Benchmarking the Operation of Quantum Heuristics and Ising Machines: Scoring Parameter Setting Strategies on Real World Optimization Applications
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David E Bernal Neira↗
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Results for “quantum optimization”
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Long Wavelength Quantum Well Infrared Photodetector (QWIP) Research at Jet Propulsion Laboratory
One of the simplest device realizations of the classic particle-in-the-box problem of basic quantum mechanics is the Quantum Well Infrared Photodetector (QWIP). Optimization of the detector design and material growth and processing has culminated in the realization of a 15 ??utoff 128x128 focal plane array camera and a camera with large (256x256 pixel) focal plane array of QWIPs which can see at 8.5 ??holding forth great promise for a variety of applications in the 6-25 ??avelength range. This paper discusses the physics of the QWIP and QWIP technology development at Jet Propulsion Laboratory
QWIP↗
Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
Smelyanskiy, Vadius↗
Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
Smelyanskiy, V. N.↗
Uncertainty relations as Hilbert space geometry
Precision measurements involve the accurate determination of parameters through repeated measurements of identically prepared experimental setups. For many parameters there is a 'natural' choice for the quantum observable which is expected to give optimal information; and from this observable one can construct an Heinsenberg uncertainty principle (HUP) bound on the precision attainable for the parameter. However, the classical statistics of multiple sampling directly gives us tools to construct bounds for the precision available for the parameters of interest (even when no obvious natural quantum observable exists, such as for phase, or time); it is found that these direct bounds are more restrictive than those of the HUP. The implication is that the natural quantum observables typically do not encode the optimal information (even for observables such as position, and momentum); we show how this can be understood simply in terms of the Hilbert space geometry. Another striking feature of these bounds to parameter uncertainty is that for a large enough number of repetitions of the measurements all V quantum states are 'minimum uncertainty' states - not just Gaussian wave-packets. Thus, these bounds tell us what precision is achievable as well as merely what is allowed.
Braunstein, Samuel L.↗
Quantum-mechanical communication theory
Quantum mechanical communication theory of optimal receivers, using statistical detection and estimation theory
Gordon, J. P.↗
Quantum Image Denoising: A Framework via Boltzmann Machines, QUBO, and Quantum Annealing
We investigate a framework for binary image denoising via restricted Boltzmann machines (RBMs) that introduces a denoising objective in quadratic unconstrained binary optimization (QUBO) form and is well-suited for quantum annealing. The denoising objective is attained by balancing the distribution learned by a trained RBM with a penalty term for derivations from the noisy image. We derive the statistically optimal choice of the penalty parameter assuming the target distribution has been well-approximated, and further suggest an empirically supported modification to make the method robust to that idealistic assumption. We also show under additional assumptions that the denoised images attained by our method are, in expectation, strictly closer to the noise-free images than the noisy images are. While we frame the model as an image denoising model, it can be applied to any binary data. As the QUBO formulation is well-suited for implementation on quantum annealers, we test the model on a D-Wave Advantage machine, and also test on data too large for current quantum annealers by approximating QUBO solutions through classical heuristics.
restricted Boltzmann machine↗
QuAIL Tools for Benchmarking, Analysis and Quantum Algorithm Development
HybridQ and PySA are open-source tools developed by NASA to support benchmarking, analysis and quantum algorithm development in areas such as simulation, optimization and machine learning. These tools leverage classical hardware acceleration via high-performance computing CPU and GPU architectures and support high-performance computing. HybridQ is a highly extensible platform designed to provide a common framework to integrate multiple state-of-the-art techniques to simulate large scale quantum circuits. PySA is an extensible platform to optimize a classical cost function. We provide an outline of each of these open-source tools and highlight projects using each of these tools in contexts of simulation, optimization and machine learning.
