• Corpus ID: 219530931

# 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}
}
• Published 6 June 2020
• Computer Science
• ArXiv
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…

## Figures and Tables from this paper

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

• Mathematics
npj Quantum Information
• 2022
An algorithm with space and time complexity O and O respectively, where d is the minimum T-depth and c ≥ 2 is a constant, is investigated, which is much better than the complexity of the algorithm by Amy et al.(2013), the previous best with a complexity O is a Constant.

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

• Computer Science, Mathematics
• 2020
. We update our security estimates against quantum adver-saries of currently deployed asymmetric (public-key) cryptographic schemes that comprise of the RSA family, as well as symmetric schemes

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

• Computer Science
IEEE Transactions on Computers
• 2022
Three methods of trade-off between time and space for the quantum implementation of the AES S-box are proposed and one of them turns out to use the smallest number of qubits among the existing methods, significantly reducing its complexity.

### Synthesizing efficient circuits for Hamiltonian simulation

• Physics
• 2022
We provide a new approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of

## References

SHOWING 1-10 OF 59 REFERENCES

### A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits

• Computer Science
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
• 2013
We present an algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speedup over simple brute force

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

• Computer Science, Mathematics
2020 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.

### Applying Grover's Algorithm to AES: Quantum Resource Estimates

• Computer Science
PQCrypto
• 2016
It is established that for all three variants of AES key size 128, 192, and 256i¾źbit that are standardized in FIPS-PUB 197, there are precise bounds for the number of qubits and thenumber of elementary logical quantum gates that are needed to implement Grover's quantum algorithm to extract the key from a small number of AES plaintext-ciphertext pairs.

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

• Computer Science, Mathematics
IACR 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.

### Quantum circuits for floating-point arithmetic

• Computer Science
RC
• 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, Mathematics
Quantum 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 Science
IEEE 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.

### Low-overhead constructions for the fault-tolerant Toffoli gate

Two constructions for the Toffoli gate are presented which substantially reduce resource costs in fault-tolerant quantum computing and a quantum circuit is presented which can detect a single ${\ensuremath{\sigma}}^{z}$ error occurring with probability $p$ in any one of eight $T$ gates required to produce the ToFFoli gate.

### Enumerating Optimal Quantum Circuits using Spectral Classification

• Computer Science
2020 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 Science
Journal 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.