars of quantum mechanics. Over the last two decades, a big breakthrough in quantum physics is its complex extension to the non-Hermitian realm, and dizzying varieties of novel phenomena and applications beyond the Hermitian framework have been uncovered. However, unique features of non-Hermitian quantum correlations, especially in the time domain, still remain to be explored. Here, for the first time, we experimentally achieve this goal by using a parity-time (PT )-symmetric trapped-ion system. The upper limit of temporal quantum correlations, known as the algebraic bound, which has so far not been achieved in the standard measurement scenario, is reached here by approaching the exceptional point (EP), thus showing the unexpected ability of EPs in tuning temporal quantum correlation effects. Our study, unveiling the fundamental interplay of non-Hermiticity, nonlinearity, and temporal quantum correlations, provides the first step towards exploring and utilizing various non-Hermitian temporal quantum effects by operating a wide range of EP devices, which are important for both fundamental studies and applications of quantum EP systems.

Abstract: Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum computing). However, measurements, like any aspect of a quantum system, are highly error-prone and difficult to model. In this paper, we introduce a new technique based on randomized compiling to transform errors in measurements into a simple form that removes particularly harmful effects and is also easy to analyze. In particular, we show that our technique reduces generic errors in a computational basis measurement to act like a confusion matrix, i.e. to report the incorrect outcome with some probability, and as a stochastic channel that is independent of the measurement outcome on any unmeasured qudits in the system. We further explore the impact of errors on indirect measurements and demonstrate that a simple and realistic noise model can cause errors that are harmful and difficult to model. Applying our technique in conjunction with randomized compiling to an indirect measurement undergoing this noise results in an effective noise which is easy to model and mitigate.

Abstract: A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this problem from the perspective of quantum control, where the system of interest is described by a drift Hamiltonian and set of control Hamiltonians. Our approach uses a combination of Lie algebra theory, Lie groups and differential geometry, and formulates the problem in terms of geodesics on a differentiable manifold. We provide explicit lower bounds on the quantum speed limit for the case of an arbitrary drift, requiring only that the control Hamiltonians generate a topologically closed subgroup of the full unitary group, and formulate criteria as to when our expression for the speed limit is exact and not merely a lower bound. These analytic results are then tested and confirmed using a numerical optimization scheme. Finally we extend the analysis to find a lower bound on the quantum speed limit in the common case where the system is described by a drift Hamiltonian and a single control Hamiltonian.

Abstract: We investigate the use of Quantum Neural Networks for discovering and implementing quantum error-correcting codes. Our research showcases the efficacy of Quantum Neural Networks through the successful implementation of the Bit-Flip quantum error-correcting code using a Quantum Autoencoder, effectively correcting bit-flip errors in arbitrary logical qubit states. Additionally, we employ Quantum Neural Networks to restore states impacted by Amplitude Damping by utilizing an approximative 4-qubit error-correcting codeword. Our models required modification to the initially proposed Quantum Neural Network structure to avoid barren plateaus of the cost function and improve training time. Moreover, we propose a strategy that leverages Quantum Neural Networks to discover new encryption protocols tailored for specific quantum channels. This is exemplified by learning to generate logical qubits explicitly for the bit-flip channel. Our modified Quantum Neural Networks consistently outperformed the standard implementations across all tasks.

Abstract: The widespread use of machine learning has raised the question of quantum supremacy for supervised learning as compared to quantum computational advantage. In fact, a recent work shows that computational and learning advantage are, in general, not equivalent, i.e., the additional information provided by a training set can reduce the hardness of some problems. This paper investigates under which conditions they are found to be equivalent or, at least, highly related. The existence of efficient algorithms to generate training sets emerges as the cornerstone of such conditions. These results are applied to prove that there is a quantum speed-up for some learning tasks based on the prime factorization problem, assuming the classical intractability of this problem.

Abstract: We give a new presentation of the main result of Arunachalam, Bri\"et and Palazuelos (SICOMP'19) and show that quantum query algorithms are characterized by a new class of polynomials which we call Fourier completely bounded polynomials. We conjecture that all such polynomials have an influential variable. This conjecture is weaker than the famous Aaronson-Ambainis (AA) conjecture (Theory of Computing'14), but has the same implications for classical simulation of quantum query algorithms. We prove a new case of the AA conjecture by showing that it holds for homogeneous Fourier completely bounded polynomials. This implies that if the output of $d$-query quantum algorithm is a homogeneous polynomial $p$ of degree $2d$, then it has a variable with influence at least $Var[p]^2$. In addition, we give an alternative proof of the results of Bansal, Sinha and de Wolf (CCC'22 and QIP'23) showing that block-multilinear completely bounded polynomials have influential variables. Our proof is simpler, obtains better constants and does not use randomness.