Quantum Computing↗
A NASA Perspective on Quantum Computing: Algorithmic Opportunities and Challenges
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can provide an advantage, and if so how to design quantum algorithms that realize such advantages. Today, classical heuristics are used to solve many of the most challenging computational problems arising in the practical world, algorithms that have been shown to be effective empirically but have not been mathematically proven to outperform other approaches. With the advent of quantum advantage, the ability of current quantum hardware to do certain computations beyond the ability of even that largest supercomputers, we have an unprecedented opportunity to explore heuristic quantum algorithms. The next few years will be exciting as empirical testing of quantum heuristic algorithms becomes more and more feasible. The talk will begin overview of the NASA QuAIL team’s ongoing quantum computing investigations, and then focus on both near-term and longer term algorithms for optimization, including distributed algorithms.
quantum computing↗
Phase space localization for anti-de Sitter quantum mechanics and its zero curvature limit
Using techniques of geometric quantization and SO(sub 0)(3,2)-coherent states, a notion of optimal localization on phase space is defined for the quantum theory of a massive and spinning particle in anti-de Sitter space time. It is shown that this notion disappears in the zero curvature limit, providing one with a concrete example of the regularizing character of the constant (nonzero) curvature of the anti-de Sitter space time. As a byproduct a geometric characterization of masslessness is obtained.
Elgradechi, Amine M.↗
Self-consistent calculations and design considerations for a GaAs nipi doping superlattice solar cell
The authors present design constraints which show that a previously proposed GaAs nipi doping superlattice solar cell structure would not work as an efficient space solar cell. A structure based on the CLEFT process, which shows promise of being an efficient cell with very high radiation tolerance, is proposed. In order to test theoretically its viability and to optimize its design, self-consistent quantum mechanical calculations were made for a number of thicknesses of the n, i, and p layers and the dopings in the n and p layers. These results show that: 1) an i layer is not necessary; in fact, its presence makes it difficult to satisfy one of the key constraints; 2) a near-optimum design with 750-A thick n and p layers with dopings of 2.5E18/cu cm and a selective contact separation of 20 microns would yield both high efficiency and very high radiation tolerance.
Clark, Ralph O.↗
Generating Far-Infrared Radiation By Two-Wave Mixing
Far-infrared radiation 1 to 6 GHz generated by two-wave mixing in asymmetrically grown GaAs/AlxGa1-xAs multiple-quantum-well devices. Two near-infrared semiconductor diode lasers phase-locked. Outputs amplified, then combined in semiconductor nonlinear multiple-quantum-well planar waveguide. Necessary to optimize design of device with respect to three factors: high degree of confinement of electromagnetic field in nonlinear medium to maximize power density, phase matching to extend length of zone of interaction between laser beams in non-linear medium, and nonlinear susceptibility. Devices used as tunable local oscillators in heterodyne-detection radiometers.
Borenstain, Shmuel↗
Photodetector Arrays for Multicolor Visible/Infrared Imaging
Monolithic focal-plane arrays of photodetectors capable of imaging the same scenes simultaneously in multiple wavelength bands in the visible and infrared spectral regions have been proposed. In prior visible/infrared imaging systems, it has been standard practice to use separate optical trains to form images in visible and infrared wavelength bands on separate visibleand infrared-photodetector arrays. Because the proposal would enable the detection of images in multiple wavelength bands on the same focal plane, the proposal would make it unnecessary to use multiple optical trains. Hence, multispectral imaging systems could be made more compact and the difficulties of aligning multiple optical trains would be eliminated. Each pixel in an array according to the proposal would contain stacks of several photodetectors. The proposal is a logical extension of prior concepts of arrays of stacked photodetectors for imaging in two or three wavelength bands. For example, such an array was described in Three-Color Focal-Plane Array of Infrared QWIPs (NPO-20683), NASA Tech Briefs, Vol. 24, No. 5 (May 2000), page 26a. In one proposed design, (see figure), each pixel would be divided into four subpixels, one being dedicated to a visible- and-near-infrared (V) band, one to a combination of the V band and a verylong- wavelength infrared (VLWIR) band, one to a combination of the V band and a long-wavelength infrared (LWIR) band, and one to a combination of the V band and a medium-wavelength infrared (MWIR) band. For this purpose, each subpixel would include a GaAs-based positive/intrinsic/negative (PIN) photodiode for detection in the V band stacked with three quantum-well infrared photodetectors (QWIPs), each optimized for one of the aforementioned infrared bands. The stacks of photodetectors in all the subpixels would be identical except for the electrical connections, which would be configured to activate the various wavelengthband combinations.
