The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Travis S. Humble - One of the best experts on this subject based on the ideXlab platform.
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Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth
IEEE Transactions on Emerging Topics in Computing, 2021Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreas, Travis S. HumbleAbstract:Quantum circuits for mathematical functions such as Division are necessary to use quantum computers for scientific computing. In this work, we propose two quantum Integer Division circuits. The first proposed quantum Integer Division circuit is based on the restoring Division algorithm and the second proposed design implements the non-restoring Division algorithm. Both proposed designs are optimized in terms of T-count, T-depth and qubits. Both proposed quantum circuit designs are based on (i) a quantum subtractor, (ii) a quantum adder-subtractor circuit, and (iii) a novel quantum conditional addition circuit. Our proposed restoring Division circuit achieves average T-count savings from 79.03% to 91.69% compared to the existing works. Our proposed non-restoring Division circuit achieves average Tcount savings from 49.75% to 90.37% compared to the existing works. Further, both our proposed designs have linear T-depth. We also illustrated the application of the proposed quantum Division circuits in quantum image processing with a case study of quantum bilinear interpolation.
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Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth
arXiv: Quantum Physics, 2018Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreas, Travis S. HumbleAbstract:Quantum circuits for mathematical functions such as Division are necessary to use quantum computers for scientific computing. Quantum circuits based on Clifford+T gates can easily be made fault-tolerant but the T gate is very costly to implement. The small number of qubits available in existing quantum computers adds another constraint on quantum circuits. As a result, reducing T-count and qubit cost have become important optimization goals. The design of quantum circuits for Integer Division has caught the attention of researchers and designs have been proposed in the literature. However, these designs suffer from excessive T gate and qubit costs. Many of these designs also produce significant garbage output resulting in additional qubit and T gate costs to eliminate these outputs. In this work, we propose two quantum Integer Division circuits. The first proposed quantum Integer Division circuit is based on the restoring Division algorithm and the second proposed design implements the non-restoring Division algorithm. Both proposed designs are optimized in terms of T-count, T-depth and qubits. Both proposed quantum circuit designs are based on (i) a quantum subtractor, (ii) a quantum adder-subtractor circuit, and (iii) a novel quantum conditional addition circuit. Our proposed restoring Division circuit achieves average T-count savings from $79.03 \%$ to $91.69 \%$ compared to the existing works. Our proposed non-restoring Division circuit achieves average T-count savings from $49.75 \%$ to $90.37 \%$ compared to the existing works. Further, both our proposed designs have linear T-depth.
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quantum circuit designs of Integer Division optimizing t count and t depth
2017 IEEE International Symposium on Nanoelectronic and Information Systems (iNIS), 2017Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Keith A. Britt, Edgard Munozcoreas, Travis S. HumbleAbstract: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.
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iNIS - Quantum Circuit Designs of Integer Division Optimizing T-Count and T-Depth
2017 IEEE International Symposium on Nanoelectronic and Information Systems (iNIS), 2017Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreas, Keith A. Britt, Travis S. HumbleAbstract: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.
Himanshu Thapliyal - One of the best experts on this subject based on the ideXlab platform.
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Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth
IEEE Transactions on Emerging Topics in Computing, 2021Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreas, Travis S. HumbleAbstract:Quantum circuits for mathematical functions such as Division are necessary to use quantum computers for scientific computing. In this work, we propose two quantum Integer Division circuits. The first proposed quantum Integer Division circuit is based on the restoring Division algorithm and the second proposed design implements the non-restoring Division algorithm. Both proposed designs are optimized in terms of T-count, T-depth and qubits. Both proposed quantum circuit designs are based on (i) a quantum subtractor, (ii) a quantum adder-subtractor circuit, and (iii) a novel quantum conditional addition circuit. Our proposed restoring Division circuit achieves average T-count savings from 79.03% to 91.69% compared to the existing works. Our proposed non-restoring Division circuit achieves average Tcount savings from 49.75% to 90.37% compared to the existing works. Further, both our proposed designs have linear T-depth. We also illustrated the application of the proposed quantum Division circuits in quantum image processing with a case study of quantum bilinear interpolation.
