Quantum Physics (quant-ph)

Abstract: Thermodynamically consistent measurements can either preserve statistics (unbiased) or preserve marginal states (non-invasive) but not both. Here we show the existence of metrological tasks which unequally favor each of the aforementioned measurement types. We consider two different metrology tasks, namely weak value amplification technique and repeated metrology without resetting. We observe that unbiased measurement is better than non-invasive measurement for the former and the converse is true for the latter. We provide finite temperature simulations of transmon sensors which estimate how much cooling, a resource for realistic measurements, is required to perform these metrology tasks.

Abstract: An issue which has attracted increasing attention in recent years are Kirkwood-Dirac quasiprobabilities. List of their use includes several questions of quantum information processing. Such quasiprobabilities naturally appear in the context of unravelings of a quantum channel. Complex tight frames also have potential applications in quantum information. Building principal Kraus operators of the frame vectors generates quasiprobabilities with interesting properties. For an equiangular tight frame, we characterize the Hilbert-Schmidt and spectral norms of the corresponding matrix. Hence, uncertainty relations are formulated in terms of R\'{e}nyi and Tsallis entropies. New inequalities for characterizing the location of eigenvalues are derived. They give an alternative to estimation on the base of Ger\v{s}gorin's theorem. The presented inequalities are exemplified with symmetric informationally complete measurement in dimension two.

Abstract: This work presents an optimization-based scalable quantum neural network framework for approximating $n$-qubit unitaries through generic parametric representation of unitaries, which are obtained as product of exponential of basis elements of a new basis that we propose as an alternative to Pauli string basis. We call this basis as the Standard Recursive Block Basis, which is constructed using a recursive method, and its elements are permutation-similar to block Hermitian unitary matrices.

Abstract: Large-scale quantum networks require the implementation of long-lived quantum memories as stationary nodes interacting with qubits of light. Epitaxially grown quantum dots hold great potential for the on-demand generation of single and entangled photons with high purity and indistinguishability. Coupling these emitters to memories with long coherence times enables the development of hybrid nanophotonic devices incorporating the advantages of both systems. Here we report the first GaAs/AlGaAs quantum dots grown by droplet etching and nanohole infilling method, emitting single photons with a narrow wavelength distribution (736.2 $\pm$ 1.7 nm) close to the zero-phonon line of Silicon-vacancy centers. Polarization entangled photons are generated via the biexciton-exciton cascade with a fidelity of (0.73 $\pm$ 0.09). High single photon purity is maintained from 4 K (g$^($$^2$$^)$(0) = 0.07 $\pm$ 0.02) up to 80 K (g$^($$^2$$^)$(0) = 0.11 $\pm$ 0.01), therefore making this hybrid system technologically attractive for real-world quantum photonic applications.

Abstract: We propose the first online quantum algorithm for zero-sum games with $\tilde O(1)$ regret under the game setting. Moreover, our quantum algorithm computes an $\varepsilon$-approximate Nash equilibrium of an $m \times n$ matrix zero-sum game in quantum time $\tilde O(\sqrt{m+n}/\varepsilon^{2.5})$, yielding a quadratic improvement over classical algorithms in terms of $m, n$. Our algorithm uses standard quantum inputs and generates classical outputs with succinct descriptions, facilitating end-to-end applications. As an application, we obtain a fast quantum linear programming solver. Technically, our online quantum algorithm "quantizes" classical algorithms based on the optimistic multiplicative weight update method. At the heart of our algorithm is a fast quantum multi-sampling procedure for the Gibbs sampling problem, which may be of independent interest.

Abstract: Variational algorithms such as the Quantum Approximate Optimization Algorithm have attracted attention due to their potential for solving problems using near-term quantum computers. The $ZZ$ interaction typically generates the primitive two-qubit gate in such algorithms applied for a time, typically a variational parameter, $\gamma$. Different compilation techniques exist with respect to the implementation of two-qubit gates. Due to the importance of the $ZZ$-gate, we present an error analysis comparing the continuous-angle controlled phase gate (CP) against the fixed angle controlled $Z$-gate (CZ). We analyze both techniques under the influence of coherent over-rotation and depolarizing noise. We show that CP and CZ compilation techniques achieve comparable $ZZ$-gate fidelities if the incoherent error is below $0.03 \, \%$ and the coherent error is below $0.8 \, \%$. Thus, we argue that for small coherent and incoherent error a non-parameterized two-qubit gate such as CZ in combination with virtual $Z$ decomposition for single-qubit gates could lead to a significant reduction in the calibration required and, therefore, a less error-prone quantum device. We show that above a coherent error of $0.04 \pi$ ($2 \, \%$), the CZ gate fidelity depends significantly on $\gamma$.

