Fermionic Quantum Computation

By Sergey Bravyi, Alexei Y. Kitaev. 2000

1,093 citations recorded by the source corpus.

We define a model of quantum computation with local fermionic modes (LFMs)—sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m LFMs and the Hilbert space of m qubits, simulation of one fermionic gate takes O(m) qubit gates and vice versa. We show that using different encodings, the simulation cost can be reduced to O(log m) and a constant, respectively. Nearest neighbors fermionic gates on a graph of bounded degree can be simulated at a constant cost. A universal set of fermionic gates is found. We also study computation with Majorana fermions which are basically halves of LFMs. Some connection to qubit quantum codes is made.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/f1b4a30c208da564727c4f4c16eaa1c90dcaa03e

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Scalable Quantum Simulation of Molecular Energies (2015, methodology): “Until this work, important aspects of scalable chemistry simulation such as the Jordan-Wigner transformation [40] or the Bravyi-Kitaev transformation [41,42] had never been used to represent a molecule in an experiment; however, prior experiments such as Ref.”
Quantum computing with neutral atoms (2020, background): “There indeed exist explicit mappings between spin models, that can be implemented natively with neutral atom devices, and electronic Hamiltonians, known as the Jordan-Wigner [59, 60] and the Bravyi-Kitaev [61] transformations (see Box 4 for details about the Jordan-Wigner transform).”
QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits (2021, methodology): “We use the Bravyi-Kitaev mapping [9] to transform a molecule Hamiltonian from its fermionic TABLE I COMPILED CIRCUIT PROPERTIES FOR QUANTUMNAS AND BASELINES.”
Classical simulation of noninteracting-fermion quantum circuits (2001, methodology): “not a problem when one considers the question of simulating the dynamics of fermionic systems on a quantum computer: fermions dynamics can be simulated eﬃciently on a quantum computer, see Refs. [9], [10] and [11]. Furthermore, it has been shown in Ref. [10] that universal quantum computation can be”
Matchgates and classical simulation of quantum circuits (2008, background): ““modified swap” operation (Bravyi and Kitaev 2002) defined, for example for lines 1 and 2, by”
Quantum computing and the entanglement frontier (2012, neutral): “19”
Quantum information processing with superconducting circuits: a review (2016, positive): “For the specific case of single qubit unitaries the Solovay–Kitaev theorem [283] guarantees that this can be done efficiently, involving only a polynomial number of gates.”