Qubits and Quantum Computers

Samuel L. Braunstein, Arun Kumar Pati

Ahmed Banafa

Quantum computing is the area of study focused on developing computer technology based on the principles of quantum theory. As we progress to smaller and faster circuits, we begin to reach the physical limits of materials and the threshold for classical laws of physics to apply. Classical computers use transistors as the physical building blocks of logic, while quantum computers may use trapped ions, superconducting loops, quantum dots or vacancies in a diamond. Physical qubits are the physical qubits in a quantum computer, whereas logical qubits are groups of physical qubits we use as a single qubit in our computation to fight noise and improve error correction. There are many estimates as to how many qubits the authors will need to perform certain calculations, but some of these estimates talk about logical qubits and others talk about physical qubits. For example, to break RSA cryptography we would need thousands of logical qubits but millions of physical qubits.

Richard B. Gomez, Anil Jayanna, Debabrata Ghoshal

As interest in quantum computing evolves, consideration must be given to the development of new methods to improve the current design of quantum computers. Such ideas are not only helping the advance towards practical quantum computation applications, but are also providing clearer understanding of quantum computation itself. Eventually, several new exploratory efforts to increase the efficiency beyond the inherent advantage of quantum computational systems to classical systems will materialize. As a part of these exploration efforts, this paper presents a modified version of the qubit, which we refer to as a "Qubit", that allows a smaller number of Qubits than qubits to reach the same result in applications such as Shor’s algorithm for the factorization of large numbers. The current model of the qubit consists of a quantum bit with two states, a zero and a one in a quantum superposition state. The Qubit, which consists of more than two states, is introduced and explained. A mathematical analysis of the Qubit within Hilbert space is given. We present examples of applications of the Qubit to several quantum computing algorithms, including discussion of the advantages and disadvantages that are involved. Finally a physical model to construct such a Qubit is considered.

Kamil A. Valiev

Julio R. Gea-Banacloche

Limitations to the performance of a quantum computer arising from direct interaction between qubits are considered, and the basic scaling laws (with the computation time and the number of qubits) are established for the specific example of the quantum Fourier transform algorithm. These results should be relevant for several of the currently proposed quantum computer systems, where the dominant interaction is of the magnetic dipole-dipole type, in the limit of many qubits and long computation times.

Pieter Kok, S. D. Barrett