Abstract: Discrete frequency-bin entanglement is an essential resource for applications in quantum information processing. In this Letter, we propose and demonstrate a scheme to generate discrete frequency-bin entanglement with a single piece of periodically poled lithium niobate waveguide in a modified Sagnac interferometer. Correlated two-photon states in both directions of the Sagnac interferometer are generated through cascaded second-order optical nonlinear processes. A relative phase difference between the two states is introduced by changing the polarization state of pump light, thus manipulating the two-photon state at the output of the Sagnac interferometer. The generated two-photon state is sent into a fiber polarization splitter, then a pure discrete frequency-bin entangled two-photon state is obtained by setting the pump light. The frequency entanglement property is measured by a spatial quantum beating with a visibility of $96.0 \pm 6.1\%$. The density matrix is further obtained with a fidelity of $98.0 \pm 3.0\%$ to the ideal state. Our demonstration provides a promising method for the generation of pure discrete frequency-bin entanglement at telecom band, which is desired in quantum photonics.

Abstract: Vector beams (VBs) are fully polarized beams with spatially varying polarization distributions, and they have found widespread use in numerous applications such as microscopy, metrology, optical trapping, nano-photonics, and communications. The entanglement of such beams has attracted significant interest, and it has been shown to have tremendous potential in expanding existing applications and enabling new ones. However, due to the complex spatially varying polarization structure of entangled VBs (EVBs), a complete entanglement characterization of these beams remains challenging and time-consuming. Here, we have used a time-tagging event camera to demonstrate the ability to simultaneously characterize approximately $2.6\times10^6$ modes between a bi-partite EVB using only 16 measurements. This achievement is an important milestone in high-dimensional entanglement characterization of structured light, and it could significantly impact the implementation of related quantum technologies. The potential applications of this technique are extensive, and it could pave the way for advancements in quantum communication, quantum imaging, and other areas where structured entangled photons play a crucial role.

Abstract: The use of nitrogen-vacancy centers in diamond as a non-invasive platform for hyperpolarizing nuclear spins in molecular samples is a promising area of research with the potential to enhance the sensitivity of nuclear magnetic resonance experiments. Transferring NV polarization out of the diamond structure has been achieved on nanoscale targets using dynamical nuclear polarization methods, but extending this to relevant NMR volumes poses significant challenges. One major technical hurdle is the presence of paramagnetic defects in the diamond surface which can interfere with polarization outflow. However, these defects can also be harnessed as intermediaries for the interaction between NVs and nuclear spins. We present a method that benefits from existing microwave sequences, namely the PulsePol, to transfer polarization efficiently and robustly using dangling bonds or other localized electronic spins, with the potential to increase polarization rates under realistic conditions.

Abstract: Recently, the Hilbert-Schmidt speed, as a special class of quantum statistical speed, has been reported to improve the interferometric phase in single-parameter quantum estimation. Here, we test this concept in the multiparameter scenario where two laser phases are estimated in a theoretical model consisting of a three-level atom interacting with two classical monochromatic fields. When the atom is initially prepared in the lower bare state taking into account the detuning parameters, we extract an exact analytical solution of the atomic density matrix in the case of two-photon resonant transition. Further, we compare the performance of laser phase parameters estimation in individual and simultaneous metrological strategies, and we explore the role of quantum coherence in improving the efficiency of unknown multi-phase shift estimation protocols. The obtained results show that the Hilbert-Schmidt speed detects the lower bound on the statistical estimation error as well as the optimal estimation regions, where its maximal corresponds to the maximal quantum Fisher information, the performance of simultaneous multiparameter estimation with individual estimation inevitably depends on the detuning parameters of the three-level atom, and not only the quantum entanglement, but also the quantum coherence is a crucial resource to improve the accuracy of a metrological protocol.

Abstract: We explain why and numerically confirm that there are no barren plateaus in the energy optimization of isometric tensor network states (TNS) for extensive Hamiltonians with finite-range interactions. Specifically, we consider matrix product states, tree tensor network states, and the multiscale entanglement renormalization ansatz. The variance of the energy gradient, evaluated by taking the Haar average over the TNS tensors, has a leading system-size independent term and decreases according to a power law in the bond dimension. For a hierarchical TNS with branching ratio $b$, the variance of the gradient with respect to a tensor in layer $\tau$ scales as $(b\eta)^\tau$, where $\eta$ is the second largest eigenvalue of the Haar-average doubled layer-transition channel and decreases algebraically with increasing bond dimension. The observed scaling properties of the gradient variance bear implications for efficient initialization procedures.

