As quantum computers scale, the rise of multi-user and cloud-based quantum platforms can lead to new security challenges. Attacks within shared execution environments become increasingly feasible due to the crosstalk noise that, in combination with quantum computer’s hardware specifications, can be exploited in form of crosstalk attack. Our work pursues crosstalk attack implementation in ion-trap quantum computers. We propose three novel quantum crosstalk attacks designed for ion trap qubits: (i) Alternate CNOT attack (ii) Superposition Alternate CNOT (SAC) attack (iii) Alternate Phase Change (APC) attack. We demonstrate the effectiveness of proposed attacks by conducting noise-based simulations on a commercial 20-qubit ion-trap quantum computer. The proposed attacks achieve an impressive reduction of up to 42.2% in output probability for Quantum Full Adders (QFA) having 6 to 9-qubit output. Finally, we investigate the possibility of mitigating crosstalk attacks by using Residue Number System (RNS) based Parallel Quantum Addition (PQA). We determine that PQA achieves higher attack resilience against crosstalk attacks in the form of 24.3% to 133.5% improvement in output probability against existing Non Parallel Quantum Addition (NPQA). Through our systematic methodology, we demonstrate how quantum properties such as superposition and phase transition can lead to crosstalk attacks and how parallel quantum computing can provide security.

Quantum modular adders are one of the most fundamental yet versatile quantum computation operations. They help implement the functions of higher complexity, such as subtraction and multiplication, which are used in applications, such as quantum cryptanalysis, quantum image processing, and securing communication. To the best of our knowledge, there is no existing design of quantum modulo ($2^{n}+1$) adder (QMA). In this work, we propose four quantum adders targeted specifically for modulo ($2^{n}+1$) addition. These adders can provide both regular and modulo ($2^{n}+1$) sum concurrently, enhancing their application in residue number system-based arithmetic. Our first design, QMA1, is a novel quantum modulo ($2^{n}+1$) adder. The second proposed adder, QMA2, optimizes the utilization of quantum gates within the QMA1, resulting in 37.5% reduced CNOT gate count, 46.15% reduced CNOT depth, and 26.5% decrease in both Toffoli gates and depth. We propose a third adder QMA3 that uses zero resets, a dynamic circuits-based feature that reuses qubits, leading to 25% savings in qubit count. Our fourth design, QMA4, demonstrates the benefit of incorporating additional zero resets to achieve a purer$|0$$\rangle $state, reducing quantum state preparation errors. Notably, we conducted experiments using 5-qubit configurations of the proposed modulo ($2^{n}+1$) adders on the IBM Washington, a 127-qubit quantum computer based on the Eagle R1 architecture, to demonstrate a 28.8% reduction in QMA1’s error of which do the following: 1) 18.63% error reduction happens due to gate/depth reduction in QMA2; 2) 2.53% drop in error due to qubit reduction in QMA3; and 3) 7.64% error decreased due to application of additional zero resets in QMA4.

The "Noisy intermediate-scale quantum" NISQ machine era primarily focuses on mitigating noise, controlling errors, and executing high-fidelity operations, hence requiring shallow circuit depth and noise robustness. Approximate computing is a novel computing paradigm that produces imprecise results by relaxing the need for fully precise output for error-tolerant applications including multimedia, data mining, and image processing. We investigate how approximate computing can improve the noise resilience of quantum adder circuits in NISQ quantum computing. We propose five designs of approximate quantum adders to reduce depth while making them noise-resilient, in which three designs are with carryout, while two are without carryout. We have used novel design approaches that include approximating the Sum only from the inputs (pass-through designs) and having zero depth, as they need no quantum gates. The second design style uses a single CNOT gate to approximate the SUM with a constant depth of O(1). We performed our experimentation on IBM Qiskit on noise models including thermal, depolarizing, amplitude damping, phase damping, and bitflip: (i) Compared to exact quantum ripple carry adder without carryout the proposed approximate adders without carryout have improved fidelity ranging from 8.34% to 219.22%, and (ii) Compared to exact quantum ripple carry adder with carryout the proposed approximate adders with carryout have improved fidelity ranging from 8.23% to 371%. Further, the proposed approximate quantum adders are evaluated in terms of various error metrics.

Quantum Computing is making significant advancements toward creating machines capable of implementing quantum algorithms in various fields, such as quantum cryptography, quantum image processing, and optimization. The development of quantum arithmetic circuits for modulo addition is vital for implementing these quantum algorithms. While it is ideal to use quantum circuits based on fault-tolerant gates to overcome noise and decoherence errors, the current Noisy Intermediate Scale Quantum (NISQ) era quantum computers cannot handle the additional computational cost associated with fault-tolerant designs. Our research aims to minimize circuit depth, which can reduce noise and facilitate the implementation of quantum modulo addition circuits on NISQ machines. This work presents quantum carry-lookahead modulo (2n - 1) adder (QCLMA), which is designed to receive two n-bit numbers and perform their addition with an O(log n) depth. Compared to existing work of O(n) depth, our proposed QCLMA reduces the depth and helps increase the noise fidelity. In order to increase error resilience, we also focus on creating a tree structure based Carry path, unlike the chain based Carry path of the current work. We run experiments on Quantum Computer IBM Cairo to evaluate the performance of the proposed QCLMA against the existing work and define Quantum State Fidelity Ratio (QSFR) to quantify the closeness of the correct output to the top output. When compared against existing work, the proposed QCLMA achieves a 47.21% increase in QSFR for 4-qubit modulo addition showcasing its superior noise fidelity.