Simulating Hamiltonian dynamics with a truncated Taylor series.

By Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, Rolando D. Somma. Physical Review Letters, 2014

763 citations recorded by the source corpus.

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/2aed708936086320dc02e463a4b1790060196771

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Citations in the corpus

Toward the first quantum simulation with quantum speedup (2017, methodology): “TS (15) O ( t log 2(t/ ) log log(t/ ) ) O ( n3 log 2 n log log n )”
Challenges and opportunities in quantum machine learning (2022, background): “[130] Dominic W Berry, Andrew M Childs, Richard Cleve, Robin Kothari, and Rolando D Somma, “Simulating hamiltonian dynamics with a truncated taylor series,” Physical Review Letters 114, 090502 (2015).”
Practical quantum advantage in quantum simulation (2022, background): “…that provide more efficient convergence with the error tolerance, which can be implemented on fault-tolerant digital quantum computers 63–66 , giving fault-tolerant devices a clear advantage for the high-accuracy calculations needed, for example, for many applications in quantum…”
Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics (2018, methodology): “The methodology we describe is a distilled version of the results of a series of works on quantum algorithms [6, 11, 16, 17, 30, 41].”
Variational quantum algorithms for nonlinear problems (2019, background): “In the context of PDEs, it has been realized that quantum computers can solve the Schrödinger equation faster than conventional computers [10–12], and these ideas have been generalized recently to other linear PDEs [13–18].”
Optimal Hamiltonian Simulation by Quantum Signal Processing. (2016, background): “Two key properties distinguish quantum signal processing from routines that can effect similar transformations, such as quantum phase estimation [23] or linearcombination-of-unitaries [16, 18, 19] which require a large number of ancilla.”
Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision (2015, methodology): “Our technique for implementing linear combinations of unitary operations arises from previous work on Hamiltonian simulation [BCC + 14, Kot14, BCC + 15, BCK15] (see also [SOG + 02, CW12] for previous related approaches).”
Diagnosing Barren Plateaus with Tools from Quantum Optimal Control (2021, background): “[3] Dominic W Berry, Andrew M Childs, Richard Cleve, Robin Kothari, and Rolando D Somma.”
Hamiltonian Simulation by Qubitization (2016, background): “o be qubitized, thus incurring a factor 2 additional cost from quering U^ and U^yeach over the asymptotic limit of 2 queries per unit of simulation time in Fig.1(Left). Similarly, the BCCKS algorithm [9] incurs a factor 3 additional cost from querying U^ twice and U^yin their use of oblivious amplit”
Hamiltonian Simulation with Nearly Optimal Dependence on all Parameters (2015, methodology): “…simulation, in terms of query complexity (i.e., the number of queries made to the oracles) and number of 2-qubit gates used, are one based on a Szegedy quantum walk [11, 13] and another based on simulating an unconventional model of query complexity called the fractional-query model [15].”
Quantum Algorithm for Linear Differential Equations with Exponentially Improved Dependence on Precision (2017, background): “More recent work has streamlined these algorithms and improved their dependence on other parameters [6, 7, 15, 8, 14, 16].”
Elucidating reaction mechanisms on quantum computers (2016, background): “[47] Dominic W Berry, Andrew M Childs, Richard Cleve, Robin Kothari, and Rolando D Somma, “Simulating hamiltonian dynamics with a truncated taylor series,” Physical review letters 114, 090502 (2015).”