Efficient Multiphoton Sampling of Molecular Vibronic Spectra on a Superconducting Bosonic Processor

The design and simulation of ultrashort pulse shaping systems require pulse propagation methods that take the combined effects of dispersion, diffraction, and system aberrations into account. In the conventional pulse propagation methods based on the spectrum of plane wave, usually large number of sampling points are needed for the correct Fourier transform operations due to the fast oscillating phase of the complex pulse field. In this work, I have developed an alternative pulse propagation method, based on the Gaussian pulsed beam decomposition, as an extension of the monochromatic Gaussian beam propagation method. Methods for the decomposition of an input pulse, with arbitrary spatial and temporal (spectral) profiles, into a set of elementary Gaussian pulsed beams are proposed. Algorithms for computing the spatio-temporal and spatio-spectral profiles of the propagated pulse as the phase correct superposition of individual Gaussian pulsed beams are developed. The proposed decomposition method allows the elementary Gaussian pulsed beams to have different parameters depending on the local spatial and spectral phase of the given input pulse which reduces the number of Gaussian pulsed beams required to decompose an input pulsed beam with a given accuracy. Furthermore, a new kind of beam called the truncated Gaussian beam, is introduced and combined with the conventional Gaussian beam decomposition method to enable decomposition of fields after hard apertures. The analytical propagation equation of the truncated Gaussian beam through a paraxial optical system is derived. Additionally, the application of the Gaussian beam decomposition method is extended to handle the propagation of vectorial fields. Several example calculations are presented to validate the proposed methods and show their application in propagating fields through optical systems which are rather complicated to model using the conventional methods.

Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is corrupted or intact, a step known as syndrome detection is performed. For stabilizer codes, this step consists of measuring a set of stabilizer operators. In this paper, inspired by the QEC approach, and specifically stabilizer codes, we propose a prototype quantum circuit model for classification of classical data. The core quantum circuit can be considered as a quantum perceptron where the classification is based on syndrome detection. In this proposal, a quantum perceptron is realized by one stabilizer as part of a stabilizer code, while a quantum neural network (QNN) layer is realized by a stabilizer code which consists of many stabilizers. The concatenation of stabilizer codes results in complex QNNs. The QNN is trained by performing measurements and optimization of a set of parametrized stabilizers. We demonstrate the concept numerically. In this paper we also consider the first challenge to most applications of quantum computers, including data classification, which is to load data into the memory of the quantum computer. This loading amounts to representing the data as a quantum state, i.e., quantum state preparation. An exact amplitude encoding algorithm requires a circuit of exponential depth. We introduce an alternative recursive algorithm which approximates amplitude encoding with only a polynomial number of elementary gates. We name it the recursive approximate-scheme algorithm.

This paper proposes a scheme for probabilistic joint remote preparation of an arbitrary high-dimensional equatorial quantum state by using high-dimensional single-particle orthogonal projective measurement and appropriate unitary operation. As a special case, a scheme of joint remote preparation of a single-qutrit equatorial state is presented in detail. The scheme is also generalized to the multi-party high-dimensional case. It shows that, only if when all the senders collaborate with each other, the receiver can reconstruct the original state with a certain probability.

We propose a quantum optical device to experimentally realize quantum processes, which perform the regularization of the---in general highly singular---Glauber-Sudarshan $P$~functions of arbitrary quantum states before their application and/or measurement. This allows us to produce a broad class of nonclassical states with regular $P$~functions, also called nonclassicality quasiprobabilities. For this purpose, the input states are combined on highly transmissive beam splitters with specific Gaussian or non-Gaussian classical states. We study both balanced and unbalanced homodyne detections for the direct sampling of the output states of the implemented processes, which requires no further regularization or state-reconstruction. By numerical simulations we demonstrate the feasibility of our approach and we outline the generalization to multimode light.

Learning methodologies on quantum devices have shown that there are advantages in utilizing quantum properties. A requirement for using quantum computing in machine learning techniques is the data representation as quantum states. In Quantum Machine Learning, quantum state preparation is paramount to attain a functional pipeline in a model. One state preparation method, amplitude encoding, allows a dataset to be mapped or encoded more robustly and enhances the learning of quantum models. Albeit more densely represented, a dataset which has been prepared by amplitude encoding provides a more learnable input to a model. The two main advantages from using amplitude encoding are an increase in classification accuracy and reduced variability of learning epoch to epoch. In this paper, we compare the basic implementations of TensorFlow Quantum’s Quantum Convolutional Neural Network and a hybrid quantum-classical network using angle encoding, with a third network of our design that utilizes amplitude encoding for enriched state preparation. Our results show there is a direct benefit in performing amplitude encoding before training a TensorFlow Quantum hybrid quantum-classical model. In the best case scenario, amplitude encoding made classifying the samples 8.9% more accurate.

