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# SCB Quantum Computers Using iSWAP and 1-Qubit Rotations

- Created: Friday, 01 July 2005

### Practical implementation in the SCB context appears to be feasible.

Units of superconducting circuitry that exploit the concept of the single-Cooper-pair box (SCB) have been built and are undergoing testing as prototypes of logic gates that could, in principle, constitute building blocks of clocked quantum computers. These units utilize quantized charge states as the quantum information-bearing degrees of freedom.

An SCB is an artificial two-level quantum system that comprises a nanoscale superconducting electrode connected to a reservoir of Cooperpair charges via a Josephson junction. The logical quantum states of the device, are implemented physically as a pair of charge-number states that differ by (where e is the charge of an electron). Typically, some 109 Cooper pairs are involved. Transitions between the logical states are accomplished by tunneling of Cooper pairs through the Josephson junction. Although the two-level system contains a macroscopic number of charges, in the superconducting regime, they behave collectively, as a Bose-Einstein condensate, making possible a coherent superposition of the two logical states. This possibility makes the SCB a candidate for the physical implementation of a qubit.

A set of quantum logic operations and the gates that implement them is characterized as universal if, in principle, one can form combinations of the operations in the set to implement any desired quantum computation. To be able to design a practical quantum computer, one must first specify how to decompose any valid quantum computation into a sequence of elementary 1- and 2-qubit quantum gates that are universal and that can be realized in hardware that is feasible to fabricate. Traditionally, the set of universal gates has been taken to be the set of all 1- qubit quantum gates in conjunction with the controlled-NOT (CNOT) gate, which is a 2-qubit gate. Also, it has been known for some time that the SWAP gate, which implements square root of the simple 2-qubit exchange interaction, is as computationally universal as is the CNOT operation. The present innovative SCB-based units are of two types: those that can implement any 1-qubit operation (phase shift and/or rotation) and those that can implement a recently discovered 2-qubit operation called “complex SWAP” or “iSWAP.” The combination of these 1- and 2-qubit operations has been shown to be universal on the basis of the governing quantum-mechanical equations. The use of iSWAP instead of CNOT as the single 2-qubit primitive operation offers an advantage over the prior art in that in the SCB context, iSWAP can be implemented in hardware more easily. The figure schematically depicts a 2-qubit gate according to the present innovation.Unlike in prior experimental quantum computer circuits, neither the starting time nor the duration of a gate operation is used as a control parameter to determine the nature of the operation. Instead, quantum gate operations are controlled by applying sequences of voltages and magnetic fluxes to single qubits or pairs of qubits: hence, quantum logic operations can be performed in predictable, fixed, time intervals; that is, they can be clocked. Hence, further, it is easier to integrate these units into large-scale circuits. The feasibility of fabricating such gates and large-scale quantum circuits by use of electron-beam lithography has been demonstrated.

*This work was done by Colin Williams and Pierre Echternach of Caltech for NASA’s Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com/tsp under the Electronics/Computers category.*

In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to:

Innovative Technology Assets Management

JPL

Mail Stop 202-233

4800 Oak Grove Drive

Pasadena, CA 91109-8099

(818) 354-2240

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Refer to NPO-30213, volume and number of this

NASA Tech Briefs issue, and the page number.

### This Brief includes a Technical Support Package (TSP).

** SCB Quantum Computers Using iSWAP and 1-Qubit Rotations** (reference NPO-30213) is currently available for download from the TSP library.

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