Distributed and Approximate Quantum Circuits for Noise Resilience and Security

Quantum computing promises to solve complex computational problems that classical computers struggle to solve efficiently. Quantum arithmetic circuits serve as essential building blocks among the quantum circuits necessary to implement quantum algorithms like quantum approximate optimization, Harrow–Hassidim–Lloyd (HHL), and quantum cryptanalysis. However, the Noisy Intermediate Scale Quantum (NISQ) era quantum computers that are available today face significant challenges like noise, decoherence, and low quantum gate fidelity. They have limited qubits and connectivity, restricting the complexity and scalability of quantum circuits. Attackers can utilize these issues to introduce critical vulnerabilities, such as crosstalk, stuck at 0/1 attacks, and errors in state preparation and quantum gates to deduce quantum states or potentially inject faults. This work focuses on resolving these challenges for quantum arithmetic circuits using alternate computing paradigms, such as distributed quantum computing and approximate computing, to create scalable quantum arithmetic circuits suitable for both NISQ and Fault Tolerant Quantum (FTQ) machines. This work presents distributed quantum arithmetic based on the Residue Number System (RNS), which distributes quantum addition or multiplication across multiple quantum modulo circuits, allowing for parallel execution over multiple jobs or quantum computers. RNS-based Distributed Quantum Addition (DQA) and multiplication offer multiple advantages like lower overall depth and scalability beyond the existing qubit capacity. To enable RNS based distributed quantum arithmetic, this work proposes: i) a quantum carry-lookahead modulo (2n - 1) adder that operates with logarithmic complexity, in contrast to existing solutions that have linear complexity; ii) quantum modulo (2n + 1) adders; and iii) a quantum modulo (2n + 1) multiplier. We also find DQA superior than non-distributed addition against noise and crosstalk attacks on ion-trap qubits. We then present five Approximate Quantum Adders (AQA) possessing constant depth, that demonstrate superior noise resilience compared to linear depth-based quantum full adders. Three of these AQA also demonstrate attack resilience against state preparation, gate and crosstalk attacks, although the exact adders fare better against the stuck at 0/1 attacks. In conclusion, this work lays the foundation for utilizing alternative computing paradigms to develop higher resilience against noise and attacks in quantum circuits.