Abstract: We characterize the set of optimal protocols for two-qubit entangling gates through a mechanism analysis based on quantum pathways, which allows us to compare and rank the different solutions. As an example of a flexible platform with a rich landscape of protocols, we consider trapped neutral atoms excited to Rydberg states by different pulse sequences that extend over several atomic sites, optimizing both the temporal and the spatial features of the pulses. Studying the rate of success of the algorithm under different constraints, we analyze the impact of the proximity of the atoms on the nature and quality of the optimal protocols. We characterize in detail the features of the solutions in parameter space, showing some striking correlations among the set of parameters. Together with the mechanism analysis, the spatio-temporal control allows us to select protocols that operate under mechanisms by design, like finding needles in the haystack.

Abstract: The academic literature contains many estimates of the resources required to operate a cryptanalytically relevant quantum computer (CRQC) in terms of rather abstract quantities like the number of qubits. But to our knowledge, there have not been any estimates of these requirements in terms of more familiar economic resources like money or electricity. We demonstrate that the electrical energy required to break one cryptographic public key can be decomposed into the product of two factors. There is an extensive literature of previous estimates for one factor, the spacetime volume, that range over about six orders of magnitude; we discuss some interesting patterns in these estimates. We could not find any quantitative estimates at all for the other factor, the average power consumption per qubit. By combining several data points from existing superconducting-transmon quantum computers and extrapolating them to enormously larger scales, we make an extremely rough estimate of a plausible value of about six watts/qubit consumed by an eventual superconducting-transmon CRQC. By combining this estimate with a plausible spacetime volume estimate of $5.9 \times 10^6$ qubit-days from the prior literature, we estimate that - even after expending the enormous costs to build a CRQC - running it would require about 125 MW of electrical power, and using it to break one public key would cost about \$64,000 for electricity alone at current prices. Even if a CRQC is eventually built, merely operating it would probably remain the domain of nation-states and large organizations for a significant period of time.

Abstract: By controlling the temporal and spatial features of light, we propose a novel protocol to prepare two-qubit entangling gates on atoms trapped at close distance, which could potentially speed up the operation of the gate from the sub-micro to the nanosecond scale. The protocol is robust to variations in the pulse areas and the position of the atoms, by virtue of the coherent properties of a dark state, which is used to drive the population through Rydberg states. From the time-domain perspective, the protocol generalizes the one proposed by Jaksch and coworkers [Jaksch et al., Phys. Rev. Lett. 85, 2208 (2000)], with three pulses that operate symmetrically in time, but with different pulse areas. From the spatial-domain perspective, it uses structured light. We analyze the map of the gate fidelity, which forms rotated and distorted lattices in the solution space. Finally, we study the effect of an additional qubit to the gate performance and propose generalizations that operate with multi-pulse sequences.

Abstract: A transition of quantum walk induced by classical randomness changes the probability distribution of the walker from a two-peak structure to a single-peak one when the random parameter exceeds a critical value or the system size exceeds the localization length. We first establish the generality of the localization by showing its emergence in the presence of random rotation or translation. The transition point can be located manually by examining the probability distribution, momentum of inertia, and inverse participation ratio. As a comparison, we implement two supervised machine learning methods, the support vector machine and multi-layer perceptron neural network, with the same data. While both manual and machine-learning methods can identify the transition, the two machine-learning methods tend to underestimate the exponent of the localization length because of the fluctuating probability distribution. Our work illustrates challenges facing machine learning of physical systems with mixed quantum and classical probabilities.

Abstract: We present an industrial end-user perspective on the current state of quantum computing hardware for one specific technological approach, the neutral atom platform. Our aim is to assist developers in understanding the impact of the specific properties of these devices on the effectiveness of algorithm execution. Based on discussions with different vendors and recent literature, we discuss the performance data of the neutral atom platform. Specifically, we focus on the physical qubit architecture, which affects state preparation, qubit-to-qubit connectivity, gate fidelities, native gate instruction set, and individual qubit stability. These factors determine both the quantum-part execution time and the end-to-end wall clock time relevant for end-users, but also the ability to perform fault-tolerant quantum computation in the future. We end with an overview of which applications have been shown to be well suited for the peculiar properties of neutral atom-based quantum computers.

