30. 3-Qubit Gates in a Microwave-controlled Trapped Ion Quantum Computer Using an Always-On Interaction
29. Accurate solution of the Index Tracking problem with a hybrid simulated annealing algorithm
An actively managed portfolio almost never beats the market in the long term. Thus, many investors often resort to passively managed portfolios whose aim is to follow a certain financial index. The task of building such passive portfolios aiming also to minimize the transaction costs is called Index Tracking (IT), where the goal is to track the index by holding only a small subset of assets in the index. As such, it is an NP-hard problem and becomes unfeasible to solve exactly for indices with more than 100 assets. In this work, we present a novel hybrid simulated annealing method that can efficiently solve the IT problem for large indices and is flexible enough to adapt to financially relevant constraints. By tracking the S&P-500 index between the years 2011 and 2018 we show that our algorithm is capable of finding optimal solutions in the in-sample period of past returns and can be tuned to provide optimal returns in the out-of-sample period of future returns. Finally, we focus on the task of holding an IT portfolio during one year and rebalancing the portfolio every month. Here, our hybrid simulated annealing algorithm is capable of producing financially optimal portfolios already for small subsets of assets and using reasonable computational resources, making it an appropriate tool for financial managers.
28. AutoQML: Automatic generation and training of robust quantum-inspired classifiers by using evolutionary algorithms on grayscale images
We propose a new hybrid system for automatically generating and training quantum-inspired classifiers on grayscale images by using multiobjective genetic algorithms. We define a dynamic fitness function to obtain the smallest possible circuit and highest accuracy on unseen data, ensuring that the proposed technique is generalizable and robust. We minimize the complexity of the generated circuits in terms of the number of entanglement gates by penalizing their appearance. We reduce the size of the images with two dimensionality reduction approaches: principal component analysis (PCA), which is encoded in the individual for optimization purpose, and a small convolutional autoencoder (CAE). These two methods are compared with one another and with a classical nonlinear approach to understand their behaviors and to ensure that the classification ability is due to the quantum circuit and not the preprocessing technique used for dimensionality reduction.
27. Blueprint for a Molecular-Spin Quantum Processor
The implementation of a universal quantum processor still poses fundamental issues related to error mitigation and correction, which demand investigation of also platforms and computing schemes alternative to the main stream. A possibility is offered by employing multilevel logical units (qudits), naturally provided by molecular spins. Here we present the blueprint of a molecular spin quantum processor consisting of single molecular nanomagnets, acting as qudits, placed within superconducting resonators adapted to the size and interactions of these molecules to achieve a strong single spin-to-photon coupling. We show how to implement a universal set of gates in such a platform and to readout the final qudit state. Single-qudit unitaries (potentially embedding multiple qubits) are implemented by fast classical drives, while an alternative scheme is introduced to obtain two-qubit gates via resonant photon exchange. The latter is compared to the dispersive approach, finding in general a significant improvement. The performance of the platform is assessed by realistic numerical simulations of gate sequences, such as Deutsch-Josza and quantum simulation algorithms. The very good results demonstrate the feasibility of the molecular route towards a universal quantum processor.
26. Cooling microwave fields into general multimode Gaussian states
25. Coupled-oscillator model to analyze the interaction between a quartz resonator and trapped ions
24. Directional spontaneous emission in photonic crystal slabs
Spontaneous emission is one of the most fundamental out-of-equilibrium processes in which an excited quantum emitter relaxes to the ground state due to quantum fluctuations. In this process, a photon is emitted that can interact with other nearby emitters and establish quantum correlations between them, e.g., via super and subradiance effects. One way to modify these photon-mediated interactions is to alter the dipole radiation patterns of the emitter, e.g., by placing photonic crystals near them. One recent example is the generation of strong directional emission patterns-key to enhancing super and subradiance effects-in two dimensions by employing photonic crystals with band structures characterized by linear isofrequency contours and saddle-points. However, these studies have predominantly used oversimplified toy models, overlooking the electromagnetic field’s intricacies in actual materials, including aspects like geometrical dependencies, emitter positions, and polarization. Our study delves into the interaction between these directional emission patterns and the aforementioned variables, revealing the untapped potential to fine-tune collective quantum optical phenomena.
23. Driven-dissipative topological phases in parametric resonator arrays
We study the phenomena of topological amplification in arrays of parametric oscillators. We find two phases of topological amplification, both with directional transport and exponential gain with the number of sites, and one of them featuring squeezing. We also find a topologically trivial phase with zero-energy modes which produces amplification but lacks the robust topological protection of the others. We characterize the resilience to disorder of the different phases and their stability, gain, and noise-to-signal ratio. Finally, we discuss their experimental implementation with state-of-the-art techniques.