Achieving unit fidelity in quantum state preparation is often impossible in the presence of environmental decoherence. While continuous monitoring and feedback control can improve fidelity, perfect state preparation remains elusive in many scenarios. Inspired by quantum speed limits, we derive a fundamental bound on the steady-state average fidelity achievable via continuous monitoring and feedback control. This bound depends only on the unconditional Lindblad dynamics, the Hamiltonian variance, and the target state. We also adapt the bound to the case of Markovian feedback strategies. We then focus on preparing Dicke states in an atomic ensemble subject to collective damping and dispersive coupling. By imposing additional constraints on control Hamiltonians and monitoring strategies, we derive tighter fidelity bounds. Finally, we propose specific control strategies and validate them using reinforcement learning. Benchmarking their performance against our theoretical bounds highlights the relevance and usefulness of these bounds in characterizing quantum feedback control strategies.

Nowadays, quantum-enhanced methods have been widely studied to solve machine learning related problems. This article presents the application of a Variational Quantum Classifier (VQC) for binary classification. We utilized three datasets: a synthetic dataset with randomly generated values between 0 and 1, the publicly available University of California Intelligence Machine learning (UCI) sonar dataset consisting of mining data, and a proprietary diabetes dataset related to diabetes with acute diseases and diabetes without acute disease. To deal with the limitation of noisy intermediate-scale quantum systems (NISQ), we used a pre-processing method to enhance the prediction rate when applying the VQC method. The process includes feature selection and state preparation. Quantum state preparation is critical for obtaining a functioning pipeline in a quantum machine learning (QML) model. Amplitude encoding is a state preparation approach that enhances the performance of data encoding and the learning of quantum models. As a result, our proposed methods achieved accuracies of 75%, 71.4%, and 68.73% by using VQC model and in contrast, the amplitude encoding-based VQC achieved 98.40%, 67.3%, and 74.50% accuracies on the synthetic, sonar, and diabetes dataset, respectively.

Quantum state preparation is a preliminary step needed by quantum algorithms that require a specific input state. Exact state preparation methods scale exponentially with the number of qubits, making them impractical on noisy intermediate-scale quantum (NISQ) devices. Approximate approaches offer therefore more flexible and scalable alternatives. In this paper, we discuss the Walsh Series Loader (WSL), a recently proposed approximate algorithm for state preparation. In particular, we observe that the paper does not describe how to implement the term of order zero of the operator WSL is based on. While this does not affect the theoretical validity of WSL, it poses obstacles for practitioners aiming to use WSL because, as we show in our experiments, an incorrect implementation leads to states with very poor fidelity. In this paper, we describe how to implement the full quantum circuit required by WSL, including the term of order zero, releasing our source code online, and show that the algorithm works correctly. Finally, we empirically show how, as was theoretically demonstrated in the original article, truncated WSL does not prepare well highly entangled states.

Quantum non-demolition (QND) measurements improve sensitivity by evading measurement back-action. The technique was first proposed to detect mechanical oscillations in gravity wave detectors,and demonstrated in the measurement of optical fields, leading to the development of rigorous criteria to distinguish QND from similar non-classical measurements. Recent QND measurements of macroscopic material systems such as atomic ensembles, and mechanical oscillators, show some QND features, but not full QND character. Here we demonstrate certified QND measurement of the collective spin of an atomic ensemble. We observe quantum state preparation (QSP) and information-damage trade-off (IDT) beyond their classical limits by seven and twelve standard deviations, respectively. Our techniques complement recent work with microscopic systems, and can be used for quantum metrology and memory, the preparation and detection of non-gaussian states, and proposed quantum simulation and information protocols. They should enable QND measurements of dynamical quantum variables and the realization of QND-based quantum information protocols.

The engineering of Kerr interactions is of great interest for processing quantum information in multipartite quantum systems and for investigating many-body physics in a complex cavity-qubit network. We study how coupling multiple different types of superconducting qubits to the same cavity modes can be used to modify the self- and cross-Kerr effects acting on the cavities and demonstrate that this type of architecture could be of significant benefit for quantum technologies. Using both analytical perturbation theory results and numerical simulations, we first show that coupling two superconducting qubits with opposite anharmonicities to a single cavity enables the effective self-Kerr interaction to be diminished, while retaining the number splitting effect that enables control and measurement of the cavity field. We demonstrate that this reduction of the self-Kerr effect can maintain the fidelity of coherent states and generalised Schrödinger cat states for much longer than typical coherence times in realistic devices. Next, we find that the cross-Kerr interaction between two cavities can be modified by coupling them both to the same pair of qubit devices. When one of the qubits is tunable in frequency, the strength of entangling interactions between the cavities can be varied on demand, forming the basis for logic operations on the two modes. Finally, we discuss the feasibility of producing an array of cavities and qubits where intermediary and on-site qubits can tune the strength of self- and cross-Kerr interactions across the whole system. This architecture could provide a way to engineer interesting many-body Hamiltonians and be a useful platform for quantum simulation in circuit quantum electrodynamics.

