# Lowering the T-depth of Quantum Circuits By Reducing the Multiplicative Depth Of Logic Networks

@article{Hner2020LoweringTT, title={Lowering the T-depth of Quantum Circuits By Reducing the Multiplicative Depth Of Logic Networks}, author={Thomas H{\"a}ner and Mathias Soeken}, journal={ArXiv}, year={2020}, volume={abs/2006.03845} }

The multiplicative depth of a logic network over the gate basis $\{\land, \oplus, \neg\}$ is the largest number of $\land$ gates on any path from a primary input to a primary output in the network. We describe a dynamic programming based logic synthesis algorithm to reduce the multiplicative depth in logic networks. It makes use of cut enumeration, tree balancing, and exclusive sum-of-products (ESOP) representations. Our algorithm has applications to cryptography and quantum computing, as a…

## 4 Citations

Alternative Tower Field Construction for Quantum Implementation of the AES S-box

- Computer Science, MathematicsIEEE Transactions on Computers
- 2021

Four methods of trade-off between time and space for the quantum implementation of the AES S-box are proposed, one of which turns out to use the smallest number of qubits among the existing methods, significantly reducing its T -depth.

T-count and T-depth of any multi-qubit unitary

- Mathematics
- 2021

While implementing a quantum algorithm it is crucial to reduce the quantum resources, in order to obtain the desired computational advantage. For most fault-tolerant quantum errorcorrecting codes the…

A Resource Estimation Framework For Quantum Attacks Against Cryptographic Functions: Recent Developments A Resource Estimation Framework For Quantum Attacks Against Cryptographic Functions-Recent Developments

- Computer Science, Mathematics
- 2021

We update our security estimates against quantum adversaries of currently deployed asymmetric (public-key) cryptographic schemes that comprise of the RSA family, as well as symmetric schemes…

A (quasi-)polynomial time heuristic algorithm for synthesizing T-depth optimal circuits

- Computer Science
- 2021

This work uses nested meet-in-the-middle (MITM) technique to develop algorithms for synthesizing provably depth-optimal and T-depth- optimal circuits for exactly implementable unitaries and designs an even more efficient algorithm for synthesized T- depth-Optimal circuits.

## References

SHOWING 1-10 OF 61 REFERENCES

A Logic Synthesis Toolbox for Reducing the Multiplicative Complexity in Logic Networks

- Computer Science, Mathematics2020 Design, Automation & Test in Europe Conference & Exhibition (DATE)
- 2020

This paper presents a logic synthesis toolbox for cryptography and security applications that consists of powerful transformations, namely resubstitution, refactoring, and rewriting, specifically designed to minimize the multiplicative complexity of an XAG.

A multi-start heuristic for multiplicative depth minimization of boolean circuits

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2017

A multi-start heuristic which aims at minimizing the multiplicative depth of boolean circuits and the experimental results show that they are rather powerful.

Reducing the Multiplicative Complexity in Logic Networks for Cryptography and Security Applications

- Computer Science2019 56th ACM/IEEE Design Automation Conference (DAC)
- 2019

This work proposes a logic synthesis algorithm and tool to minimize the number of AND gates in a logic network composed of AND, XOR, and inverter gates and exploits cut enumeration algorithms to explore optimization potentials in local subcircuits.

Quantum circuits for floating-point arithmetic

- Computer ScienceRC
- 2018

This paper provides quantum circuits for floating-point addition and multiplication which are found using two vastly different approaches: to automatically generate circuits from classical Verilog implementations using synthesis tools and to generate and optimize these circuits by hand.

Constant-optimized quantum circuits for modular multiplication and exponentiation

- Computer Science, MathematicsQuantum Inf. Comput.
- 2012

In the context of modular exponentiation, this work offers several constant-factor improvements, as well as an improvement by a constant additive term that is significant for few-qubit circuits arising in ongoing laboratory experiments with Shor's algorithm.

Synthesis of reversible logic circuits

- Computer ScienceIEEE Trans. Comput. Aided Des. Integr. Circuits Syst.
- 2003

In an application important to quantum computing, the synthesis of oracle circuits for Grover's search algorithm are synthesized, and a significant improvement over a previously proposed synthesis algorithm is shown.

Enumerating Optimal Quantum Circuits using Spectral Classification

- Computer Science2020 IEEE International Symposium on Circuits and Systems (ISCAS)
- 2020

An automatically-generated database containing minimal-cost quantum circuits for Boolean functions up to 5 inputs is presented and it is shown that any Boolean function can be derived from the implementation of its class representative without increasing any of the stated cost functions.

Logic Minimization Techniques with Applications to Cryptology

- Computer ScienceJournal of Cryptology
- 2012

The technique can be applied to arbitrary combinational logic problems, and often yields improvements even after optimization by standard methods has been performed, and a special case of the corresponding decision problem is Max SNP-complete, implying limits to its approximability.

Faster Quantum Number Factoring via Circuit Synthesis

- Computer ScienceArXiv
- 2013

A circuit-synthesis procedure exploits spectral properties of multiplication operators and constructs optimized circuits from the traces of the execution of an appropriate GCD algorithm, reducing gate counts and circuit latency by up to 4-5 times.

Reducing the Cost of Implementing AES as a Quantum Circuit

- Computer Science, PhysicsIEEE Transactions on Quantum Engineering
- 2020

This article presents a quantum circuit to implement the S-box of AES and identifies new quantum circuits for all three AES key lengths that can be used to simplify a Grover-based key search for AES.