T-Count Optimized Quantum Circuit Designs for Single-Precision Floating-Point Division

Abstract

The implementation of quantum computing processors for scientific applications includes quantum floating points circuits for arithmetic operations. This work adopts the standard division algorithms for floating-point numbers with restoring, non-restoring, and Goldschmidt division algorithms for single-precision inputs. The design proposals are carried out while using the quantum Clifford+T gates set, and resource estimates in terms of numbers of qubits, T-count, and T-depth are provided for the proposed circuits. By improving the leading zero detector (LZD) unit structure, the proposed division circuits show a significant reduction in the T-count when compared to the existing works on floating-point division.

Efficient Floating-point Division Quantum Circuit using Newton-Raphson Division

“…Quantum circuits for solving integer problems received major interest in the literature [13,[17][18][19]22] whereas, problems that employ floating-point numbers has received less attention in literature [23][24][25]. Many scientific, information and communication technology, fields rely on floating-point division.…”

“…The reciprocal approximation is observed with the help of a lookup table that computes the initial guess, which serves as the seed for the calculation. The iteration begins with a quantum multiplier that calculates DX * Xi after the other existing quantum circuit model, which used Goldschmidt division circuits, a type of fast division algorithm [25], and the resource used is shown in Table 2.…”

“…S R T di vi si o n, Restoring and Non-restoring division algorithms are slow division algorithms as they are digit by digit recurrence algorithms. The fast division algorithms are Goldschmidt division and Newton-Raphson division, as their number of iterations is O (log n)[25]. For computing one iterative process, the Newton-Raphson convergence time is much faster.…”

Implementation of three efficient 4-digit fault-tolerant quantum carry lookahead adders

“…It is intuitive to solve this operation using circuits that perform multiplication or exponentiation. However, such circuits are currently too resource-intensive for current quantum computers [9,10]. Instead, adders are commonly used to perform this operation in a more resource-efficient way [11].…”

“…Although initially the quantum cost and delay metrics were used, which contemplate all the gates involved in the circuit, the high cost of the T gates makes the cost of the rest of the gates negligible [26]. Therefore, the T-count and T-depth metrics are increasingly displacing these other metrics [9,27,28].…”