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Computation at a distance
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We consider a model of computation motivated by possible limitations on quantum computers. We have a linear array of n wires, and we may perform operations only on pairs of adjacent wires. Our goal is to build a circuits that perform specified operations spanning all n wires. We show that the natural lower bound of n-1 on circuit depth is nearly tight for a variety of problems, and we prove linear upper bounds for additional problems. In particular, using only gates adding a wire (mod 2) into an adjacent wire, we can realize any linear operation in GL_n(2) as a circuit of depth 5n. We show that some linear operations require depth at least 2n+1.
Forward citations
Cited by 3 Pith papers
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Asymptotically Optimal Depth Fermionic Permutation on 2D Grid Quantum Architecture without Ancillas
A fermionic permutation protocol on 2D nearest-neighbor grids achieves the optimal O(sqrt(N)) depth with O(N sqrt(N)) gates, no ancillas, and extends to Jordan-Wigner, Bravyi-Kitaev, and Parity encodings via Hilbert-c...
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Block Encoding of Sparse Matrices via Coherent Permutation
A new framework for block encoding sparse matrices that uses coherent permutations to reorder amplitudes while preserving superposition and combinatorial optimization to meet hardware connectivity limits.
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Multi-Controlled Quantum Gates in Linear Nearest Neighbor
Multi-controlled X and SU(2) gates on linear-nearest-neighbor qubit arrays require at most 4k+8n-16 and 4k+8n-14 CNOT gates, respectively, improving earlier bounds.
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