Notes on Quantum Computation and Information

We discuss fundamentals of quantum computing and information - quantum gates, circuits, algorithms, theorems, error correction, and provide collection of QISKIT programs and exercises for the interested reader.Comment: v2: 86 pages, 97 references. Refined the text, fixed several typos, added some text on continuous variables, and added few solved example problems. v1: 72 pages, 76 references. Suggestions, comments, and corrections are very welcome

Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations

We present a quantum algorithm based on the Generalized Quantum Master Equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system-bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining degrees of freedom is used as input to calculate the corresponding non-unitary propagator. We demonstrate how the Sz.-Nagy dilation theorem can be employed to transform the non-unitary propagator into a unitary one in a higher-dimensional Hilbert space, which can then be implemented on quantum circuits of NISQ computers. We validate our quantum algorithm as applied to the spin-boson benchmark model by analyzing the impact of the quantum circuit depth on the accuracy of the results when the subset is limited to the diagonal elements of the reduced density matrix. Our findings demonstrate that our approach yields reliable results on NISQ IBM computers.Comment: 47 pages, 10 figures, updated to the most current version of the manuscrip

Quantum Vulnerability Analysis to Guide Robust Quantum Computing System Design

While quantum computers provide exciting opportunities for information processing, they currently suffer from noise during computation that is not fully understood. Incomplete noise models have led to discrepancies between quantum program success rate (SR) estimates and actual machine outcomes. For example, the estimated probability of success (ESP) is the state-of-the-art metric used to gauge quantum program performance. The ESP suffers poor prediction since it fails to account for the unique combination of circuit structure, quantum state, and quantum computer properties specific to each program execution. Thus, an urgent need exists for a systematic approach that can elucidate various noise impacts and accurately and robustly predict quantum computer success rates, emphasizing application and device scaling. In this article, we propose quantum vulnerability analysis (QVA) to systematically quantify the error impact on quantum applications and address the gap between current success rate (SR) estimators and real quantum computer results. The QVA determines the cumulative quantum vulnerability (CQV) of the target quantum computation, which quantifies the quantum error impact based on the entire algorithm applied to the target quantum machine. By evaluating the CQV with well-known benchmarks on three 27-qubit quantum computers, the CQV success estimation outperforms the estimated probability of success state-of-the-art prediction technique by achieving on average six times less relative prediction error, with best cases at 30 times, for benchmarks with a real SR rate above 0.1%. Direct application of QVA has been provided that helps researchers choose a promising compiling strategy at compile time