In recent years, there have been significant advancements in various aspects of quantum computing. However, despite this substantial progress, the availability of fault-tolerant quantum computers is still out of reach and may remain so for decades. Therefore, a key challenge is to leverage current NISQ devices to achieve a quantum advantage effectively. In this context, the Quantum Approximate Optimization Algorithm (QAOA) was proposed to potentially demonstrate computational advantages in combinatorial optimization problems using NISQ computers. Meanwhile, quantum error mitigation (QEM) techniques have been developed to address errors, with their effectiveness validated in practical problems involving more than 100 qubits. Therefore, in this paper, we optimize QAOA circuits and apply various error mitigation methods, such as dynamic decoupling and Pauli-twirling, to scale problem sizes on IBM quantum processors. Additionally, we discuss optimal implementation strategies for scalable QAOA. We test our implementations on Max-Cut problems and compare our results with previous works.
We report an experimental demonstration of x-ray Ghost Imaging (GI) to observe the internal structure of a cardamom seed. To the best of our knowledge, this is the first use of GI to see the internal structure of biological samples. GI has been successfully demonstrated at visible and infrared wavelengths as a tool to perform precise imaging. At x-ray energies GI has a further potential to reach this goal with the additional advantage of reducing disruptive radiation doses to biological samples. The experiment was performed using 9.6keV x-rays at the 11-ID Coherent Hard X-ray Scattering (CHX) beamline of the National Synchrotron Light Source II (NSLS-II) facility at Brookhaven National Laboratory (BNL). This imaging technique has application potential in non-destructive examination of sensitive materials in the industrial and commercial sectors.
In recent years, significant progress has been made in building quantum computers by several companies. Despite the progress, these noisy intermediate-scale quantum (NISQ) computers still suffer from several noises and errors such as measurement errors, multi-qubit gate errors, and worse, short decoherence times. Though quantum computer vendors are releasing better quantum computers in terms of Quantum Volume, the quantum device still remains far from quantum supremacy in practical problems. The Quantum Approximate Optimization Algorithm (QAOA) was suggested to potentially demonstrate a computational advantage in combinatorial optimization problems on NISQ computers. In this paper, we optimize the QAOA circuits and to scale the problem size on IBM quantum processors. In addition, we study the effect of the length of the QAOA ansatz on IBM quantum processors and discuss optimal implementation methods for scalable QAOA. We test our implementations on the MaxCut problems.
A variant of QAE algorithm by Suzuki et al. called maximum likelihood amplitude estimation (MLAE) achieves the amplitude estimation by varying depths of Grover operators and post-processing for maximum likelihood estimation without the additional controlled operations and QFT. However, MLAE requires running multiple circuits of different depths of Grover operators. On the other hand, quantum multi-programming (QMP) is a computing method that executes multiple quantum circuits concurrently on a quantum computer. The quantum circuits executed concurrently can be different and even have different circuit depths. The main motivation of the QMP is that the number of qubits of NISQ computers is much greater than their quantum volume. In this work, using QMP in conjunction with MLAE makes it possible to run MLAE using a single circuit, thus requiring sampling much fewer times. We validate this algorithm for a numerical integration problem using NVIDIA’s open-source platform CUDA Quantum (simulator), Qiskit (simulator) and Quantinuum H2 device.
The quantum annealing devices, which encode the solution to a computational problem in the ground state of a quantum Hamiltonian, are implemented in D-Wave systems with more than 2,000 qubits. However, quantum annealing can solve only a classical combinatorial optimization problem such as an Ising model, or equivalently, a quadratic unconstrained binary optimization (QUBO) problem. In this paper, we formulate the QUBO model to solve elliptic problems with Dirichlet and Neumann boundary conditions using the finite element method. In this formulation, we develop the objective function of quadratic binary variables represented by qubits and the system finds the binary string combination minimizing the objective function globally. Based on the QUBO formulation, we introduce an iterative algorithm to solve the elliptic problems. We discuss the validation of the modeling on the D-Wave quantum annealing system.
Growing interest in quantum machine learning has resulted into very innovative algorithms and vigorous studies that demonstrate their power. These studies, although very useful, are often designed for fault-tolerant quantum computers that are far from reality of today's noise-prone quantum computers. While companies such as IBM have ushered in a new era of quantum computing by allowing public access to their quantum computers, quantum noise as well as decoherence are daunting obstacles that not only degrade the performance of quantum algorithms, but also make them infeasible for running on current-era quantum processors. We address the feasibility of a quantum machine learning algorithm on IBM quantum processors to shed light on their efficacy and weaknesses to design noise-aware algorithms that work around these limitations. We compare and discuss the results by implementing a quantum convolutional filter on a real quantum processor as well as a simulator.
