Quantum Algorithms: A Survey of Applications and End-to-end Complexities

Alexander M. Dalzell; Sam McArdle; Mario Berta; Przemyslaw Bienias; Chi-Fang Chen; András Gilyén; Connor T. Hann; Michael J. Kastoryano; Emil T. Khabiboulline; Aleksander Kubica; Grant Salton; Samson Wang; Fernando G. S. L. Brandão

doi:10.1017/9781009639651

The 1994 discovery of Shor's quantum algorithm for integer factorization—an important practical problem in the area of cryptography—demonstrated quantum computing's potential for real-world impact. Since then, researchers have worked intensively to expand the list of practical problems that quantum algorithms can solve effectively. This book surveys the fruits of this effort, covering proposed quantum algorithms for concrete problems in many application areas, including quantum chemistry, optimization, finance, and machine learning. For each quantum algorithm considered, the book clearly states the problem being solved and the full computational complexity of the procedure, making sure to account for the contribution from all the underlying primitive ingredients. Separately, the book provides a detailed, independent summary of the most common algorithmic primitives. It has a modular, encyclopedic format to facilitate navigation of the material and to provide a quick reference for designers of quantum algorithms and quantum computing researchers.

‘This timely and forward-looking survey captures the state-of-the-art in quantum computing. Focusing on cutting-edge applications and recent advances in quantum primitives, it serves as an essential resource for understanding the rapidly evolving role of quantum algorithms in scientific discovery.’

Lin Lin - University of California, Berkeley

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Contents

Frontmatter
pp i-iv
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Contents
pp v-viii
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Preface
pp ix-xiv
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Part I - Areas of application
pp 1-3
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1 - Condensed matter physics
pp 4-28
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2 - Quantum chemistry
pp 29-50
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3 - Nuclear and particle physics
pp 51-61
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4 - Combinatorial optimization
pp 62-77
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5 - Continuous optimization
pp 78-97
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6 - Breaking cryptosystems
pp 98-110
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7 - Solving differential equations
pp 111-129
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8 - Finance
pp 130-147
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9 - Machine learning with classical data
pp 148-184
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Part II - Quantum algorithmic primitives
pp 185-187
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10 - Quantum linear algebra
pp 188-209
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11 - Hamiltonian simulation
pp 210-224
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12 - Quantum Fourier transform
pp 225-227
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13 - Quantum phase estimation
pp 228-234
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14 - Amplitude amplification and estimation
pp 235-242
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15 - Gibbs sampling
pp 243-249
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16 - Quantum adiabatic algorithm
pp 250-254
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17 - Loading classical data
pp 255-269
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18 - Quantum linear system solvers
pp 270-275
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19 - Quantum gradient estimation
pp 276-280
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20 - Variational quantum algorithms
pp 281-285
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21 - Quantum tomography
pp 286-290
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22 - Quantum interior point methods
pp 291-298
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23 - Multiplicative weights update method
pp 299-304
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24 - Approximate tensor network contraction
pp 305-310
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Part III - Fault-tolerant quantum computing
pp 311-313
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Quantum Algorithms

A Survey of Applications and End-to-end Complexities

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