# Improved Low-Depth SHA3 Quantum Circuit for Fault-Tolerant Quantum Computers
## 1 Introduction  
As the world evolves into the information age, data encryption is essential to protect digital content. Currently, digital content is protected through symmetric-key cryptography (e.g., the Advanced Encryption Standard (AES)) and public-key cryptography (e.g., Riverst-Shamir-Adleman (RSA), Elliptic Curve Cryptography (ECC)). With the unexpected rapid development in quantum computers, the security of modern cryptography against quantum algorithms has become unclear. [PERSON]'s algorithm, proposed by [PERSON] in 1996 [1], is known to accelerate brute-force attacks and pre-image attacks on symmetric-key cryptography and hash functions. [PERSON]'s algorithm, proposed by [PERSON] in 1994 [2], is known to be able to solve the basic problems of existing public-key cryptography systems, such as factorization and discrete logarithms, in polynomial time. In the past, quantum computers were an abstract concept, but many companies have recently established fault-tolerant quantum computers, showing the possibility of their use in practical applications. To operate a quantum computer, it is necessary to provide certain quantum resources (i.e., a certain number of qubits, quantum gates) that are required for operation. When quantum resources meet the requirements of quantum algorithms for a target cryptographic attack, the cryptography is considered to be no longer effective in data protection. In order to resolve this issue, symmetric-key cryptography increases the key size, and the hash function increases the output length. In the case of public-key cryptography, the current system should be replaced with other post-quantum cryptography standards. It is also important to establish an efficient security system for symmetric-key cryptography and hash functions by finding the minimum security parameters that ensure a certain level of security for fault-tolerant quantum computers. This can be achieved by estimatingthe resources required for an attack through the implementation of quantum circuits for symmetric-key cryptography and hash functions. Since a quantum computer operates using the quantum mechanical phenomena of qubits, it is important to preserve the integrity of the qubit state in the operation. Qubit data can be corrupted when the value of an unstable qubit fluctuates during calculation due to the nature of high noise rates. To be operational, a fault-tolerant quantum computer should tolerate appropriate errors, error correction, and error detection for unstable qubits. Various studies have been conducted regarding these tasks [3; 4; 5; 6]. The number of qubits and the quantum circuit depth are generally inversely proportional to each other in a quantum circuit implementation. When implementing a quantum circuit, two methods can be considered. One can reduce the depth of a quantum circuit by increasing the number of qubits, or one can reduce the number of qubits by increasing the depth of the quantum circuit. In the era of noisy intermediate-scale quantum (NISQ), quantum computers are not yet a stable technology [7]. For this reason, it is difficult to determine which is the more efficient and optimized method for implementing a quantum circuit. However, researchers need to conduct research in all aspects, and this factor is likely to be discussed again when quantum computers become more realistic. Approaches that increase the number of qubits and decrease the quantum circuit depth are more suitable in terms of optimizing the noise of the quantum circuit. As the depth of the quantum circuit increases, the operation time also increases, which affects the increase in the error rate of the quantum circuit. With this research aim, this paper presents an improved low-depth SHA3 quantum circuit for fault-tolerant quantum computers to reduce errors. Error detection and correction are essential for fault-tolerant quantum computers, and errors increase proportionally with depth.