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dc.contributor.advisorLukin, Mikhail
dc.contributor.advisorAspuru-Guzik, Alán
dc.contributor.authorKivlichan, Ian David
dc.date.accessioned2020-09-15T10:30:55Z
dash.embargo.terms2022-03-01
dc.date.created2020-03
dc.date.issued2020-01-08
dc.date.submitted2020
dc.identifier.citationKivlichan, Ian David. 2020. Faster quantum simulation of quantum chemistry with tailored algorithms and Hamiltonians. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.
dc.identifier.urihttps://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37365114*
dc.description.abstractWith quantum computers on the horizon, it is essential to understand what problems they can be used to solve. One potential application is simulating quantum systems, in particular, systems with many interacting electrons. However, there is a disparity between the computational resources required to study these problems and the capabilities of modern experimental quantum devices. In this thesis, we make progress toward closing this gap by reducing the cost of quantum simulation of quantum chemistry on a number of fronts. In the first half, we develop three improved quantum simulation algorithms by approximating time evolution under the Hamiltonian using a truncated Taylor series rather than the Trotter-Suzuki decomposition. We do this first for the molecular electronic structure Hamiltonian in two representations, obtaining asymptotic improvements in terms of both the number of orbitals and the required precision. We also apply the truncated Taylor series paradigm to quantum simulation in real space, where we consider simulation of general wave functions discretized on a uniform grid. In the second half, by working with Hamiltonians tailored specifically to quantum algorithms, we demonstrate that Trotter steps of the electronic structure Hamiltonian can be simulated in exactly N depth and with only linear connectivity, where N is the number of spin-orbitals. This resolves the problem of non-locality in fermion-to-qubit mappings, and has wide-ranging applications for variational and phase estimation-based quantum simulation of quantum chemistry. We further study this algorithm on an error-corrected quantum computer using the surface code. Benchmarking it alongside other product formula approaches, we show that quantum simulation of scientifically important instances of the electronic structure problem that are classically intractable can be performed with only a few hundred thousand physical qubits and fewer than one billion costly fault-tolerant gates. Finally, we study the effect of using randomized Hamiltonians in iterative phase estimation, and how this allows us to reduce the costs of simulation as well as to exploit knowledge of the ground state in how we design our simulation algorithm.
dc.description.sponsorshipPhysics
dc.format.mimetypeapplication/pdf
dc.language.isoen
dash.licenseLAA
dc.subjectphysics
dc.subjectquantum computing
dc.subjectquantum simulation
dc.titleFaster quantum simulation of quantum chemistry with tailored algorithms and Hamiltonians
dc.typeThesis or Dissertation
dash.depositing.authorKivlichan, Ian David
dash.embargo.until2022-03-01
dc.date.available2020-09-15T10:30:55Z
thesis.degree.date2020
thesis.degree.grantorGraduate School of Arts & Sciences
thesis.degree.grantorGraduate School of Arts & Sciences
thesis.degree.levelDoctoral
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
thesis.degree.nameDoctor of Philosophy
dc.contributor.committeeMemberKaxiras, Efthimios
dc.type.materialtext
thesis.degree.departmentPhysics
thesis.degree.departmentPhysics
dash.identifier.vireo
dash.author.emailian.kivlichan@gmail.com


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