On a generalized quantum SWAP gate

The SWAP gate plays a central role in network designs for qubit quantum computation. However, there has been a view to generalize qubit quantum computing to higher dimensional quantum systems. In this paper we construct a generalized SWAP gate using only instances of the generalized controlled-NOT gate to cyclically permute the states of d qudits for d prime

Towards an optimal swap gate

We present a novel approach that generalizes the well known quantum SWAP gate to higher dimensions and construct a regular quantum gate composed entirely in terms of the generalized CNOT gate that cyclically permutes the states of d qudits for d prime. We also investigate the case for d other than prime. A key feature of the construction design relates to the periodicity evaluation for a family of linear recurrences which we achieve by exploiting generating functions and their factorization over the complex reals

Weak randomness completely trounces the security of QKD

In usual security proofs of quantum protocols the adversary (Eve) is expected to have full control over any quantum communication between any communicating parties (Alice and Bob). Eve is also expected to have full access to an authenticated classical channel between Alice and Bob. Unconditional security against any attack by Eve can be proved even in the realistic setting of device and channel imperfection. In this Letter we show that the security of QKD protocols is ruined if one allows Eve to possess a very limited access to the random sources used by Alice. Such knowledge should always be expected in realistic experimental conditions via different side channels

Algorithm for characterizing stochastic local operations and classical communication classes of multiparticle entanglement

It is well known that the classification of pure multiparticle entangled states according to stochastic local operations leads to a natural classification of mixed states in terms of convex sets. We present a simple algorithmic procedure to prove that a quantum state lies within a given convex set. Our algorithm generalizes a recent algorithm for proving separability of quantum states [Barreiro et al., Nat. Phys. 6, 943 (2010)]. We give several examples which show the wide applicability of our approach. We also propose a procedure to determine a vicinity of a given quantum state which still belongs to the considered convex set

Simulating the non-Hermitian dynamics of financial option pricing with quantum computers

The Schrodinger equation describes how quantum states evolve according to the Hamiltonian of the system. For physical systems, we have it that the Hamiltonian must be a Hermitian operator to ensure unitary dynamics. For anti-Hermitian Hamiltonians, the Schrodinger equation instead models the evolution of quantum states in imaginary time. This process of imaginary time evolution has been used successfully to calculate the ground state of a quantum system. Although imaginary time evolution is non-unitary, the normalised dynamics of this evolution can be simulated on a quantum computer using the quantum imaginary time evolution (QITE) algorithm. In this paper, we broaden the scope of QITE by removing its restriction to anti-Hermitian Hamiltonians, which allows us to solve any partial differential equation (PDE) that is equivalent to the Schrodinger equation with an arbitrary, non-Hermitian Hamiltonian. An example of such a PDE is the famous Black-Scholes equation that models the price of financial derivatives. We will demonstrate how our generalised QITE methodology offers a feasible approach for real-world applications by using it to price various European option contracts modelled according to the Black-Scholes equation.Comment: 15 pages, 2 figure