TY - GEN
T1 - Quantum circuit designs of integer division optimizing T-count and T-depth
AU - Thapliyal, Himanshu
AU - Varun, T. S.S.
AU - Munoz-Coreas, Edgard
AU - Britt, Keith A.
AU - Humble, Travis S.
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/7/2
Y1 - 2017/7/2
N2 - Quantum circuits for basic mathematical functions such as division are required to implement scientific computing algorithms on quantum computers. In this work, we propose two designs for quantum integer division. The designs are based on quantum Clifford+T gates and are optimized for T-count and T-depth. Quantum circuits that are based on Clifford+T gates can be made fault tolerant in nature but the T gate is very costly to implement. As a result, reducing T-count and T-depth have become important optimization goals. Existing quantum hardware is limited in terms of number of available qubits. Thus, ancillary qubits are a circuit overhead that needs to be kept to a minimum. We propose two quantum integer division circuits. The first quantum integer division circuit is based on the non-restoring division algorithm. The proposed non-restoring division circuit is optimized for total quantum hardware (T-count and T-depth) cost but requires 2∗ n + 1 ancillary qubits. We also propose a quantum integer division circuit based on the restoring division algorithm. The proposed restoring division circuit is optimized for total qubits. The design requires only n ancillary qubits but will need more quantum hardware than the non-restoring division circuit. Both proposed quantum circuits are based on (i) a new quantum conditional addition circuit, (ii) a new quantum adder-subtractor and (iii) a new quantum subtraction circuit. Further, both designs are compared and shown to be superior to existing work in terms of T-count and T-depth. The proposed quantum non-restoring integer division circuit has a 96% improvement in terms of T-count and a 93% improvement in terms of T-depth compared to existing work. The proposed quantum restoring integer division circuit has a 91% improvement in terms of T-count and a 86% improvement in terms of T-count compared to the existing work.
AB - Quantum circuits for basic mathematical functions such as division are required to implement scientific computing algorithms on quantum computers. In this work, we propose two designs for quantum integer division. The designs are based on quantum Clifford+T gates and are optimized for T-count and T-depth. Quantum circuits that are based on Clifford+T gates can be made fault tolerant in nature but the T gate is very costly to implement. As a result, reducing T-count and T-depth have become important optimization goals. Existing quantum hardware is limited in terms of number of available qubits. Thus, ancillary qubits are a circuit overhead that needs to be kept to a minimum. We propose two quantum integer division circuits. The first quantum integer division circuit is based on the non-restoring division algorithm. The proposed non-restoring division circuit is optimized for total quantum hardware (T-count and T-depth) cost but requires 2∗ n + 1 ancillary qubits. We also propose a quantum integer division circuit based on the restoring division algorithm. The proposed restoring division circuit is optimized for total qubits. The design requires only n ancillary qubits but will need more quantum hardware than the non-restoring division circuit. Both proposed quantum circuits are based on (i) a new quantum conditional addition circuit, (ii) a new quantum adder-subtractor and (iii) a new quantum subtraction circuit. Further, both designs are compared and shown to be superior to existing work in terms of T-count and T-depth. The proposed quantum non-restoring integer division circuit has a 96% improvement in terms of T-count and a 93% improvement in terms of T-depth compared to existing work. The proposed quantum restoring integer division circuit has a 91% improvement in terms of T-count and a 86% improvement in terms of T-count compared to the existing work.
KW - Quantum Arithmetic Circuits
KW - Quantum Circuits
KW - Quantum Division Circuit
UR - http://www.scopus.com/inward/record.url?scp=85052388895&partnerID=8YFLogxK
U2 - 10.1109/iNIS.2017.34
DO - 10.1109/iNIS.2017.34
M3 - Conference contribution
AN - SCOPUS:85052388895
T3 - Proceedings - 2017 IEEE International Symposium on Nanoelectronic and Information Systems, iNIS 2017
SP - 123
EP - 128
BT - Proceedings - 2017 IEEE International Symposium on Nanoelectronic and Information Systems, iNIS 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 3rd IEEE International Symposium on Nanoelectronic and Information Systems, iNIS 2017
Y2 - 18 December 2017 through 20 December 2017
ER -