22. Frequency-resolved Purcell effect for the dissipative generation of steady-state entanglement
We report a driven-dissipative mechanism to generate stationary entangled $W$ states among strongly-interacting quantum emitters placed within a cavity. Driving the ensemble into the highest energy state — whether coherently or incoherently — enables a subsequent cavity-enhanced decay into an entangled steady state consisting of a single de-excitation shared coherently among all emitters, i.e., a $W$ state, well known for its robustness against qubit loss. The non-harmonic energy structure of the interacting ensemble allows this transition to be resonantly selected by the cavity, while quenching subsequent off-resonant decays. Evidence of this purely dissipative mechanism should be observable in state-of-the-art cavity QED systems in the solid-state, enabling new prospects for the scalable stabilization of quantum states in dissipative quantum platforms.
21. Global optimization of MPS in quantum-inspired numerical analysis
This work discusses the solution of partial differential equations (PDEs) using matrix product states (MPS). The study focuses on the search for the lowest eigenstates of a Hamiltonian equation, for which five algorithms are introduced: imaginary-time evolution, steepest gradient descent, an improved gradient descent, an implicitly restarted Arnoldi method, and density matrix renormalization group (DMRG) optimization. The first four methods are engineered using a framework of limited-precision linear algebra, where operations between MPS and matrix product operators (MPOs) are implemented with finite resources. All methods are benchmarked using the PDE for a quantum harmonic oscillator in up to two dimensions, over a regular grid with up to $2^{28}$ points. Our study reveals that all MPS-based techniques outperform exact diagonalization techniques based on vectors, with respect to memory usage. Imaginary-time algorithms are shown to underperform any type of gradient descent, both in terms of calibration needs and costs. Finally, Arnoldi like methods and DMRG asymptotically outperform all other methods, including exact diagonalization, as problem size increases, with an exponential advantage in memory and time usage.
20. Hardware-Efficient Entangled Measurements for Variational Quantum Algorithms
Variational algorithms have received significant attention in recent years due to their potential to solve practical problems using noisy intermediate-scale quantum (NISQ) devices. A fundamental step of these algorithms is the evaluation of the expected value of Hamiltonians, and hence efficient schemes to perform this task are required. The standard approach employs local measurements of Pauli operators and requires a large number of circuits. An alternative is to make use of entangled measurements, which might introduce additional gates between physically disconnected qubits that harm the performance. As a solution to this problem, we propose hardware-efficient entangled measurements (HEEM), that is, measurements that permit only entanglement between physically connected qubits. We show that this strategy enhances the evaluation of molecular Hamiltonians in NISQ devices by reducing the number of circuits required without increasing their depth. We provide quantitative metrics of how this approach offers better results than local measurements and arbitrarily entangled measurements. We estimate the ground-state energy of the H$_2$O molecule with classical simulators and quantum hardware using the variational quantum eigensolver with HEEM.
19. Improving quantum state transfer: correcting non-Markovian and distortion effects
18. Jornadas Nacionales de Robótica y Bioingeniería 2023: Libro de actas
17. Kibble–Zurek mechanism of Ising domains
The formation of topological defects after a symmetry-breaking phase transition is an overarching phenomenon that encodes the underlying dynamics. The Kibble–Zurek mechanism (KZM) describes these non-equilibrium dynamics of second-order phase transitions and predicts a power-law relationship between the cooling rates and the density of topological defects. It has been verified as a successful model in a wide variety of physical systems, including structure formation in the early Universe and condensed-matter materials. However, it is uncertain if the KZM mechanism is also valid for topologically trivial Ising domains, one of the most common and fundamental types of domain in condensed-matter systems. Here we show that the cooling rate dependence of Ising domain density follows the KZM power law in two different three-dimensional structural Ising domains: ferro-rotation domains in NiTiO3 and polar domains in BiTeI. However, although the KZM slope of NiTiO3 agrees with the prediction of the 3D Ising model, the KZM slope of BiTeI exceeds the theoretical limit, providing an example of steepening KZM slope with long-range dipolar interactions. Our results demonstrate the validity of KZM for Ising domains and reveal an enhancement of the power-law exponent for transitions of non-topological quantities with long-range interactions.
16. Light-matter correlations in Quantum Floquet engineering of cavity quantum materials
Quantum Floquet engineering (QFE) seeks to generalize the control of quantum systems with classical external fields, widely known as Semi-Classical Floquet engineering (SCFE), to quantum fields. However, to faithfully capture the physics at arbitrary coupling, a gauge-invariant description of light-matter interaction in cavity-QED materials is required, which makes the Hamiltonian highly non-linear in photonic operators. We provide a non-perturbative truncation scheme of the Hamiltonian, which is valid or arbitrary coupling strength, and use it to investigate the role of light-matter correlations, which are absent in SCFE. We find that even in the high-frequency regime, light-matter correlations can be crucial, in particular for the topological properties of a system. As an example, we show that for a SSH chain coupled to a cavity, light-matter correlations break the original chiral symmetry of the chain, strongly affecting the robustness of its edge states. In addition, we show how light-matter correlations are imprinted in the photonic spectral function and discuss their relation with the topology of the bands.