Abstract: The Heisenberg limit provides a fundamental bound on the achievable estimation precision with a limited number of $N$ resources used (e.g., atoms, photons, etc.). Using entangled quantum states makes it possible to scale the precision with $N$ better than when resources would be used independently. Consequently, the optimal use of all resources involves accumulating them in a single execution of the experiment. Unfortunately, that implies that the most common theoretical tool used to analyze metrological protocols - quantum Fisher information (QFI) - does not allow for a reliable description of this problem, as it becomes operationally meaningful only with multiple repetitions of the experiment. In this thesis, using the formalism of Bayesian estimation and the minimax estimator, I derive asymptotically saturable bounds on the precision of the estimation for the case of noiseless unitary evolution. For the case where the number of resources $N$ is strictly constrained, I show that the final measurement uncertainty is $\pi$ times larger than would be implied by a naive use of QFI. I also analyze the case where a constraint is imposed only on the average amount of resources, the exact value of which may fluctuate (in which case QFI does not provide any universal bound for precision). In both cases, I study the asymptotic saturability and the rate of convergence of these bounds. In the following part, I analyze the problem of the Heisenberg limit when multiple parameters are measured simultaneously on the same physical system. In particular, I investigate the existence of a gain from measuring all parameters simultaneously compared to distributing the same amount of resources to measure them independently. I focus on two examples - the measurement of multiple phase shifts in a multi-arm interferometer and the measurement of three magnetic field components.

Abstract: Quantum singular value transformation (QSVT) enables the application of polynomial functions to the singular values of near arbitrary linear operators embedded in unitary transforms, and has been used to unify, simplify, and improve most quantum algorithms. QSVT depends on precise results in representation theory, with the desired polynomial functions acting simultaneously within invariant two-dimensional subspaces of a larger Hilbert space. These two-dimensional transformations are largely determined by the related theory of quantum signal processing (QSP). While QSP appears to rely on properties specific to the compact Lie group SU(2), many other Lie groups appear naturally in physical systems relevant to quantum information. This work considers settings in which SU(1,1) describes system dynamics and finds that, surprisingly, despite the non-compactness of SU(1,1), one can recover a QSP-type ansatz, and show its ability to approximate near arbitrary polynomial transformations. We discuss various experimental uses of this construction, as well as prospects for expanded relevance of QSP-like ans\"atze to other Lie groups.

Abstract: The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation's realizing dynamics. As quantum computing matures, a similar need has developed for an assurance of the correctness of high-level quantum algorithmic reasoning. Parallel to this need, many quantum algorithms have been unified and improved using quantum signal processing (QSP) and quantum singular value transformation (QSVT), which characterize the ability, by alternating circuit ans\"atze, to transform the singular values of sub-blocks of unitary matrices by polynomial functions. However, while the algebraic manipulation of polynomials is simple (e.g., compositions and products), the QSP/QSVT circuits realizing analogous manipulations of their embedded polynomials are non-obvious. This work constructs and characterizes the runtime and expressivity of QSP/QSVT protocols where circuit manipulation maps naturally to the algebraic manipulation of functional transforms (termed semantic embedding). In this way, QSP/QSVT can be treated and combined modularly, purely in terms of the functional transforms they embed, with key guarantees on the computability and modularity of the realizing circuits. We also identify existing quantum algorithms whose use of semantic embedding is implicit, spanning from distributed search to proofs of soundness in quantum cryptography. The methods used, based in category theory, establish a theory of semantically embeddable quantum algorithms, and provide a new role for QSP/QSVT in reducing sophisticated algorithmic problems to simpler algebraic ones.

Abstract: Although different architectures of quantum perceptrons have been recently put forward, the capabilities of such quantum devices versus their classical counterparts remain debated. Here, we consider random patterns and targets independently distributed with biased probabilities and investigate the storage capacity of a continuous quantum perceptron model that admits a classical limit, thus facilitating the comparison of performances. Such a more general context extends a previous study of the quantum storage capacity where using statistical mechanics techniques in the limit of a large number of inputs, it was proved that no quantum advantages are to be expected concerning the storage properties. This outcome is due to the fuzziness inevitably introduced by the intrinsic stochasticity of quantum devices. We strengthen such an indication by showing that the possibility of indefinitely enhancing the storage capacity for highly correlated patterns, as it occurs in a classical setting, is instead prevented at the quantum level.