Synthesis of Quantum Logic Circuits

We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the state-space of an n-qubit register is not finite and contains exponential superpositions of classical bit strings. Our proposed circuits are asymptotically optimal for respective tasks and improve published results by at least a factor of two. The circuits for generic quantum computation constructed by our algorithms are the most efficient known today in terms of the number of expensive gates (quantum controlled-NOTs). They are based on an analogue of the Shannon decomposition of Boolean functions and a new circuit block, quantum multiplexor, that generalizes several known constructions. A theoretical lower bound implies that our circuits cannot be improved by more than a factor of two. We additionally show how to accommodate the severe architectural limitation of using only nearest-neighbor gates that is representative of current implementation technologies. This increases the number of gates by almost an order of magnitude, but preserves the asymptotic optimality of gate counts.Comment: 18 pages; v5 fixes minor bugs; v4 is a complete rewrite of v3, with 6x more content, a theory of quantum multiplexors and Quantum Shannon Decomposition. A key result on generic circuit synthesis has been improved to ~23/48*4^n CNOTs for n qubit

Fast Tensor Disentangling Algorithm

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an approximate, fast, and simple algorithm to optimize disentangling unitary tensors. Our algorithm is asymptotically faster than previous iterative algorithms and often results in a residual entanglement entropy that is within 10 to 40% of the minimum. For certain input tensors, our algorithm returns an optimal solution. When disentangling order-4 tensors with equal bond dimensions, our algorithm achieves an entanglement spectrum where nearly half of the singular values are zero. We further validate our algorithm by showing that it can efficiently disentangle random 1D states of qubits.Comment: 8+4 pages, 3 figures; v3 improves the extended algorithm in Appendix