Duality Quantum Computers and Quantum Operations

Gui Lu Long

Long, Gui-Lu, Liu . +1 more

Maaz Khan, Syed Anausha Bin Zakir Khan, Mohd, Arif

We study the Kramers-Wannier duality for the transverse-field Ising lattice on a ring. A careful consideration of the ring boundary conditions shows that the duality has to be implemented with a proper treatment of different charge sectors of both the twisted and untwisted Ising and the dual-Ising Hilbert spaces. We construct a superoperator that explicitly maps the Ising operators to the dual-Ising operators. The superoperator naturally acts on the tensor product of the Ising and the dual-Ising Hilbert space. We then show that the relation between our superoperator and the Kramers-Wannier duality operator that maps the Ising Hilbert space to the dual-Ising Hilbert space is naturally provided by quantum operations and the duality can be understood as a quantum operation that we construct. We provide the operator-sum representation for the Kramers-Wannier quantum operations and reproduce the well-known fusion rules. In addition to providing the quantum information perspective on the Kramers-Wannier duality, our explicit protocol will also be useful in implementing the Kramers-Wannier duality on a quantum computer.

C. Y. Li, W. Y. Wang, C. Wang +6 more

Quantum mechanical systems exhibit particle wave duality property. This duality property has been exploited for information processing. A duality quantum computer is a quantum computer on the move and passing through a multi‐slits. It offers quantum wave divider and quantum wave combiner operations in addition to those allowed in an ordinary quantum computer. It has been shown that all linear bounded operators can be realized in a duality quantum computer, and a duality quantum computer with n qubits and d‐slits can be realized in an ordinary quantum computer with n qubits and a qudit in the so‐called duality quantum computing mode. The quantum particle‐wave duality can be used in providing secure communication. In this paper, we will review duality quantum computing and duality quantum key distribution.

pXiangyu Kong, Gui Lu Longp

Wei, Shi-Jie, Gui‐Lu Long

In this paper, we firstly briefly review the duality quantum computer. Distinctly, the generalized quantum gates, the basic evolution operators in a duality quantum computer are no longer unitary, and they can be expressed in terms of linear combinations of unitary operators. All linear bounded operators can be realized in a duality quantum computer, and unitary operators are just the extreme points of the set of generalized quantum gates. A d-slits duality quantum computer can be realized in an ordinary quantum computer with an additional qudit using the duality quantum computing mode. Duality quantum computer provides flexibility and clear physical picture in designing quantum algorithms, serving as a useful bridge between quantum and classical algorithms. In this review, we will show that duality quantum computer can simulate quantum systems more efficiently than ordinary quantum computers by providing descriptions of the recent efficient quantum simulation algorithms of Childs et al [Quantum Information & Computation, 12(11-12): 901-924 (2012)] for the fast simulation of quantum systems with a sparse Hamiltonian, and the quantum simulation algorithm by Berry et al [Phys. Rev. Lett. 114, 090502 (2015)], which provides exponential improvement in precision for simulating systems with a sparse Hamiltonian.