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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

A Quantum Algorithm to Simulate Open Quantum Systems

Given the advent of quantum algorithms for a wide array of problems in linear algebra and machine learning, it is important to develop general methods for the simulation of arbitrary (ie non-unitary) operators on quantum hardware. In this talk, we present a novel quantum algorithm based on the quantum singular value transformation (QSVT) to apply an arbitrary operator K to some input state and subsequently estimate the expectation value of some observable. Our construction then immediately yields a route to estimating observables of states undergoing open quantum dynamics, whose effect is captured by a set of non-unitary Kraus operators. Our algorithm succeeds deterministically given the Sz-Nagy dilation, and we provide details on the algorithm's query and gate complexity, numerical verification, and comparisons with prior methods.

Quantum computing↗
NASA NTRS1999

Quantum Algorithms

This thesis describes several new quantum algorithms. These include a polynomial time algorithm that uses a quantum fast Fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases for which all know classical algorithms require exponential time.

Quantum Algorithms polynomial time algorithm Hamil↗
NASA NTRSDate not supplied

Planning for Compilation of a Quantum Algorithm for Graph Coloring

Recently, the problem of compiling general quantum algorithms for implementation on near-term quantum processors has been introduced to the AI community. Previous work demonstrated that temporal planning is an attractive approach for part of this compilation task, specifically, the routing of circuits that implement the Quantum Alternating Operator Ansatz (QAOA) applied to theMaxCut problem on a quantum processor architecture. In this paper, we extend the earlier work to route circuits that implement QAOAfor Graph Coloring problems. QAOA for coloring requires execution of more, and more complex, operations on the chip, which makes routing a more challenging problem. We evaluate the approach on state-of-the-art hardware architectures from leading quantum computing companies. Additionally, we investigate applying the planning approach to qubit initialization as well as routing. Our empirical evaluation shows that temporal planning compares well to reasonable analytic upper bounds [20], and that solving qubit initialization with a classical planner generally helps temporal planners in finding shorter-makespan compilations for QAOA for Graph Coloring.These advances suggest that temporal planning can be an effective approach for more complex quantum computing algorithms and architectures.

Minh Do↗
NASA NTRS1999

Fast Quantum Algorithms for Numerical Integrals and Stochastic Processes

We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.

quantum algorithms numerical integrals↗
NASA NTRS1999

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

Williams Colin P.↗
NASA NTRSDate not supplied

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↗
NASA NTRS2017

A Circuit-Based Quantum Algorithm Driven by Transverse Fields for Grover's Problem

We designed a quantum search algorithm, giving the same quadratic speedup achieved by Grover's original algorithm; we replace Grover's diffusion operator (hard to implement) with a product diffusion operator generated by transverse fields (easy to implement). In our algorithm, the problem Hamiltonian (oracle) and the transverse fields are applied to the system alternatively. We construct such a sequence that the corresponding unitary generates a closed transition between the initial state (even superposition of all states) and a modified target state, which has a high degree of overlap with the original target state.

quantum computing↗
NASA NTRS2013

Complexity of the Quantum Adiabatic Algorithm

The Quantum Adiabatic Algorithm (QAA) has been proposed as a mechanism for efficiently solving optimization problems on a quantum computer. Since adiabatic computation is analog in nature and does not require the design and use of quantum gates, it can be thought of as a simpler and perhaps more profound method for performing quantum computations that might also be easier to implement experimentally. While these features have generated substantial research in QAA, to date there is still a lack of solid evidence that the algorithm can outperform classical optimization algorithms.

Hen, Itay↗
NASA NTRSDate not supplied

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↗
NASA NTRSDate not supplied

Quantum Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

We present two algorithms in the Quantum CONGEST- CLIQUE model of distributed computation that succeed with high probability; one for producing an approximately optimal Steiner Tree, and one for producing an exact directed minimum spanning tree, each of which uses O ̃(n1/4) rounds of communication and O ̃(n9/4) messages, achieving a lower asymptotic round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. Additionally, we characterize the constants and logarithmic factors involved in our algorithms, as well as related classical algorithms, revealing that advances are needed to render both practical.

quantum computing↗