Quantum error correction is essential for achieving practical quantum computing but has a significant computational overhead. Among fault-tolerant (FT) gate operations, non-Clifford gates, such as T, are particularly expensive due to their reliance on magic state distillation. These costly T gates appear frequently in FT circuits as many quantum algorithms require arbitrary single-qubit rotations, such as Rx and Rz gates, which must be decomposed into a sequence of T and Clifford gates. In many quantum circuits, Rx and Rz gates can be fused to form a single U3 unitary. However, existing synthesis methods, such as gridsynth, rely on indirect decompositions, requiring separate Rz decompositions that result in a threefold increase in T count.

In recent years, quantum computing has emerged as a transformative force in the field of combinatorial optimization, offering novel approaches to tackling complex problems that have long challenged classical computational methods. Among these, the Quantum Approximate Optimization Algorithm (QAOA) stands out for its potential to efficiently solve the Max-Cut problem, a quintessential example of combinatorial optimization. However, practical application faces challenges due to current limitations on quantum computational resource. Our work optimizes QAOA initialization, using Graph Neural Networks (GNN) as a warm-start technique. This sacrifices affordable computational resource on classical computer to reduce quantum computational resource overhead, enhancing QAOA's effectiveness. Experiments with various GNN architectures demonstrate the adaptability and stability of our framework, highlighting the synergy between quantum algorithms and machine learning. Our findings show GNN's potential in improving QAOA performance, opening new avenues for hybrid quantum-classical approaches in quantum computing and contributing to practical applications.

In this paper, we explore the integration of parameterized quantum pulses with the contextual subspace method. The advent of parameterized quantum pulses marks a transition from traditional quantum gates to a more flexible and efficient approach to quantum computing. Working with pulses allows us to potentially access areas of the Hilbert space that are inaccessible with a CNOT-based circuit decomposition. Compared to solving the complete Hamiltonian via the traditional Variational Quantum Eigensolver (VQE), the computation of the contextual correction generally requires fewer qubits and measurements, thus improving computational efficiency. Plus a Pauli grouping strategy, our framework, SpacePulse, can minimize the quantum resource cost for the VQE and enhance the potential for processing larger molecular structures.

Quantum computing has shown promise in solving complex problems by leveraging the principles of superposition and entanglement. Variational quantum algorithms (VQA) are a class of algorithms suited for near-term quantum computers due to their modest requirements of qubits and depths of computation. This paper introduces Tetris – a compilation framework for VQA applications on near-term quantum devices. Tetris focuses on reducing two-qubit gates in the compilation process since a two-qubit gate has an order of magnitude more significant error and execution time than a single-qubit gate. Tetris exploits unique opportunities in the circuit synthesis stage often overlooked by the state-of-the-art VQA compilers for reducing the number of two-qubit gates. Tetris comes with a refined IR of Pauli string to express such a two-qubit gate optimization opportunity. Moreover, Tetris is equipped with a fast bridging approach that mitigates the hardware mapping cost. Overall, Tetris demonstrates a reduction of up to $41.3 \%$ in CNOT gate counts, $37.9 \%$ in circuit depth, and $\mathbf{4 2. 6 \%}$ in circuit duration for various molecules of different sizes and structures compared with the state-of-the-art approaches. Tetris is open-sourced at this link.

Variational quantum algorithms (VQAs) can potentially solve practical problems using contemporary Noisy Intermediate Scale Quantum (NISQ) computers. VQAs find near-optimal solutions in the presence of qubit errors by classically optimizing a loss function computed by parameterized quantum circuits. However, developing and testing VQAs is challenging due to the limited availability of quantum hardware, their high error rates, and the significant overhead of classical simulations. Furthermore, VQA researchers must pick the right initialization for circuit parameters, utilize suitable classical optimizer configurations, and deploy appropriate error mitigation methods. Unfortunately, these tasks are done in an ad-hoc manner today, as there are no software tools to configure and tune the VQA hyperparameters.

Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States (PEPS) are well-suited for key classes of physical systems and quantum circuits. However, direct contraction of PEPS networks has exponential cost, while approximate algorithms require computations with large tensors. We propose new scalable algorithms and software abstractions for PEPS-based methods, accelerating the bottleneck operation of contraction and refactorization of a tensor subnetwork. We employ randomized SVD with an implicit matrix to reduce cost and memory footprint asymptotically. Further, we develop a distributed-memory PEPS library and study accuracy and efficiency of alternative algorithms for PEPS contraction and evolution on the Stampede2 supercomputer. We also simulate a popular near-term quantum algorithm, the Variational Quantum Eigensolver (VQE), and benchmark Imaginary Time Evolution (ITE), which compute ground states of Hamiltonians.