Embedding Classical Variational Methods in Quantum Circuits

We introduce a novel quantum-classical variational method that extends the quantum devices capabilities to approximate ground states of interacting quantum systems. The proposed method enhances parameterized quantum circuit ansatzes implemented on quantum devices with classical variational functions, such as neural-network quantum states. The quantum hardware is used as a high-accuracy solver on the most correlated degrees of freedom, while the remaining contributions are treated on a classical device. Our approach is completely variational, providing a well-defined route to systematically improve the accuracy by increasing the number of variational parameters, and performs a global optimization of the two partitions at the same time. We demonstrate the effectiveness of the protocol on spin chains and small molecules and provide insights into its accuracy and computational cost. We prove that our method is able to converge to exact diagonalization results via the addition of classical degrees of freedom, while the quantum circuit is kept fixed in both depth and width.Comment: 11 pages, 6 figure

An efficient quantum algorithm for the time evolution of parameterized circuits

We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected - Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection of the exact time evolution onto the parameterized manifold. In the small time-step limit, this is equivalent to the McLachlan's variational principle. Our approach is efficient in the sense that it exhibits an optimal linear scaling with the total number of variational parameters. Furthermore, it is global in the sense that it uses the variational principle to optimize all parameters at once. The global nature of our approach then significantly extends the scope of existing efficient variational methods, that instead typically rely on the iterative optimization of a restricted subset of variational parameters. Through numerical experiments, we also show that our approach is particularly advantageous over existing global optimization algorithms based on the time-dependent variational principle that, due to a demanding quadratic scaling with parameter numbers, are unsuitable for large parameterized quantum circuits.Comment: 7+4 pages, 8 figures; Manuscript revised for publication. Method: added Section 2.2, Results: added Figure 6, Appendix: added Appendix E with Figure

Sequence of penalties method to study excited states using VQE

We propose an extension of the Variational Quantum Eigensolver (VQE) that leads to more accurate energy estimations and can be used to study excited states. The method is based on the introduction of a sequence of increasing penalties in the cost function. This approach does not require circuit modifications and thus can be applied with no additional depth cost. Through numerical simulations, we show that we are able to produce variational states with desired physical properties, such as total spin and charge. We assess its performance both on classical simulators and on currently available quantum devices, calculating the potential energy curves of small molecular systems in different physical configurations. Finally, we compare our method to the original VQE and to another extension, obtaining a better agreement with exact simulations for both energy and targeted physical quantities.Comment: 11 pages, 9 figures, accepted in IOP Quantum Science and Technolog

Adaptive projected variational quantum dynamics

We propose an adaptive quantum algorithm to prepare accurate variational time evolved wave functions. The method is based on the projected Variational Quantum Dynamics (pVQD) algorithm, that performs a global optimization with linear scaling in the number of variational parameters. Instead of fixing a variational ansatz at the beginning of the simulation, the circuit is grown systematically during the time evolution. Moreover, the adaptive step does not require auxiliary qubits and the gate search can be performed in parallel on different quantum devices. We apply the new algorithm, named Adaptive pVQD, to the simulation of driven spin models and fermionic systems, where it shows an advantage when compared to both Trotterized circuits and non-adaptive variational methods. Finally, we use the shallower circuits prepared using the Adaptive pVQD algorithm to obtain more accurate measurements of physical properties of quantum systems on hardware.Comment: 11 pages, 9 figure

Wild-type transthyretin cardiac amyloidosis is not rare in elderly subjects: the CATCH screening study

Background: Wild-type transthyretin cardiac amyloidosis (ATTRwt-CA) affects older adults and is currently considered as a rare disorder. Objective: We investigated for the first time the prevalence of ATTRwt-CA in elderly individuals from the general population. Methods: General practitioners from Pisa, Italy, proposed a screening for ATTRwt-CA to all their patients aged 65-90 years, until 1,000 accepted. The following red flags were searched: interventricular septal thickness ≥12 mm, any echocardiographic, ECG or clinical hallmark of CA, or high sensitivity-troponin T ≥14 ng/L. Individuals with at least one red flag (n=346) were asked to undergo the search for a monoclonal protein and bone scintigraphy, and 216 accepted. Results: Four patients received a non-invasive diagnosis of ATTRwt-CA. All complained of dyspnea on moderate effort. A woman and a man aged 79 and 85 years, respectively, showed an intense cardiac tracer uptake (grade 3), left ventricular (LV) wall thickening, grade 2 to 3 diastolic dysfunction, and N-terminal pro-B-type natriuretic peptide (NT-proBNP) >1,000 ng/L. Two other patients (a man aged 74 years and a woman aged 83 years) showed a grade 2 uptake, an increased LV septal thickness, but preserved diastolic function, and NT-proBNP <300 ng/L. The prevalence of ATTR-CA in subjects ≥65 years was calculated as 0.46% (i.e., 4 out of the 870 subjects completing the screening, namely 654 not meeting the criteria for Step 2 and 216 progressing to Step 2). Conclusions: ATTRwt-CA is uncommon in elderly subjects from the general population, but more frequent than expected for a rare disease

Microwave assisted sintering of Na-β’’-Al2O3 in single mode cavities: Insights in the use of 2450 MHz frequency and preliminary experiments at 5800 MHz

Microwave assisted sintering of Na-beta’’-Al2O3 in single mode cavities was accurately investigated. The use of single mode cavity allowed monitoring the parameters affecting the sintering process, like the forward power, together with the temperature evolution, making possible to perform energy efficiency and specific energy consumption evaluations. Experiments have been performed at the frequency of 2450 MHz, but preliminary results are also reported using the higher frequency of 5800 MHz, in order to investigate its effect on important parameters like the power density distribution as well as the penetration depth, which are responsible of the resulting heating rate and sintering outcome. Dielectric properties of the powders were measured as a function of temperature in order to partially predict and support the understanding of their experimental heating behaviour. Furthermore, dielectric properties provide the fundamental information needed for the multiphysics numerical simulation, performed with the aim to reach insights into the power density evolution in the specimen as sintering proceeds

Embedding Classical Variational Methods in Quantum Circuits

International audienceWe introduce a novel quantum-classical variational method that extends the quantum devices capabilities to approximate ground states of interacting quantum systems. The proposed method enhances parameterized quantum circuit ansatzes implemented on quantum devices with classical variational functions, such as neural-network quantum states. The quantum hardware is used as a high-accuracy solver on the most correlated degrees of freedom, while the remaining contributions are treated on a classical device. Our approach is completely variational, providing a well-defined route to systematically improve the accuracy by increasing the number of variational parameters, and performs a global optimization of the two partitions at the same time. We demonstrate the effectiveness of the protocol on spin chains and small molecules and provide insights into its accuracy and computational cost. We prove that our method is able to converge to exact diagonalization results via the addition of classical degrees of freedom, while the quantum circuit is kept fixed in both depth and width