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Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth
arXiv: Quantum Physics, 2018Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreas, Travis S. HumbleAbstract:Quantum circuits for mathematical functions such as Division are necessary to use quantum computers for scientific computing. Quantum circuits based on Clifford+T gates can easily be made fault-tolerant but the T gate is very costly to implement. The small number of qubits available in existing quantum computers adds another constraint on quantum circuits. As a result, reducing T-count and qubit cost have become important optimization goals. The design of quantum circuits for Integer Division has caught the attention of researchers and designs have been proposed in the literature. However, these designs suffer from excessive T gate and qubit costs. Many of these designs also produce significant garbage output resulting in additional qubit and T gate costs to eliminate these outputs. In this work, we propose two quantum Integer Division circuits. The first proposed quantum Integer Division circuit is based on the restoring Division algorithm and the second proposed design implements the non-restoring Division algorithm. Both proposed designs are optimized in terms of T-count, T-depth and qubits. Both proposed quantum circuit designs are based on (i) a quantum subtractor, (ii) a quantum adder-subtractor circuit, and (iii) a novel quantum conditional addition circuit. Our proposed restoring Division circuit achieves average T-count savings from $79.03 \%$ to $91.69 \%$ compared to the existing works. Our proposed non-restoring Division circuit achieves average T-count savings from $49.75 \%$ to $90.37 \%$ compared to the existing works. Further, both our proposed designs have linear T-depth.
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quantum circuit designs of Integer Division optimizing t count and t depth
2017 IEEE International Symposium on Nanoelectronic and Information Systems (iNIS), 2017Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Keith A. Britt, Edgard Munozcoreas, Travis S. HumbleAbstract: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.
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iNIS - Quantum Circuit Designs of Integer Division Optimizing T-Count and T-Depth
2017 IEEE International Symposium on Nanoelectronic and Information Systems (iNIS), 2017Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreas, Keith A. Britt, Travis S. HumbleAbstract: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.
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Quantum Circuit Design of Integer Division Optimizing Ancillary Qubits and T-Count
arXiv: Quantum Physics, 2016Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreasAbstract:In this paper, we present Clifford+T gates based quantum circuit design of Integer Division having $n$ ancillary qubits. The proposed quantum circuit is based on restoring Division algorithm. The proposed quantum circuit of Integer Division consists of (i) quantum circuitry of conditional addition operation, (ii) quantum circuitry of Integer subtraction. To design ancillary and T-count optimized design of quantum Integer Division, the optimized quantum circuit design of Integer conditional addition operation and Integer subtraction are presented. The proposed quantum Integer Division circuitry has 50\% improvement in terms of ancillary qubits, and 90\% improvement in terms of T-count compared to the existing design of Integer quantum Division based on quantum fourier transform.
Thijs Veugen - One of the best experts on this subject based on the ideXlab platform.
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content based recommendations with approximate Integer Division
International Conference on Acoustics Speech and Signal Processing, 2015Co-Authors: Thijs Veugen, Zekeriya ErkinAbstract:Recommender systems have become a vital part of e-commerce and online media applications, since they increased the profit by generating personalized recommendations to the customers. As one of the techniques to generate recommendations, content-based algorithms offer items or products that are most similar to those previously purchased or consumed. These algorithms rely on user-generated content to compute accurate recommendations. Collecting and storing such data, which is considered to be privacy-sensitive, creates serious privacy risks for the customers. A number of threats to mention are: service providers could process the collected rating data for other purposes, sell them to third parties, or fail to provide adequate physical security. In this paper, we propose a cryptographic approach to protect the privacy of individuals in a recommender system. Our proposal is founded on homomorphic encryption, which is used to obscure the private rating information of the customers from the service provider. Our proposal explores basic and efficient cryptographic techniques to generate private recommendations using a server-client model, which neither relies on (trusted) third parties, nor requires interaction with peer users. The main strength of our contribution lies in providing a highly efficient Division protocol which enables us to hide commercially sensitive similarity values, which was not the case in previous works.
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ICASSP - Content-based recommendations with approximate Integer Division
2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015Co-Authors: Thijs Veugen, Zekeriya ErkinAbstract:Recommender systems have become a vital part of e-commerce and online media applications, since they increased the profit by generating personalized recommendations to the customers. As one of the techniques to generate recommendations, content-based algorithms offer items or products that are most similar to those previously purchased or consumed. These algorithms rely on user-generated content to compute accurate recommendations. Collecting and storing such data, which is considered to be privacy-sensitive, creates serious privacy risks for the customers. A number of threats to mention are: service providers could process the collected rating data for other purposes, sell them to third parties, or fail to provide adequate physical security. In this paper, we propose a cryptographic approach to protect the privacy of individuals in a recommender system. Our proposal is founded on homomorphic encryption, which is used to obscure the private rating information of the customers from the service provider. Our proposal explores basic and efficient cryptographic techniques to generate private recommendations using a server-client model, which neither relies on (trusted) third parties, nor requires interaction with peer users. The main strength of our contribution lies in providing a highly efficient Division protocol which enables us to hide commercially sensitive similarity values, which was not the case in previous works.
