VQE method: a short survey and recent developments

The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation (QPE) because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schrödinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by the choice of the variational ansatz used to represent the trial wave function. Hence, the construction of an efficient ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatzes for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing efficient ansatzes that fall into two categories—chemistry–inspired and hardware–efficient—that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.

Comparison of Phase Estimation Methods for Quantitative Susceptibility Mapping Using a Rotating-Tube Phantom

Quantitative Susceptibility Mapping (QSM) is an MRI tool with the potential to reveal pathological changes from magnetic susceptibility measurements. Before phase data can be used to recover susceptibility ( Δ χ ), the QSM process begins with two steps: data acquisition and phase estimation. We assess the performance of these steps, when applied without user intervention, on several variations of a phantom imaging task. We used a rotating-tube phantom with five tubes ranging from Δ χ = 0.05 ppm to Δ χ = 0.336 ppm. MRI data was acquired at nine angles of rotation for four different pulse sequences. The images were processed by 10 phase estimation algorithms including Laplacian, region-growing, branch-cut, temporal unwrapping, and maximum-likelihood methods, resulting in approximately 90 different combinations of data acquisition and phase estimation methods. We analyzed errors between measured and expected phases using the probability mass function and Cumulative Distribution Function. Repeatable acquisition and estimation methods were identified based on the probability of relative phase errors. For single-echo GRE and segmented EPI sequences, a region-growing method was most reliable with Pr (relative error <0.1) = 0.95 and 0.90, respectively. For multiecho sequences, a maximum-likelihood method was most reliable with Pr (relative error <0.1) = 0.97. The most repeatable multiecho methods outperformed the most repeatable single-echo methods. We found a wide range of repeatability and reproducibility for off-the-shelf MRI acquisition and phase estimation approaches, and this variability may prevent the techniques from being widely integrated in clinical workflows. The error was dominated in many cases by spatially discontinuous phase unwrapping errors. Any postprocessing applied on erroneous phase estimates, such as QSM’s background field removal and dipole inversion, would suffer from error propagation. Our paradigm identifies methods that yield consistent and accurate phase estimates that would ultimately yield consistent and accurate Δ χ estimates.

High precision phase estimation with controllable sensitivity and dynamic range

High precision phase estimation is at the core of modern physics and practical applications. We investigate a method for high precision phase estimation via inserting a reference state which enables weak measurement technique to be used in wide dynamic range. A reference phase is introduced artificially to offset the time delay between preselection state and reference state. The sensitivity of measured phase and the linear dynamic range are controllable by adjusting reference phase. Moreover, an arbitrary postselection in measurement is applicable by choosing appropriate reference phase. This method has merits of controllable sensitivity and wide dynamic range, which shows great potential practical applications in high precision phase measurement.

Identifikasi Amplitudo dan Sudut Kedatangan Sinyal Menggunakan Metode Forward-Backward APES pada Radar Multi-Antena

Jenis sistem radar multi-antena ada dua macam yaitu phased-array (PA) dan Multiple-input Multiple-Output (MIMO). Parameter yang digunakan untuk menguji kinerja radar PA dan MIMO ada banyak sekali yang salah satunya adalah estimasi parameter yang berkaitan dengan jumlah target deteksi. Estimasi parameter termasuk di dalamnya yaitu sudut kedatangan sinyal (direction of arrival, DoA) dan amplitudo sinyal pantulan. Penelitian ini mengusulkan perluasan dari pendekatan estimasi parameter yaitu amplitudo and phase estimation (APES) yang dinamakan forward-backward APES (FBAPES). Pendekatan ini memberikan perbaikan resolusi terhadap estimasi amplitudo dan DoA dari sinyal pantulan target radar yang dikomparasikan dengan estimator konvensional seperti least squares (LS). Formulasi dan evaluasi kinerja estimator yang diusulkan akan diuji berdasarkan berbagai faktor seperti besar radar cross section (RCS), resolusi sudut antar dua target, dan jumlah elemen antena di transmitter-receiver (Tx-Rx). Resolusi sudut deteksi yang diperoleh untuk estimator ini lebih baik dari estimator LS, sebagai contoh untuk M = N = 8 maka diperoleh resolusi sudut 3o sedangkan estimator LS sebesar 5,8o. There are two types of multi-antenna radar systems, i.e. the phased-array (PA) and the multiple-input multiple-output (MIMO). There are many parameters used to test the performance of the PA and the MIMO radars, one of which is parameter estimation related to the number of detection targets. Estimated parameters include the angle of arrival of the signal (direction of arrival, DoA) and the amplitude of the reflected signal. This study proposes an extension of the parameter estimation approach, namely amplitude and phase estimation (APES), which is called forward-backward APES (FBAPES). This approach provides improved resolution of the amplitude and DoA estimates of the reflected radar target signal compared to conventional estimators such as least squares (LS). The formulation and evaluation of the performance of the proposed estimator will be carried out based on various factors such as variations in radar cross section (RCS), angular resolution between two targets, and the number of antenna elements in the transmitter-receiver (Tx-Rx). The resolution of the detection angle obtained for this estimator is better than the LS estimator, for example for M = N = 8 then the angle resolution is 3o while the LS estimator is 5.8o.