Related papers: Minimizing CNOT-count in quantum circuit of the ex…
The elliptic curve discrete logarithm problem is of fundamental importance in public-key cryptography. It is in use for a long time. Moreover, it is an interesting challenge in computational mathematics. Its solution is supposed to provide…
Works on quantum computing and cryptanalysis has increased significantly in the past few years. Various constructions of quantum arithmetic circuits, as one of the essential components in the field, has also been proposed. However, there…
We use Shor's algorithm for the computation of elliptic curve private keys as a case study for resource estimates in the silicon-photonics-inspired active-volume architecture. Here, a fault-tolerant surface-code quantum computer consists of…
In recent years, quantum computing has started to demonstrate superior efficiency to classical computing. In quantum computing, quantum circuits that implement specific quantum algorithms are usually not directly executable on quantum…
The Discrete Logarithm Problem (DLP) for elliptic curves has been extensively studied since, for instance, it is the core of the security of cryptosystems like Elliptic Curve Cryptography (ECC). In this paper, we present an attack to the…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
We consider how to optimize memory use and computation time in operating a quantum computer. In particular, we estimate the number of memory qubits and the number of operations required to perform factorization, using the algorithm…
Cat qubits provide appealing building blocks for quantum computing. They exhibit a tunable noise bias yielding an exponential suppression of bit flips with the average photon number and a protection against the remaining phase errors can be…
Quantum computers pose a fundamental threat to widely deployed public-key cryptosystems, such as RSA and ECC, by enabling efficient integer factorization using Shor's algorithm. Theoretical resource estimates suggest that 2048-bit RSA keys…
We heuristically show that Shor's algorithm for computing general discrete logarithms achieves an expected success probability of approximately 60% to 82% in a single run when modified to enable efficient implementation with the…
While mapping a quantum circuit to the physical layer one has to consider the numerous constraints imposed by the underlying hardware architecture. Connectivity of the physical qubits is one such constraint that restricts two-qubit…
Typical circuit implementations of Shor's algorithm involve controlled rotation gates of magnitude $\pi/2^{2L}$ where $L$ is the binary length of the integer N to be factored. Such gates cannot be implemented exactly using existing…
Quantum computing is expected to become a foundational technology for solving problems that exceed the capabilities of classical systems. As quantum algorithms and hardware technologies continue to advance, the need for scalable…
Compiling quantum circuits to account for hardware restrictions is an essential part of the quantum computing stack. Circuit compilation allows us to adapt algorithm descriptions into a sequence of operations supported by real quantum…
Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…
Elliptic curves are planar curves which can be used to define an abelian group. The efficient computation of discrete logarithms over this group is a longstanding problem relevant to cryptography. It may be possible to efficiently compute…
Specific quantum algorithms exist to-in theory-break elliptic curve cryptographic protocols. Implementing these algorithms requires designing quantum circuits that perform elliptic curve arithmetic. To accurately judge a cryptographic…
Decoherence -- in the current physical implementations of quantum computers -- makes depth reduction a vital task in quantum-circuit design. Moore and Nilsson (SIAM Journal of Computing, 2001) demonstrated that additional qubits -- known as…
In recent years, advancements in quantum chip technology, such as Willow, have contributed to reducing quantum computation error rates, potentially accelerating the practical adoption of quantum computing. As a result, the design of quantum…
Shor's algorithm is one of the most prominent quantum algorithms, yet finding efficient implementations remains an active research challenge. While many approaches focus on low-level modular arithmetic optimizations, a broader perspective…