# SQUBIT Sintesi della relazione

Project ID:
IST-1999-10673

Finanziato nell'ambito di:
FP5-IST

Paese:
Italy

## Proposal for Deutsch-Josza algorithm with super-conducting qubits

The interest in quantum computation, in particular, is stimulated by the discovery of quantum algorithms, which can outperform their classical counterparts in solving problems of significant practical relevance.

In the field of solid-state quantum computation, and in particular in the area of super-conducting nano-circuits, considerable progress has been made in the field of quantum hardware. It is equally important in the development of quantum computing to experimentally realize complete quantum algorithms. It is also particularly important to see whether at the present it is already possible to implement also quantum algorithms using super-conducting nanocircuits.

We showed how the Deutsch algorithm and the Bernstein-Vazirani algorithm can be run on a Josephson quantum computer. We analyse the experiment by Nakamura et al in terms of quantum interferometry and show that it corresponds to the implementation of the one-qubit version of Deutsch's algorithm. By generalizing this idea we show how the N-qubit Deutsch algorithm, with N<3, can be implemented. Finally we showed explicitly that the Bernstein-Vazirani algorithm can be implemented using uncoupled qubits (for arbitrary N). Therefore it can be realized by means of the set-up of Nakamura et al. experiment.

Our proposed implementation realizes the algorithms by using only state-of-the-art technology. A peculiarity is that the gate operations representing the algorithm are carried out in a basis, which is different from the one, which is measured. This helped us to obtain the desired results with a minimum number of operations. Thus, one may hope to see the expected behaviour of the system even with the decoherence times which are measured at the present in these systems. In addition the experimental implementation of this proposal may serve to study entanglement and decoherence on entangled states in great details. The methods outlined above can also be used to study other interesting problems such as the production and measurement of Bell states and GHZ states.

From a practical point of view, it would be particularly interesting to find ways to create such states in a 'single shot' with one appropriate gate operation. Even though it appears rather difficult to avoid the locality loophole in this kind of set-up it is nevertheless a remarkable challenge to measure such quantum correlations in a macroscopic system.

In the field of solid-state quantum computation, and in particular in the area of super-conducting nano-circuits, considerable progress has been made in the field of quantum hardware. It is equally important in the development of quantum computing to experimentally realize complete quantum algorithms. It is also particularly important to see whether at the present it is already possible to implement also quantum algorithms using super-conducting nanocircuits.

We showed how the Deutsch algorithm and the Bernstein-Vazirani algorithm can be run on a Josephson quantum computer. We analyse the experiment by Nakamura et al in terms of quantum interferometry and show that it corresponds to the implementation of the one-qubit version of Deutsch's algorithm. By generalizing this idea we show how the N-qubit Deutsch algorithm, with N<3, can be implemented. Finally we showed explicitly that the Bernstein-Vazirani algorithm can be implemented using uncoupled qubits (for arbitrary N). Therefore it can be realized by means of the set-up of Nakamura et al. experiment.

Our proposed implementation realizes the algorithms by using only state-of-the-art technology. A peculiarity is that the gate operations representing the algorithm are carried out in a basis, which is different from the one, which is measured. This helped us to obtain the desired results with a minimum number of operations. Thus, one may hope to see the expected behaviour of the system even with the decoherence times which are measured at the present in these systems. In addition the experimental implementation of this proposal may serve to study entanglement and decoherence on entangled states in great details. The methods outlined above can also be used to study other interesting problems such as the production and measurement of Bell states and GHZ states.

From a practical point of view, it would be particularly interesting to find ways to create such states in a 'single shot' with one appropriate gate operation. Even though it appears rather difficult to avoid the locality loophole in this kind of set-up it is nevertheless a remarkable challenge to measure such quantum correlations in a macroscopic system.