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Fermionic Quantum Computation
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
Lieb-Robinson bounds and the generation of correlations and topological quantum order.
The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails.
A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
It is shown that for D=1,2 the height of the energy barrier separating different logical states is upper bounded by a constant independent of the lattice size L, and it is demonstrated that a self-correcting quantum memory cannot be built using stabilizer codes in dimensions D= 1,2.
Error Mitigation for Short-Depth Quantum Circuits.
Two schemes are presented that mitigate the effect of errors and decoherence in short-depth quantum circuits by resampling randomized circuits according to a quasiprobability distribution.
Quantum codes on a lattice with boundary
A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices.
Magic-state distillation with low overhead
A new family of error detecting stabilizer codes with an encoding rate 1/3 that permit a transversal implementation of the pi/8-rotation on all logical qubits are proposed and lead to a two-fold overhead reduction for distilling magic states with output accuracy compared with the best previously known protocol.
Improved Classical Simulation of Quantum Circuits Dominated by Clifford Gates.
The algorithm may serve as a verification tool for near-term quantum computers which cannot in practice be simulated by other means and can be used in practice to simulate medium-sized quantum circuits dominated by Clifford gates.
Simulation of quantum circuits by low-rank stabilizer decompositions
A comprehensive mathematical theory of the stabilizerRank and the related approximate stabilizer rank is developed and a suite of classical simulation algorithms with broader applicability and significantly improved performance over the previous state-of-the-art are presented.
Tapering off qubits to simulate fermionic Hamiltonians
It is shown that encodings with a given filling fraction $\nu=N/M$ and a qubit-per-mode ratio $\eta=Q/M<1$ can be constructed from efficiently decodable classical LDPC codes with the relative distance $2\nu$ and the encoding rate $1-\eta$.