Radiation sources from Langmuir waves has been a topic of interest for their relevance to experimental approaches in plasma laboratories as well as for estimating physical models to explain cosmic radio bursts. Since the mechanism for converting energy from electrostatic Langmuir waves to electromagnetic waves is complex, diverse scenarios of such energy conversion have been studied, e.g. mode conversion, antenna radiation, nonlinear scattering, etc. Previously, we introduced a novel perspective of plasma dipole oscillation (PDO) which generates strong radiation bursts at the plasma frequency and high harmonics. In this paper, we report our discovery of radiation that result from electron-laser beam driven Langmuir waves and their interactions. In 2-D PIC simulations, we have observed that obliquely colliding Langmuir waves or even a single Langmuir wave generate localized radiation sources at the plasma frequency and high harmonics. These mechanisms differ from conventional two-plasmon mergers, where only the second harmonic of the plasma frequency is dominant: a strong radiation is observed even at the fundamental harmonic. In addition, from 3-D PIC simulations of electron laser beam driven plasma oscillators in magnetized plasma, the radiation from a local plasma oscillator, i.e. PDO, is found to be robust with diverse spectral peaks at the X-mode and the upper-hybrid mode. Nonlinear theory demonstrates that the relative strength of the harmonics of the plasma frequency depends on the shape of the PDO. The studies imply that the PDO has a more complicated internal structure than the simple model of a solid charge. We discuss the potential of the PDO generated from electron-beam driven plasmas or laser-driven plasmas as a radiation source and its relevance to cosmic radio bursts.
Many quantum computing algorithms are being developed with the advent of quantum computers. Solving linear systems is one of the most fundamental problems in almost all of science and engineering. HHL algorithm, a monumental quantum algorithm for solving linear systems on the gate model quantum computers, was invented and several advanced variations have been developed. However, HHL-based algorithms have a lot of limitations in spite of their importance. We address solving linear systems on a D-Wave quantum annealing device. To formulate a quadratic unconstrained binary optimization (QUBO) model for a linear system solving problem, we make use of a linear least-square problem with binary representation of the solution. We validate this QUBO model on the D-Wave system and discuss the results.
Laser-plasma interactions have many theoretical and technological applications. One is the use of coherently accelerated electrons to provide novel sources of THz radiation. Our research focuses on simulating the cross/self-interactions between two high intensity, ultra-short, counter propagating and detuned laser pulses and an initial neutral target for controlled ionization. Unlike our previous studies of laser-matter interaction over preformed plasma, we explore the injection and collision of laser pulses to induce background plasma driven by the self-guided laser wakefield mechanism, which is then used to perturb the plasma resulting in induced dipole oscillations leading to transverse radiation. Inducing a cylindrical spatial plasma column within the laser beam radius regime provides a stable, spatially localized plasma channel. The emitted radiation from the plasma dipole oscillation (PDO) will not be affected by surrounding plasma absorption, resulting in effective radiation distribution. Results include 3D EM-PIC simulations and a comparison of the self- ionizing plasma against the preformed plasma to assess the efficiency of the mechanisms.
Since the publication of the Quantum Amplitude Estimation (QAE) algorithm by Brassard et al., 2002, several variations have been proposed, such as Aaronson et al., 2019, Grinko et al., 2019, and Suzuki et al., 2020. The main difference between the original and the variants is the exclusion of Quantum Phase Estimation (QPE) by the latter. This difference is notable given that QPE is the key component of original QAE, but is composed of many operations considered expensive for the current NISQ era devices. We compare two recently proposed variants (Grinko et al., 2019 and Suzuki et al., 2020) by implementing them on the IBM Quantum device using Qiskit, an open source framework for quantum computing. We analyze and discuss advantages of each algorithm from the point of view of their implementation and performance on a quantum computer.
This paper addresses the practical aspects of quantum algorithms used in numerical integration, specifically their implementation on Noisy Intermediate-Scale Quantum (NISQ) devices. Quantum algorithms for numerical integration utilize Quantum Amplitude Estimation (QAE) (Brassard et al., 2002) in conjunction with Grover’s algorithm. However, QAE is daunting to implement on NISQ devices since it typically relies on Quantum Phase Estimation (QPE), which requires many ancilla qubits and controlled operations. To mitigate these challenges, a recently published QAE algorithm (Suzuki et al., 2020), which does not rely on QPE, requires a much smaller number of controlled operations and does not require ancilla qubits. We implement this new algorithm for numerical integration on IBM quantum devices using Qiskit and optimize the circuit on each target device. We discuss the application of this algorithm on two qubits and its scalability to more than two qubits on NISQ devices.
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