Quantum Algorithms and Circuits for Scientific Computing

Bhaskar, Mihir K.; Hadfield, Stuart; Papageorgiou, Anargyros; Petras, Iasonas

doi:10.48550/arxiv.1511.08253

Cited by 7 publications

(10 citation statements)

References 21 publications

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“…One can use the circuit to compute the n-bit reciprocal 1/x by setting a = 2 n and b = x in a 2n-bit version of the circuit in order to match the precision of our designs. We also manually created a design following the Newton-Raphson method, which is similar but more accurate to the designs proposed in [12] and [13] and we refer to it as QNEWTON. In contrast to the NEWTON design that follows the standard algorithm, we adjusted the algorithm as follows to reduce the number of lines needed.…”

Section: Methodsmentioning

confidence: 99%

“…Most notably, it is essential for quantum linear systems algorithms [10], [11]. Recent work has shown that the space requirements imposed by having to implement the reciprocal reversibly can be prohibitive for implementations on a small quantum computer [12], [13]. The implementation of the reciprocal is used as an example to illustrate the proposed design flows.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Design automation and design space exploration for quantum computers

Soeken

Roetteler

Wiebe

et al. 2017

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2017

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Abstract-A major hurdle to the deployment of quantum linear systems algorithms and recent quantum simulation algorithms lies in the difficulty to find inexpensive reversible circuits for arithmetic using existing hand coded methods. Motivated by recent advances in reversible logic synthesis, we synthesize arithmetic circuits using classical design automation flows and tools. The combination of classical and reversible logic synthesis enables the automatic design of large components in reversible logic starting from well-known hardware description languages such as Verilog. As a prototype example for our approach we automatically generate high quality networks for the reciprocal 1/x, which is necessary for quantum linear systems algorithms.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design automation and design space exploration for quantum computers

Soeken

Roetteler

Wiebe

et al. 2017

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2017

View full text Add to dashboard Cite

show abstract

“…If we are interested in properties of g(X), as discussed in the previous section, then, depending on g, we can use basic arithmetic operations to construct the operator G. Numerous quantum algorithms exist for arithmetic operations [19][20][21][22][23] as well as tools to translate classical logic into quantum circuits [24,25]. However, since the latter are not necessarily efficient, the development of new and improved algorithms is ongoing research.…”

Section: Quantum Circuitsmentioning

confidence: 99%

Quantum risk analysis

2019

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We present a quantum algorithm that analyzes risk more efficiently than Monte Carlo simulations traditionally used on classical computers. We employ quantum amplitude estimation to evaluate risk measures such as Value at Risk and Conditional Value at Risk on a gate-based quantum computer. Additionally, we show how to implement this algorithm and how to trade off the convergence rate of the algorithm and the circuit depth. The shortest possible circuit depth -growing polynomially in the number of qubits representing the uncertainty -leads to a convergence rate of O(M −2/3 ). This is already faster than classical Monte Carlo simulations which converge at a rate of O(M −1/2 ). If we allow the circuit depth to grow faster, but still polynomially, the convergence rate quickly approaches the optimum of O(M −1 ). Thus, for slowly increasing circuit depths our algorithm provides a near quadratic speed-up compared to Monte Carlo methods. We demonstrate our algorithm using two toy models. In the first model we use real hardware, such as the IBM Q Experience, to measure the financial risk in a Treasury-bill (T-bill) faced by a possible interest rate increase. In the second model, we simulate our algorithm to illustrate how a quantum computer can determine financial risk for a two-asset portfolio made up of Government debt with different maturity dates. Both models confirm the improved convergence rate over Monte Carlo methods. Using simulations, we also evaluate the impact of cross-talk and energy relaxation errors.I.

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“…Note that these distances are pre-calculated on conventional computers and provided as a matrix to the circuit to decrease the complexity of our circuits. Note that Bhaskar et al [24] have reported the cost of calculating the reciprocals to be O(log 2 (p)) × O(m + p), where m is the total number of qubits dedicated to representing a number (both decimal and integer part) and p is the number of qubits to represent the significant digits after the decimal points. m is discussed in more detail later in this section.…”

Section: A Protein Structures and Energy Tablesmentioning

confidence: 99%

Gate-based Quantum Computing for Protein Design

Khatami¹,

Mendes²,

Wiebe³

et al. 2022

Preprint

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Protein design is a technique to engineer proteins by modifying their sequence to obtain novel functionalities. In this method, amino acids in the sequence are permutated to find the low energy states satisfying the configuration. However, exploring all possible combinations of amino acids is generally impossible to achieve on conventional computers due to the exponential growth of possibilities with the number of designable sites. Thus, sampling methods are currently used as a conventional approach to address the protein design problems. Recently, quantum computation methods have shown the potential to solve similar types of problems. In the present work, we use the general idea of Grover's algorithm, a pure quantum computation method, to design circuits at the gate-based level and address the protein design problem. In our quantum algorithms, we use custom pair-wise energy tables consisting of eight different amino acids. Also, the distance reciprocals between designable sites are included in calculating energies in the circuits. Due to the noisy state of current quantum computers, we mainly use quantum computer simulators for this study. However, a very simple version of our circuits is implemented on real quantum devices to examine their capabilities to run these algorithms. Our results show that using O( √ N ) iterations, the circuits find the correct results among all N possibilities, providing the expected quadratic speed up of Grover's algorithm over classical methods.

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Quantum Algorithms and Circuits for Scientific Computing

Cited by 7 publications

References 21 publications

Design automation and design space exploration for quantum computers

Design automation and design space exploration for quantum computers

Quantum risk analysis

Gate-based Quantum Computing for Protein Design

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