1,289 research outputs found
Local spin operators for fermion simulations
Digital quantum simulation of fermionic systems is important in the context
of chemistry and physics. Simulating fermionic models on general purpose
quantum computers requires imposing a fermionic algebra on spins. The
previously studied Jordan-Wigner and Bravyi-Kitaev transformations are two
techniques for accomplishing this task. Here we re-examine an auxiliary fermion
construction which maps fermionic operators to local operators on spins. The
local simulation is performed by relaxing the requirement that the number of
spins should match the number of fermionic modes. Instead, auxiliary modes are
introduced to enable non-consecutive fermionic couplings to be simulated with
constant low-rank tensor products on spins. We connect the auxiliary fermion
construction to other topological models and give examples of the construction
Loop Algorithms for Asymmetric Hamiltonians
Generalized rules for building and flipping clusters in the quantum Monte
Carlo loop algorithm are presented for the XXZ-model in a uniform magnetic
field along the Z-axis. As is demonstrated for the Heisenberg antiferromagnet
it is possible from these rules to select a new algorithm which performs
significantly better than the standard loop algorithm in strong magnetic fields
at low temperatures.Comment: Replaced measurement of helicity modulus at H=2J with a measurement
at H=3.95J + other small changes in the section on numerical result
Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
We present an adaptive algorithm which optimizes the statistical-mechanical
ensemble in a generalized broad-histogram Monte Carlo simulation to maximize
the system's rate of round trips in total energy. The scaling of the mean
round-trip time from the ground state to the maximum entropy state for this
local-update method is found to be O([N log N]^2) for both the ferromagnetic
and the fully frustrated 2D Ising model with N spins. Our new algorithm thereby
substantially outperforms flat-histogram methods such as the Wang-Landau
algorithm.Comment: 6 pages, 5 figure
Operator Locality in the Quantum Simulation of Fermionic Models
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 rectangular lattice. We conclude that the most compact encoding of the fermionic operators can be done using ancilla qubits with the Auxiliary Fermion scheme. Without introducing ancillas, a variant of the Bravyi-Kitaev transform provides the most compact fermion-to-qubit mapping for Hubbard-like models
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