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Encrypted Integer Division and secure comparison
International Journal of Applied Cryptography, 2014Co-Authors: Thijs VeugenAbstract:When processing data in the encrypted domain, homomorphic encryption can be used to enable linear operations on encrypted data. Integer Division of encrypted data however requires an additional protocol between the client and the server and will be relatively expensive. We present new solutions for dividing encrypted data in the semi-honest model using homomorphic encryption and additive blinding, having low computational and communication complexity. In most of our protocols we assume the divisor is publicly known. The Division result is not only computed exactly, but may also be approximated leading to further improved performance. The idea of approximating the result of an Integer Division is extended to similar results for secure comparison, secure minimum, and secure maximum in the client-server model, yielding new efficient protocols with demonstrated application in biometrics. The exact minimum protocol is shown to outperform existing approaches.
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encrypted Integer Division
International Workshop on Information Forensics and Security, 2010Co-Authors: Thijs VeugenAbstract:When processing signals in the encrypted domain, homomorphic encryption can be used to enable linear operations on encrypted data. Integer Division of encrypted data however requires an additional protocol with the server and will be relatively expensive. We present new solutions for dividing encrypted data, having low computational complexity. Two protocols for computing exact Division, and two for approximating the Division result.
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WIFS - Encrypted Integer Division
2010 IEEE International Workshop on Information Forensics and Security, 2010Co-Authors: Thijs VeugenAbstract:When processing signals in the encrypted domain, homomorphic encryption can be used to enable linear operations on encrypted data. Integer Division of encrypted data however requires an additional protocol with the server and will be relatively expensive. We present new solutions for dividing encrypted data, having low computational complexity. Two protocols for computing exact Division, and two for approximating the Division result.
Edgard Munoz-coreas - One of the best experts on this subject based on the ideXlab platform.
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Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth
IEEE Transactions on Emerging Topics in Computing, 2021Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreas, Travis S. HumbleAbstract:Quantum circuits for mathematical functions such as Division are necessary to use quantum computers for scientific computing. In this work, we propose two quantum Integer Division circuits. The first proposed quantum Integer Division circuit is based on the restoring Division algorithm and the second proposed design implements the non-restoring Division algorithm. Both proposed designs are optimized in terms of T-count, T-depth and qubits. Both proposed quantum circuit designs are based on (i) a quantum subtractor, (ii) a quantum adder-subtractor circuit, and (iii) a novel quantum conditional addition circuit. Our proposed restoring Division circuit achieves average T-count savings from 79.03% to 91.69% compared to the existing works. Our proposed non-restoring Division circuit achieves average Tcount savings from 49.75% to 90.37% compared to the existing works. Further, both our proposed designs have linear T-depth. We also illustrated the application of the proposed quantum Division circuits in quantum image processing with a case study of quantum bilinear interpolation.
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Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth
arXiv: Quantum Physics, 2018Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreas, Travis S. HumbleAbstract:Quantum circuits for mathematical functions such as Division are necessary to use quantum computers for scientific computing. Quantum circuits based on Clifford+T gates can easily be made fault-tolerant but the T gate is very costly to implement. The small number of qubits available in existing quantum computers adds another constraint on quantum circuits. As a result, reducing T-count and qubit cost have become important optimization goals. The design of quantum circuits for Integer Division has caught the attention of researchers and designs have been proposed in the literature. However, these designs suffer from excessive T gate and qubit costs. Many of these designs also produce significant garbage output resulting in additional qubit and T gate costs to eliminate these outputs. In this work, we propose two quantum Integer Division circuits. The first proposed quantum Integer Division circuit is based on the restoring Division algorithm and the second proposed design implements the non-restoring Division algorithm. Both proposed designs are optimized in terms of T-count, T-depth and qubits. Both proposed quantum circuit designs are based on (i) a quantum subtractor, (ii) a quantum adder-subtractor circuit, and (iii) a novel quantum conditional addition circuit. Our proposed restoring Division circuit achieves average T-count savings from $79.03 \%$ to $91.69 \%$ compared to the existing works. Our proposed non-restoring Division circuit achieves average T-count savings from $49.75 \%$ to $90.37 \%$ compared to the existing works. Further, both our proposed designs have linear T-depth.
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iNIS - Quantum Circuit Designs of Integer Division Optimizing T-Count and T-Depth
2017 IEEE International Symposium on Nanoelectronic and Information Systems (iNIS), 2017Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreas, Keith A. Britt, Travis S. HumbleAbstract: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.
