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Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have been demonstrated in several physical architectures. A serious obstacle to a full-scale implementation is the sheer number of these gates required to implement even small quantum algorithms. Here we present and demonstrate a general technique that harnesses higher dimensions of quantum systems to significantly reduce this number, allowing the construction of key quantum circuits with existing technology. We are thereby able to present the first implementation of two key quantum circuits: the three-qubit Toffoli and the two-qubit controlled-unitary. The gates are realised in a linear optical architecture, which would otherwise be absolutely infeasible with current technology.
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space. This yiel
We construct a three-dimensional quantum cellular automaton (QCA), an automorphism of the local operator algebra on a lattice of qubits, which disentangles the ground state of the Walker-Wang three fermion model. We show that if this QCA can be reali
The Clifford hierarchy is a nested sequence of sets of quantum gates critical to achieving fault-tolerant quantum computation. Diagonal gates of the Clifford hierarchy and nearly diagonal semi-Clifford gates are particularly important: they admit eff
Thinning antenna arrays through quantum Fourier transform (QFT) is proposed. Given the lattice of the candidate locations for the array elements, the problem of selecting which antenna location has to be either occupied or not by an array element is
In search of a quantum key distribution scheme that could stand up for more drastic eavesdropping attack, I discover a prepare-and-measure scheme using $N$-dimensional quantum particles as information carriers where $N$ is a prime power. Using the Sh