15. Many-body origin of anomalous Floquet phases in cavity-QED materials
Anomalous Floquet topological phases are a hallmark, without a static analog, of periodically driven systems. Recently, Quantum Floquet Engineering has emerged as an interesting approach to cavity-QED materials, which recovers the physics of Floquet engineering in its semi-classical limit. However, the mapping between these two widely different scenarios remains mysterious in many aspects. We discuss the emergence of anomalous topological phases in cavity-QED materials, and link topological phase transitions in the many-body spectrum with those in the $0$- and $\pi$-gaps of Floquet quasienergies. Our results allow to establish the microscopic origin of an emergent discrete time-translation symmetry in the matter sector, and link the physics of isolated many-body systems with that of periodically driven ones. Finally, the relation between many-body and Floquet topological invariants is discussed, as well as the bulk-edge correspondence.
14. Multiobjective variational quantum optimization for constrained problems: an application to cash handling
Combinatorial optimization problems are ubiquitous in industry. In addition to finding a solution with minimum cost, problems of high relevance involve a number of constraints that the solution must satisfy. Variational quantum algorithms have emerged as promising candidates for solving these problems in the noisy intermediate-scale quantum stage. However, the constraints are often complex enough to make their efficient mapping to quantum hardware difficult or even infeasible. An alternative standard approach is to transform the optimization problem to include these constraints as penalty terms, but this method involves additional hyperparameters and does not ensure that the constraints are satisfied due to the existence of local minima. In this paper, we introduce a new method for solving combinatorial optimization problems with challenging constraints using variational quantum algorithms. We propose the Multi-Objective Variational Constrained Optimizer (MOVCO) to classically update the variational parameters by a multiobjective optimization performed by a genetic algorithm. This optimization allows the algorithm to progressively sample only states within the in-constraints space, while optimizing the energy of these states. We test our proposal on a real-world problem with great relevance in finance: the Cash Management problem. We introduce a novel mathematical formulation for this problem, and compare the performance of MOVCO versus a penalty based optimization. Our empirical results show a significant improvement in terms of the cost of the achieved solutions, but especially in the avoidance of local minima that do not satisfy any of the mandatory constraints.
13. New Approach to Designing Functional Materials for Stealth Technology: Radar Experiment with Bilayer Absorbers and Optimization of the Reflection Loss
12. Numerical Simulation of Large-Scale Nonlinear Open Quantum Mechanics
We introduce a numerical method to simulate nonlinear open quantum dynamics of a particle in situations where its state undergoes significant expansion in phase space while generating small quantum features at the phase-space Planck scale. Our approach involves simulating the Wigner function in a time-dependent frame that leverages information from the classical trajectory to efficiently represent the quantum state in phase space. To demonstrate the capabilities of our method, we examine the open quantum dynamics of a particle evolving in a one-dimensional weak quartic potential after initially being ground-state cooled in a tight harmonic potential. This numerical approach is particularly relevant to ongoing efforts to design, optimize, and understand experiments targeting the preparation of macroscopic quantum superposition states of massive particles through nonlinear quantum dynamics.
11. Parallel tomography of quantum non-demolition measurements in multi-qubit devices
An efficient characterization of QND measurements is an important ingredient towards certifying and improving the performance and scalability of quantum processors. In this work, we introduce a parallel tomography of QND measurements that addresses single- and two-qubit readout on a multi-qubit quantum processor. We provide an experimental demonstration of the tomographic protocol on a 7-qubit IBM-Q device, characterizing the quality of conventional qubit readout as well as generalized measurements such as parity or measurement-and-reset schemes. Our protocol reconstructs the Choi matrices of the measurement processes, extracts relevant quantifiers — fidelity, QND-ness, destructiveness — and identifies sources of errors that limit the performance of the device for repeated QND measurements. We also show how to quantify measurement cross-talk and use it to certify the quality of simultaneous readout on multiple qubits.