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Quantum Circuit Design of Integer Division Optimizing Ancillary Qubits and T-Count
arXiv: Quantum Physics, 2016Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreasAbstract:In this paper, we present Clifford+T gates based quantum circuit design of Integer Division having $n$ ancillary qubits. The proposed quantum circuit is based on restoring Division algorithm. The proposed quantum circuit of Integer Division consists of (i) quantum circuitry of conditional addition operation, (ii) quantum circuitry of Integer subtraction. To design ancillary and T-count optimized design of quantum Integer Division, the optimized quantum circuit design of Integer conditional addition operation and Integer subtraction are presented. The proposed quantum Integer Division circuitry has 50\% improvement in terms of ancillary qubits, and 90\% improvement in terms of T-count compared to the existing design of Integer quantum Division based on quantum fourier transform.
T. S. S. Varun - One of the best experts on this subject based on the ideXlab platform.
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Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth
IEEE Transactions on Emerging Topics in Computing, 2021Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreas, Travis S. HumbleAbstract:Quantum circuits for mathematical functions such as Division are necessary to use quantum computers for scientific computing. In this work, we propose two quantum Integer Division circuits. The first proposed quantum Integer Division circuit is based on the restoring Division algorithm and the second proposed design implements the non-restoring Division algorithm. Both proposed designs are optimized in terms of T-count, T-depth and qubits. Both proposed quantum circuit designs are based on (i) a quantum subtractor, (ii) a quantum adder-subtractor circuit, and (iii) a novel quantum conditional addition circuit. Our proposed restoring Division circuit achieves average T-count savings from 79.03% to 91.69% compared to the existing works. Our proposed non-restoring Division circuit achieves average Tcount savings from 49.75% to 90.37% compared to the existing works. Further, both our proposed designs have linear T-depth. We also illustrated the application of the proposed quantum Division circuits in quantum image processing with a case study of quantum bilinear interpolation.
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Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth
arXiv: Quantum Physics, 2018Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreas, Travis S. HumbleAbstract:Quantum circuits for mathematical functions such as Division are necessary to use quantum computers for scientific computing. Quantum circuits based on Clifford+T gates can easily be made fault-tolerant but the T gate is very costly to implement. The small number of qubits available in existing quantum computers adds another constraint on quantum circuits. As a result, reducing T-count and qubit cost have become important optimization goals. The design of quantum circuits for Integer Division has caught the attention of researchers and designs have been proposed in the literature. However, these designs suffer from excessive T gate and qubit costs. Many of these designs also produce significant garbage output resulting in additional qubit and T gate costs to eliminate these outputs. In this work, we propose two quantum Integer Division circuits. The first proposed quantum Integer Division circuit is based on the restoring Division algorithm and the second proposed design implements the non-restoring Division algorithm. Both proposed designs are optimized in terms of T-count, T-depth and qubits. Both proposed quantum circuit designs are based on (i) a quantum subtractor, (ii) a quantum adder-subtractor circuit, and (iii) a novel quantum conditional addition circuit. Our proposed restoring Division circuit achieves average T-count savings from $79.03 \%$ to $91.69 \%$ compared to the existing works. Our proposed non-restoring Division circuit achieves average T-count savings from $49.75 \%$ to $90.37 \%$ compared to the existing works. Further, both our proposed designs have linear T-depth.
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quantum circuit designs of Integer Division optimizing t count and t depth
2017 IEEE International Symposium on Nanoelectronic and Information Systems (iNIS), 2017Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Keith A. Britt, Edgard Munozcoreas, Travis S. HumbleAbstract: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.
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iNIS - Quantum Circuit Designs of Integer Division Optimizing T-Count and T-Depth
2017 IEEE International Symposium on Nanoelectronic and Information Systems (iNIS), 2017Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreas, Keith A. Britt, Travis S. HumbleAbstract: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.
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Quantum Circuit Design of Integer Division Optimizing Ancillary Qubits and T-Count
arXiv: Quantum Physics, 2016Co-Authors: Himanshu Thapliyal, T. S. S. Varun, Edgard Munoz-coreasAbstract:In this paper, we present Clifford+T gates based quantum circuit design of Integer Division having $n$ ancillary qubits. The proposed quantum circuit is based on restoring Division algorithm. The proposed quantum circuit of Integer Division consists of (i) quantum circuitry of conditional addition operation, (ii) quantum circuitry of Integer subtraction. To design ancillary and T-count optimized design of quantum Integer Division, the optimized quantum circuit design of Integer conditional addition operation and Integer subtraction are presented. The proposed quantum Integer Division circuitry has 50\% improvement in terms of ancillary qubits, and 90\% improvement in terms of T-count compared to the existing design of Integer quantum Division based on quantum fourier transform.