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Mermin Inequalities For Perfect Correlations In Many-Qutrit Systems, Jay Lawrence
Mermin Inequalities For Perfect Correlations In Many-Qutrit Systems, Jay Lawrence
Dartmouth Scholarship
The existence of Greenberger-Horne-Zeilinger (GHZ) contradictions in many-qutrit systems was a long-standing theoretical question until its (affirmative) resolution in 2013. To enable experimental tests, we derive Mermin inequalities from concurrent observable sets identified in those proofs. These employ a weighted sum of observables, called M, in which every term has the chosen GHZ state as an eigenstate with eigenvalue unity. The quantum prediction for M is then just the number of concurrent observables, and this grows asymptotically as 2N/3 as the number of qutrits N→∞. The maximum classical value falls short for every N≥3, so that the quantum to classical …
Operator Locality In The Quantum Simulation Of Fermionic Models, Vojtěch Havlíček, Matthias Troyer, James D. Whitfield
Operator Locality In The Quantum Simulation Of Fermionic Models, Vojtěch Havlíček, Matthias Troyer, James D. Whitfield
Dartmouth Scholarship
Simulating fermionic lattice models with qubits requires mapping fermionic degrees of freedom to qubits. The simplest method for this task, the Jordan-Wigner transformation, yields strings of Pauli operators acting on an extensive number of qubits. This overhead can be a hindrance to implementation of qubit-based quantum simulators, especially in the analog context. Here we thus review and analyze alternative fermion-to-qubit mappings, including the two approaches by Bravyi and Kitaev and the Auxiliary Fermion transformation. The Bravyi-Kitaev transform is reformulated in terms of a classical data structure and generalized to achieve a further locality improvement for local fermionic models on a …