10. Probing and harnessing photonic Fermi arc surface states using light-matter interactions
Fermi arcs, i.e., surface states connecting topologically-distinct Weyl points, represent a paradigmatic manifestation of the topological aspects of Weyl physics. Here, we investigate a light-matter interface based on the photonic counterpart of these states and we prove that it can lead to phenomena with no analogue in other setups. First, we show how to image the Fermi arcs by studying the spontaneous decay of one or many emitters coupled to the system’s border. Second, we demonstrate that the Fermi arc surface states can act as a robust quantum link. To do that we exploit the negative refraction experienced by these modes at the hinges of the system. Thanks to this mechanism a circulatory photonic current is created which, depending on the occurrence of revivals, yields two distinct regimes. In the absence of revivals, the surface states behave as a dissipative chiral quantum channel enabling, e.g., perfect quantum state transfer. In the presence of revivals, an effective off-resonant cavity is induced, which leads to coherent emitter couplings that can entangle them maximally. In addition to their fundamental interest, our findings evidence the potential offered by the photonic Fermi arc light-matter interfaces for the design of more robust quantum technologies.
9. Quantum Approximate Optimization Algorithm Pseudo-Boltzmann States
In this letter, we provide analytical and numerical evidence that the single-layer Quantum Approximate Optimization Algorithm (QAOA) on universal Ising spin models produces thermal-like states. We find that these pseudo-Boltzmann states can not be efficiently simulated on classical computers according to the general state-of-the-art condition that ensures rapid mixing for Ising models. Moreover, we observe that the temperature depends on a hidden universal correlation between the energy of a state and the covariance of other energy levels and the Hamming distances of the state to those energies.
8. Quantum control of tunable-coupling transmons using dynamical invariants of motion
7. Quantum metrology with critical driven-dissipative collective spin system
6. Topological multimode waveguide QED
5. Transmon-qubit readout using an in situ bifurcation amplification in the mesoscopic regime
We demonstrate a transmon qubit readout based on the nonlinear response to a drive of polaritonic meters in-situ coupled to the qubit. Inside a 3D readout cavity, we place a transmon molecule consisting of a transmon qubit and an ancilla mode interacting via non-perturbative cross-Kerr coupling. The cavity couples strongly only to the ancilla mode, leading to hybridized lower and upper polaritonic meters. Both polaritons are anharmonic and dissipative, as they inherit a self-Kerr nonlinearity $U$ from the ancilla and effective decay $\kappa$ from the open cavity. Via the ancilla, the polariton meters also inherit the non-perturbative cross-Kerr coupling to the qubit. This results in a high qubit-dependent displacement $2\chi > \kappa, ~U$ that can be read out via the cavity without causing Purcell decay. Moreover, the polariton meters, being nonlinear resonators, present bistability, and bifurcation behavior when the probing power increases. In this work, we focus on the bifurcation at low power in the few-photon regime, called the mesoscopic regime, which is accessible when the self-Kerr and decay rates of the polariton meter are similar $U\sim \kappa$. Capitalizing on a latching mechanism by bifurcation, the readout is sensitive to transmon qubit relaxation error only in the first tens of nanoseconds. We thus report a single-shot fidelity of 98.6 $\%$ while having an integration time of a 500 ns and no requirement for an external quantum-limited amplifier.
4. Universal Time-Dependent Control Scheme for Realizing Arbitrary Linear Bosonic Transformations
We study the implementation of arbitrary excitation-conserving linear transformations between two sets of $N$ stationary bosonic modes, which are connected through a photonic quantum channel. By controlling the individual couplings between the modes and the channel, an initial $N$-partite quantum state in register $A$ can be released as a multiphoton wave packet and, successively, be reabsorbed in register $B$. Here we prove that there exists a set of control pulses that implement this transfer with arbitrarily high fidelity and, simultaneously, realize a prespecified $N\times N$ unitary transformation between the two sets of modes. Moreover, we provide a numerical algorithm for constructing these control pulses and discuss the scaling and robustness of this protocol in terms of several illustrative examples. By being purely control-based and not relying on any adaptations of the underlying hardware, the presented scheme is extremely flexible and can find widespread applications, for example, for boson-sampling experiments, multiqubit state transfer protocols or in continuous-variable quantum computing architectures.
3. Variational Quantum Simulators Based on Waveguide QED
Waveguide QED simulators are analogue quantum simulators made by quantum emitters interacting with one-dimensional photonic band-gap materials. One of their remarkable features is that they can be used to engineer tunable-range emitter interactions. Here, we demonstrate how these interactions can be a resource to develop more efficient variational quantum algorithms for certain problems. In particular, we illustrate their power in creating wavefunction ans\”atze that capture accurately the ground state of quantum critical spin models (XXZ and Ising) with less gates and optimization parameters than other variational ans\”atze based on nearest-neighbor or infinite-range entangling gates. Finally, we study the potential advantages of these waveguide ans\”atze in the presence of noise. Overall, these results evidence the potential of using the interaction range as a variational parameter and place waveguide QED simulators as a promising platform for variational quantum algorithms.