Michael Kaicher
Saarland University
Wave functionAlgorithmPhysical systemPhysicsStatistical physicsQuantum circuitTopologyAnsatzJordan–Wigner transformationQuantum algorithmToffoli gateQuantum simulatorHamiltonian (quantum mechanics)Controlled NOT gateEnergy functionalAdiabatic quantum computationQubitSuperposition principleParity (physics)Dynamical decouplingQuantum controlMany bodyTime complexityMathematicsMathematical physicsLogarithmComputer scienceLandau quantizationQuantum error correctionSuperconductivityQuantum computerQuantum gateTerm (time)Quantum mechanicsCreation and annihilation operatorsVariational methodFractional quantum Hall effectSpeedupGround stateOperator (computer programming)QuantumImaginary timeRobustness (computer science)
Publications 8
Low-rank decompositions to reduce the Coulomb operator to a pairwise form suitable for its quantum simulation are well-known in quantum chemistry, where the underlying basis functions are real-valued. We generalize the result of Motta \textit{et al.} [arXiv:1808.02625] to \textit{complex} basis functions \psi_p(\mathbf r)\in\mathds Cby means of the Schur decomposition and decomposing matrices into their symmetric and anti-symmetric components. This allows the application of low-rank decomposi...
#1Michael KaicherH-Index: 2
#2Simon B. JägerH-Index: 8
Last. Frank K. WilhelmH-Index: 3
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We present explicit expressions for the central piece of a variational method developed by Shi et al. which extends variational wave functions that are efficiently computable on classical computers beyond mean-field to generalized Gaussian states [1]. In particular, we derive iterative analytical expressions for the evaluation of expectation values of products of fermionic creation and annihilation operators in a Grassmann variable-free representation. Using this result we find a closed expressi...
1 CitationsSource
#1Michael KaicherH-Index: 2
#2Simon B. JägerH-Index: 8
Last. Frank K. WilhelmH-Index: 44
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A major motivation for building a quantum computer is that it provides a tool to efficiently simulate strongly correlated quantum systems. In this work, we present a detailed roadmap on how to simulate a two-dimensional electron gas---cooled to absolute zero and pierced by a strong transversal magnetic field---on a quantum computer. This system describes the setting of the Fractional Quantum Hall Effect (FQHE), one of the pillars of modern condensed matter theory. We give analytical expressions ...
3 CitationsSource
#1Felix Motzoi (AU: Aarhus University)H-Index: 18
#2Michael Kaicher (Saarland University)H-Index: 2
Last. Frank K. Wilhelm (Saarland University)H-Index: 44
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We develop a generalized framework for constructing many-body-interaction operations either in linear time, or in logarithmic time with a linear number of ancilla qubits. Exact gate decompositions are given in particular for Pauli strings, many-control Toffoli gates, number-~and parity-conserving interactions, Unitary Coupled Cluster operations, and sparse matrix generators. We provide a linear time protocol that works by creating a superposition of exponentially many different possible operator...
22 CitationsSource
#1Tobias ChasseurH-Index: 3
#2Felix MotzoiH-Index: 18
Last. Frank K. WilhelmH-Index: 44
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As quantum devices scale up, many-body quantum gates and algorithms begin to surpass what is possible to simulate classically. Validation methods which rely on such classical simulation, such as process tomography and randomized benchmarking, cannot efficiently check correctness of most of the processes involved. In particular non-Clifford gates are a requirement for not only universal quantum computation but for any algorithm or quantum simulation that yields fundamental speedup in comparison w...
#1Andrew TranterH-Index: 6
#2Sarah E. Sofia (MIT: Massachusetts Institute of Technology)H-Index: 9
Last. Peter J. Love (Haverford College)H-Index: 28
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Quantum chemistry is an important area of application for quantum computation. In particular, quantum algorithms applied to the electronic structure problem promise exact, efficient methods for determination of the electronic energy of atoms and molecules. The Bravyi–Kitaev transformation is a method of mapping the occupation state of a fermionic system onto qubits. This transformation maps the Hamiltonian of n interacting fermions to an O(log⁡n)-local Hamiltonian of n qubits. This is an improve...
95 CitationsSource