Reservoir engineering enables the robust preparation of pure quantum states in noisy environments. We show how a new family of quantum states of a mechanical oscillator can be stabilized in a cavity that is parametrically coupled to both the mechanical displacement and the displacement squared. The cavity is driven with three tones, on the red sideband, on the cavity resonance and on the second blue sideband. The states so stabilized are (squeezed and displaced) superpositions of a finite number of phonons. They show the unique feature of encompassing two prototypes of nonclassicality for bosonic systems: by adjusting the strength of the drives, one can in fact move from a single-phonon- to a Schrodinger-cat-like state. The scheme is deterministic, supersedes the need for measurement-and-feedback loops and does not require initialization of the oscillator to the ground state. As such, it enables the unconditional preparation of nonclassical states of a macroscopic object.

Spin is a fundamental property of electrons and plays an important role in information storage. For spin-based quantum information technology, preparation and read-out of the electron spin state must be spin coherent, but both the traditional preparation and read-out of the spin state are projective to up/down spin states, which do not have spin coherence. We have recently demonstrated that the polarization coherence of light can be coherently transferred to the spin coherence of electrons in a semiconductor. We have also developed a new scheme named tomographic Kerr rotation (TKR) by generalizing the traditional KR to directly readout the spin coherence of optically prepared electrons without the need for the spin dynamics, which allows the spin projection measurement in an arbitrary set of basis states. These demonstrations were performed using g-factor-controlled semiconductor quantum wells with precessing and nonprecessing electrons. The developed scheme offers a tool for performing basis-independent preparation and read-out of a spin quantum state in a solid. These results encourage us to make a quantum media converter between flying photon qubits and stationary electron spin qubits in semiconductors.

The quantum Monte Carlo algorithm can provide significant speedup compared to its classical counterpart. So far, most reported works have utilized Grover’s state preparation algorithm. However, this algorithm relies on costly controlled Y rotations to apply the correct amplitudes onto the superposition states. Recently, a comparison-based state preparation method was proposed to reduce computational complexity by avoiding rotation operations. One critical aspect of this method is the generation of the comparison threshold associated with the amplitude of the quantum superposition states. The direct computation of the comparison threshold is often very costly. An alternative is to estimate the threshold with a Taylor approximation. However, Taylor approximations do not work well with heavy-tailed distribution functions such as the Cauchy distribution, which is widely used in applications such as financial modeling. Therefore, a new state preparation method needs to be developed. In this study, an efficient comparison-based state preparation method is proposed for the heavy-tailed Cauchy distribution. Instead of a single Taylor approximation for the entire function domain, this study uses quantum piecewise arithmetic to increase accuracy and reduce computational cost. The proposed piecewise function is in the simplest form to estimate the comparison threshold associated with the amplitudes. Numerical analysis shows that the number of required subdomains increases linearly as the maximum tolerated approximation error decreases exponentially. 197 subdomains are required to keep the error below 18192 of the maximum amplitude. Quantum parallelism ensures that the computational complexity of estimating the amplitudes is independent from the number of subdomains.

The security of cryptographic keys in quantum cryptography systems is guaranteed by fundamental quantum mechanical exclusion principles. A quantum channel through which quantum states are transferred is not controlled and an eavesdropper can perform any modifications with it. The security of quantum key distribution protocols has already been proved [M. Tomamichel et al., Nature Commun. 3, 634 (2011); S. N. Molotkov, J. Exp. Theor. Phys. 115, 969 (2012)], including the realistic case of a finite length of transmitted sequences. It is always assumed that the eavesdropper has neither direct nor indirect access to the transmitting and receiving equipment. The real situation is somewhat different. The preparation and detection of quantum states occur according to random sequences that are generated on the transmitter and receiver sides. Detecting electromagnetic radiation generated in these processes, the eavesdropper can obtain additional information on a key. The upper quantum-mechanical bound on the amount of information of the eavesdropper on the key that can be obtained through a side channel has been determined.

Integrated single-photon detectors open new possibilities for monitoring inside quantum photonic circuits. We present a concept for the in-line measurement of spatially-encoded multi-photon quantum states, while keeping the transmitted ones undisturbed. We theoretically establish that by recording photon correlations from optimally positioned detectors on top of coupled waveguides with detuned propagation constants, one can perform robust reconstruction of the density matrix describing the amplitude, phase, coherence and quantum entanglement. We report proof-of-principle experiments using classical light, which emulates single-photon regime. Our method opens a pathway towards practical and fast in-line quantum measurements for diverse applications in quantum photonics.