We introduce and analyze circuits that are the quantum mechanical generalization of classical algebraic circuits. Using the algebraic operations of addition and multiplication, as well as the quantum Fourier transform, such circuits are well-defined for rings Z/mZ and finite fields Fq. The acceptance probabilities of such algebraic quantum circuits can be expressed as exponential sums ∑x exp(2π...

Finite fields of the form F2m play an important role in coding theory and cryptography. We show that the choice of how to represent the elements of these fields can have a significant impact on the resource requirements for quantum arithmetic. In particular, we show how the use of Gaussian normal basis representations and of ‘ghost-bit basis’ representations can be used to implement inverters w...

The ability to generate particles from the quantum vacuum is one of the most profound consequences of Heisenberg’s uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable qu...

Quantum circuits are time dependent diagrams describing the process of quantum computation. Every (quantum) algorithm must be mapped into a quantum circuit to be able to run it on a quantum hardware. Optimal synthesis of quantum circuits is intractable and heuristic methods must be employed, resulting in non-optimal circuit speci£cations. In this paper, we consider the use of local optimization...

It is shown that the fault testing for quantum circuits does not follow conventional classical techniques. If probabilistic gate like Hadamard gate is included in a circuit then the classical notion of test vector is shown to fail. We have reported several new and distinguishing features of quantum fault and also presented a general methodology for detection of functional faults in a quantum ci...

This paper present a divide based simultable quantum circuit for spatial optimized coding, which is using only elementary quantum gates. The proposed approach provides the techniques for spatial optimized quantum algorithms. This approach might be useful only as a tool for spatial optimization of quantum algorithms, it is not particularly valuable for saving bandwidth.

Quantum walk represents one of the most promising resources for the simulation of physical quantum systems, and has also emerged as an alternative to the standard circuit model for quantum computing. Here we investigate how the particle statistics, either bosonic or fermionic, influences a two-particle discrete quantum walk. Such an experiment has been realized by exploiting polarization entang...

We observed the recently predicted quantum suppression of dynamical Coulomb blockade on short coherent conductors by measuring the conductance of a quantum point contact embedded in a tunable on-chip circuit. Taking advantage of the circuit modularity we measured most parameters used by the theory. This allowed us to perform a reliable and quantitative experimental test of the theory. Dynamical...