The quantum square root circuit

Hafiz Md. Hasan Babu

Sohrab Sajadimanesh, Hanieh Aghaee Rad, Jean Paul Latyr Faye +1 more

Noisy intermediate-scale quantum (NISQ) computers face significant reliability challenges because they are vulnerable to quantum noise, which severely limits their fidelity in quantum applications. In particular, deep circuits with a large number of quantum gates are susceptible to errors as they are more likely to lose their states in a deep circuit. In this paper, we propose a quantum circuit for square root operation that generates correct results on NISQ devices. The square root operation is used in many applications such as complex number computations, computer graphics, etc. While there have been limited studies on quantum square root circuits, none of them can be implemented on NISQ devices. In this work, we simplify the structure of an exact quantum square root circuit and reduce the number of quantum gates. The proposed design reduces the complexity of the square root circuit while maintaining the same level of precision in outputs. In addition, we exploit approximate computing to simplify the circuit further and run it on a real quantum computer. Approximate computing is used in classical computers to enhance the power and/or performance in exchange for accuracy. We exploit approximate computing for a different purpose, which is reducing the depth as well as the number of quantum gates in the square root circuit. To validate the effectiveness of our approach, we conduct experiments on an IBM quantum computer, where our circuit produces meaningful results. Furthermore, we present examples of error-resilient applications to demonstrate the validity of our approximate circuit.

Madhusudan Singh Irish Singh, Bharat S. Rawal

Sayeeda Sultana, Katarzyna Radecka

In this paper we present a novel reversible implementation of a square-root circuit with an array structure. In scientific computations such as numerical analysis, computer graphics, complex number computations, square root is an important operation. In classical irreversible arena we find different realizations of square root circuit. Since reversible circuit is emerging as an alternative to classical circuit, here we introduce a novel reversible realization of this operation. As a basic module, we propose a reversible controlled adder/subtractor (RCAS) block based on 2's Complement computation. In our design we use an array of such RCAS blocks which perform addition or subtraction based on the result generated from digit-by-digit square root operation. To our best knowledge this is the first methodical approach for implementing reversible square root circuit. The new structure of the circuit and different parameters - number of gates, garbage bits and quantum cost for n-bit realization is presented here.

Steven Vandenbrande, Raphaël Van Laer, Alexis De Vos

The quantum gates called`square root of NOT' and `controlled square root of NOT' can be applied to synthesize circuits, many more than all classical reversible circuits, but also many less than all quantum circuits. The circuits form an infinite but discrete group, i.e. a group with a countable infinity of elements. They are represented by unitary matrices. Classifying these matrices by `level' allows a detailed quantification of the computational power of the circuits.