Gunapala, Sarath↗
Computational Role of Tunneling in a Programmable Quantum Annealer
Quantum tunneling is a phenomenon in which a quantum state tunnels through energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We developed a theoretical model based on a NIBA Quantum Master Equation to describe the multi-qubit dissipative cotunneling effects under the complex noise characteristics of such quantum devices.We start by considering a computational primitive, the simplest non-convex optimization problem consisting of just one global and one local minimum. The quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. In our study the non-convex potentials are realized by frustrated networks of qubit clusters with strong intra-cluster coupling. We show that the collective effect of the quantum environment is suppressed in the critical phase during the evolution where quantum tunneling decides the right path to solution. In a later stage dissipation facilitates the multiqubit cotunneling leading to the solution state. The predictions of the model accurately describe the experimental data from the D-WaveII quantum annealer at NASA Ames. In our computational primitive the temperature dependence of the probability of success in the quantum model is opposite to that of the classical paths with thermal hopping. Specially, we provide an analysis of an optimization problem with sixteen qubits,demonstrating eight qubit cotunneling that increases success probabilities. Furthermore, we report results for larger problems with up to 200 qubits that contain the primitive as subproblems.
hard problems↗
The quantum efficiency of HgCdTe photodiodes in relation to the direction of illumination and to their geometry
A theoretical study of the effect of the direction of the incident light on the quantum efficiency of homogeneous HgCdTe photodiodes suitable for sensing infrared radiation in the 8-12 microns atmospheric window is presented. The probability of an excess minority carrier to reach the junction is derived as a function of its distance from the edge of the depletion region. Accordingly, the quantum efficiency of photodiodes is presented for two geometries. In the first, the light is introduced directly to the area in which it is absorbed (opaque region), while in the second, the light passes through a transparent region before it reaches the opaque region. Finally, the performance of the two types of diodes is analyzed with the objective of finding the optimal width of the absorption area. The quantum efficiency depends strongly on the way in which the light is introduced. The structure in which the radiation is absorbed following its crossing the transparent region is associated with both higher quantum efficiency and homogeneity. In addition, for absorption region widths higher than a certain minimum, the quantum efficiency in this case is insensitive to the width of the absorption region.
Rosenfeld, D.↗
Highly Sensitive Quantum Well Infrared Photodetectors
A fundametally new method for light coupling in quantum well infrared photodetectors that provides a 10-fold improvement over an optimized grating coupler is presented.
Quantum well detectors↗
QSPIN: A High Level Java API for Quantum Computing Experimentation
QSPIN is a high level Java language API for experimentation in QC models used in the calculation of Ising spin glass ground states and related quadratic unconstrained binary optimization (QUBO) problems. The Java API is intended to facilitate research in advanced QC algorithms such as hybrid quantum-classical solvers, automatic selection of constraint and optimization parameters, and techniques for the correction and mitigation of model and solution errors. QSPIN includes high level solver objects tailored to the D-Wave quantum annealing architecture that implement hybrid quantum-classical algorithms [Booth et al.] for solving large problems on small quantum devices, elimination of variables via roof duality, and classical computing optimization methods such as GPU accelerated simulated annealing and tabu search for comparison. A test suite of documented NP-complete applications ranging from graph coloring, covering, and partitioning to integer programming and scheduling are provided to demonstrate current capabilities.
Quantu↗
Solid state photomultiplier for astronomy, phase 2
Epitaxial layers with varying donor concentration profiles were grown on silicon substrate wafers using chemical vapor deposition (CVD) techniques, and solid state photomultiplier (SSPM) devices were fabricated from the wafers. Representative detectors were tested in a low background photon flux, low temperature environment to determine the device characteristics for comparison to NASA goals for astronomical applications. The SSPM temperatures varied between 6 and 11 K with background fluxes in the range from less than 5 x 10 to the 6th power to 10 to the 13th power photons/square cm per second at wavelengths of 3.2 and 20 cm. Measured parameters included quantum efficiency, dark count rate and bias current. Temperature for optimal performance is 10 K, the highest ever obtained for SSPMs. The devices exhibit a combination of the lowest dark current and highest quantum efficiency yet achieved. Experimental data were reduced, analyzed and used to generate recommendations for future studies. The background and present status of the microscopic theory of SSPM operation were reviewed and summarized. Present emphasis is on modeling of the avalanche process which is the basis for SSPM operation. Approaches to the solution of the Boltzmann transport equation are described and the treatment of electron scattering mechanisms is presented. The microscopic single-electron transport theory is ready to be implemented for large-scale computations.
Besser, P. J.↗