Research Projects

Quantum computers have a tremendous potential toward solving various real-life problems related to cybersecurity, traffic optimization, weather forecasting etc. Realizing such practical problems requires a large number of qubits, which need to be protected against noise and decoherence for reliable quantum computing. Analogous to classical ECCs, quantum ECCs can be used to protect these quantum states. Fortunately, the theoretical framework for quantum error correction has been well explored. Mapping these theoretical QECCs to encoding and decoding circuits for stabilizer codes can be done through Gottesman's algorithm. These circuits are often large for state-of-the-art QECCs such as LDPC and RS codes. To improve circuit reliability, it is essential to optimize these circuits. However, for large quantum circuits, global optimization is known to be NP-hard. Researchers have tried to explore strategies such as stabilizer overlap, small circuit equivalence rules, graph-based matrix methods, and heuristic approaches toward optimization of quantum circuits. However, a generalized and efficient optimization process does not exist. In this proposal, our first task is to use three strategies to formulate a generalized optimization procedure for large QECC circuits. We will explore various open questions such as optimal division into sub-circuits, greedy algorithm for shortest route between nodes in the graph, detection of overlap patterns etc. We also plan to extend the optimization of QECC circuits to general quantum circuits. As the number of qubits increase, complexity of the optimization procedure scales exponentially. CAD tools are universally used for the optimization of digital circuits in academia and industry. Thus, our second task would be to develop dedicated CAD tools for auto-optimization of quantum circuits, thus streamlining the process. Testing and validating the optimized quantum circuits is a complicated task. IBM Qiskit allows software simulation of quantum circuits. However, the time taken for such simulations scales exponentially depending on the number of qubits involved. Our third task is to build FPGA-based hardware emulators to significantly reduce testing and validation time. If we solve the three tasks, we would be equipped with a robust optimization engine which is fully automated, and uses hardware emulators in tandem for testing and validation. This engine can be used in different fields of quantum computation such as implementation of quantum algorithms, quantum machine learning, quantum chemistry, and quantum cryptography.