Quantum Information Processing最新文献

The substitution box (S-box) is often used as the only nonlinear component in symmetric-key ciphers, leading to a significant impact on the implementation performance of ciphers in both classical and quantum application scenarios by S-box circuits. Taking the Pauli-X gate, the CNOT gate, and the Toffoli gate (i.e., the NCT gate set) as the underlying logic gates, this work investigates the quantum circuit implementation of S-boxes based on the SAT solver. Firstly, we propose encoding methods of the logic gates and the NCT-based circuit, based on which we construct STP models for implementing S-boxes. By applying the proposed models to the S-boxes of several well-known cryptographic algorithms, we construct optimal implementations with different criteria for the 4-bit S-boxes and provide the implementation bounds of different criteria for the 5-bit S-boxes. Since S-boxes in the same affine equivalence class share most of the important properties, we then build STP models to further investigate optimizing S-box circuits based on affine equivalence. According to the applications, for almost all the tested 4-bit S-boxes, there always exists an equivalent S-box that can be implemented with half the number of logic gates. Besides, we encode some important cryptographic properties and construct STP models to design S-boxes with given criteria configurations on implementation and properties. As an application, we find an S-box with the same cryptographic properties as the S-box of KECCAK that can be implemented with only 5 NCT gates, even though the application of our models indicates that implementing the KECCAK S-box requires more than 9 NCT gates. Notably, the inputs of the proposed models are tweakable, which makes the models possess some functions not currently available in the public tools for constructing optimized NCT-based circuits for S-boxes.

The sum of quantum computing errors is the key element both for the estimation and control of errors in quantum computing and for its statistical study. In this article, we analyze the sum of two independent quantum computing errors in an (n-)qubit and obtain a formula for the fidelity of the sum of these errors. We prove this result for isotropic quantum computing errors and conjecture that it also holds true for general quantum computing errors.

The Quadratic Assignment Problem (QAP) is an NP-hard fundamental combinatorial optimization problem introduced by Koopmans and Beckmann in 1957. The problem is to assign n facilities to n different locations with the goal of minimizing the cost of the total distances between facilities weighted by the corresponding flows. We initiate the study of using Rydberg arrays to find optimal solutions to the QAP and provide a complementing circuit theory to facilitate an easy representation of other hard problems. We provide an algorithm for finding valid and optimal solutions to the QAP using Rydberg arrays.

In this paper, we use generalized Reed–Solomon (GRS) codes as block codes to construct classical convolutional codes and classical convolutional GRS codes with arbitrary memory and flexible degrees are derived. Particularly, for unit-memory and double-memory, some of the convolutional GRS codes are exactly convolutional maximum-distance-separable (MDS) codes. From the resulting convolutional GRS codes, under Euclidean and Hermitian inner products, quantum convolutional codes are obtained, respectively. A connection between quantum convolutional codes and GRS codes is also established.

The variational quantum eigensolver (VQE) is a key algorithm for near-term quantum computers, yet its performance is often limited by the classical optimization of circuit parameters. We propose using the velocity Verlet algorithm, inspired by classical molecular dynamics, to address this challenge. By introducing an inertial “velocity” term, our method efficiently explores complex energy landscapes. We compare its performance against standard optimizers on H₂ and LiH molecules. For H₂, our method achieves chemical accuracy with fewer quantum circuit evaluations than L-BFGS-B. For LiH, it attains the lowest final energy, demonstrating its potential for high-accuracy VQE simulations.

Two-way quantum key distribution (TWQKD) holds great potential for achieving high secure key rates over a certain transmission distance range. However, in practice, flaws in measurement detectors (the primary source of security loopholes) in TWQKD are vulnerable to side-channel attacks, potentially leading to undetectable key leakage. To tackle this problem and enhance the key performance of TWQKD, this paper introduces a measurement-device-independent high-dimensional TWQKD protocol (MDI-HD-TWQKD). The security formula for this protocol is derived, and its key performances are simulated under an imperfect devices model based on current technology. The results indicate that TWQKD can deliver high performance when utilizing high-dimensional sources in the measurement-device-independent scenario.

