Related papers: A Sierpinski Triangle Fermion-to-Qubit Transform
The quaternionic description of semiconductor single-electron devices is given in the single-electron regime. The conversion scheme of complex value Hamiltonian into a quaternion is formulated for the case of single-electron semiconductor…
Many-body fermionic quantum calculations performed on analog quantum computers are restricted by the presence of k-local terms, which represent interactions among more than two qubits. These originate from the fermion-to-qubit mapping…
Anyons are exotic quasiparticles living in two dimensions that do not fit into the usual categories of fermions and bosons, but obey a new form of fractional statistics. Following a recent proposal [Phys. Rev. Lett. 98, 150404 (2007)], we…
A reasonable quantum information theory for fermions must respect the parity super-selection rule to comply with the special theory of relativity and the no-signaling principle. This rule restricts the possibility of any quantum state to…
The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to explore the underlying physics is to study the wave function that incorporates Fermi-Dirac…
We develop a workflow to use current quantum computing hardware for solving quantum many-body problems, using the example of the fermionic Hubbard model. Concretely, we study a four-site Hubbard ring that exhibits a transition from a…
Proposed is a generalization of Jordan-Wigner transform that allows to exactly fermionize a large family of quantum spin Hamiltonians in dimensions higher than one. The key new steps are to enlarge the Hilbert space of the original model by…
The quantum Fourier transform (QFT) is a fundamental primitive in quantum computation and quantum information. In this work, we generalize the QFT for finite groups to a QFT for finite-dimensional semisimple algebras, and give efficient…
Performing large-scale, accurate quantum simulations of many-fermion systems is a central challenge in quantum science, with applications in chemistry, materials, and high-energy physics. Despite significant progress, realizing generic…
One of the key features of information geometry in the classical setting is the existence of a metric structure and a family of connections on the space of probability distributions. The uniqueness of the Fisher--Rao metric and the duality…
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…
Fermions, as a major class of quantum particles, provide platforms for quantum information processing beyond the possibilities of spins or bosons which have been studied more extensively. One particularly interesting model to study, in view…
Though the no-cloning theorem [1] prohibits exact replication of arbitrary quantum states, there are many instances in quantum information processing and entanglement measurement in which a weaker form of cloning may be useful. Here, I…
In this paper we analyze the ground state phase diagram of a class of fermionic Hamiltonians by looking at the fidelity of ground states corresponding to slightly different Hamiltonian parameters. The Hamiltonians under investigation can be…
Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational bottleneck is the sampling from the Gibbs density of the…
As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the…
Routing is the task of permuting qubits in such a way that quantum operations can be parallelized maximally, given constraints on the hardware geometry. When simulating fermions in the Jordan-Wigner encoding with qubits, a one-dimensional…
We use the variational quantum eigensolver (VQE) to simulate Kitaev spin models with and without integrability breaking perturbations, focusing in particular on the honeycomb and square-octagon lattices. These models are well known for…
We consider quantum spin chains with a hidden free fermionic structure, distinct from the Jordan-Wigner transformation and its generalizations. We express selected local operators with the hidden fermions. This way we can exactly solve the…
Quantum computers are the ideal platform for quantum simulations. Given enough coherent operations and qubits, such machines can be leveraged to simulate strongly correlated materials, where intricate quantum effects give rise to…