9 research outputs found
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