In this paper, we have investigated the features of tripartite quantum-memory-assisted entropic uncertainty (tQMA-EU) and its two corresponding lower bounds in three-qubit Heisenberg XXZ spin chain model with Dzyaloshinskii–Moriya (DM) interaction and Kaplan–Shekhtman–Entin–Wohlman–Aharony (KSEA) interaction. The results show that, when the DM and KSEA interaction are taken account, the Dolatkhah’s lower bound is always equal to the tQMA-EU and remains higher than the Ming’s lower bound in both ferromagnetic and antiferromagnetic cases. The increasing of DM and KSEA interactions can effectively reduce the value of tQMA-EU, the varying behaviors of tQMA-EU with respect to DM and KSEA interactions from positive and negative intervals demonstrate central symmetry. Particularly, in ferromagnetic case, this reduction effect is more pronounced than that in antiferromagnetic case. In addition, the dynamical features of Dolatkhah’s lower bound and Ming’s lower bound with respect to the spin chain systemic parameters display distinct differences in the ferromagnetic and antiferromagnetic cases. Specifically, in the ferromagnetic case and with weak DM interaction, during the lower temperature range, under the influence of the KSEA interaction and under an external magnetic field, the Dolatkhah’s lower bound dosen’t negatively correlated to tripartite negativity quantum correlation (mathcal {N}_{ABC}). in contrast, the dynamics of Ming’s lower bound show negative-correlated to (mathcal {N}_{ABC}).

We address the issue of multi-shot discrimination between two qubit channels by invoking a simple adaptive protocol that employs Helstrom measurement at each step and classical information feedforward, beside separable inputs. We contrast the performance of Bayesian and Markovian strategies. We show that the former is only slightly advantageous and for a limited parameters’ region.

One of the key operations in various quantum algorithms, including Grover’s algorithm, is the multi-controlled Toffoli (MCT) gate. This work proposes optimal design techniques for the MCT gate using the conditionally clean ancillae strategy, assuming that an arbitrary number of clean ancillae are available. We consider two primary cases: first, when only a single clean ancilla is available; and second, when the number of clean ancillae is (mathcal {O}(n)), where n is the number of controls in the MCT gate. For the case of a single clean ancilla, we propose a novel design method that achieves better efficiency compared to a previous approach. While prior work yields a Toffoli-depth of (mathcal {O}(n)), our proposed method reduces the Toffoli-depth to (mathcal {O}(sqrt{n})). Moreover, by employing this new technique as a subroutine within previously proposed methods for the cases of two or three clean ancillae, we demonstrate both logically and empirically an improvement in time complexity. Additionally, prior work addressed optimal designs only when the number of clean ancillae was up to approximately (log n), without providing efficient strategies beyond this regime. In this study, we also present efficient MCT gate constructions when a sufficiently large number of clean ancillae are available. We confirm, both theoretically and empirically, that the Toffoli-depth decreases as the number of clean ancillae increases. In conclusion, this work highlights that the optimal MCT design strategy depends on the availability of clean ancillae. It also indirectly suggests a threshold point at which the optimal design strategy transitions, depending on the number of ancillae provided.

In this work, we consider a novel heuristic decomposition algorithm for n-qubit gates that implement specified amplitude permutations on sparse states with m non-zero amplitudes. These gates can be useful as an algorithmic primitive for higher-order algorithms. We demonstrate this by showing how it can be used as a building block for a novel sparse state preparation algorithm, Cluster Swaps, which is able to significantly reduce CX gate count compared to alternative methods of state preparation considered in this paper when the target states are clustered, i.e., such that there are many pairs of non-zero amplitude basis states whose Hamming distance is 1. Cluster Swaps can be useful for amplitude encoding of sparse data vectors in quantum machine learning applications.