Improving quantum algorithms run-time performance involves several strategies such as reducing the quantum gate counts, decreasing the number of measurements, advancement in QPU technology for faster gate operations, or optimizing the classical processing. This work focuses on the latter, specifically reducing classical processing and compilation time via hardware-assisted parameterized circuit execution (PCE) for computing dynamical properties of quantum systems. PCE was previously validated for QCVV protocols, which leverages structural circuit equivalencies. We demonstrate the applicability of this approach to computing dynamical properties of quantum many-body systems using structurally equivalent time evolution circuits, specifically calculating correlation functions of spin models using constant-depth circuits generated via Cartan decomposition. Implementing this for spin-spin correlation functions in Transverse field XY (up to 6-sites) and Heisenberg spin models (up to 3-sites), we observed a run-time reduction of up to$\mathbf{5 0 \%}$compared to standard compilation methods. This highlights the adaptability of time-evolution circuit with hardware-assisted PCE to potentially mitigate the classical bottlenecks in near-term quantum algorithms.
Improving quantum algorithms run-time performance involves several strategies such as reducing the quantum gate counts, decreasing the number of measurements, advancement in QPU technology for faster gate operations, or optimizing the classical processing. This work focuses on the latter, specifically reducing classical processing and compilation time via hardware-assisted parameterized circuit execution (PCE) for computing dynamical properties of quantum systems. PCE was previously validated for QCVV protocols, which leverages structural circuit equivalencies. We demonstrate the applicability of this approach to computing dynamical properties of quantum many-body systems using structurally equivalent time evolution circuits, specifically calculating correlation functions of spin models using constant-depth circuits generated via Cartan decomposition. Implementing this for spin-spin correlation functions in Transverse field XY (up to 6-sites) and Heisenberg spin models (up to 3-sites), we observed a run-time reduction of up to50%compared to standard compilation methods. This highlights the adaptability of time-evolution circuit with hardware-assisted PCE to potentially mitigate the classical bottlenecks in near-term quantum algorithms.
Standard compilers for quantum circuits decompose arbitrary single-qubit gates into a sequence of physical X(pi/2) pulses and virtual-Z phase gates. Consequently, many circuit classes implement different logic operations but have an equivalent structure of physical pulses that only differ by changes in virtual phases. When many structurally-equivalent circuits need to be measured, generating sequences for each circuit is unnecessary and cumbersome, since compiling and loading sequences onto classical control hardware is a primary bottleneck in quantum circuit execution. In this work, we develop a hardware-assisted protocol for executing parameterized circuits on our FPGA-based control hardware, QubiC. This protocol relies on a hardware-software co-design technique in which software identifies structural equivalency in circuits and "peels" off the relevant parameterized angles to reduce the overall waveform compilation time. The hardware architecture then performs real-time "stitching" of the parameters in the circuit to measure circuits that implement a different overall logical operation. This work demonstrates significant speed ups in the total execution time for several different classes of quantum circuits.
Simulation of quantum many-body systems is one of the most promising applications of quantum computers. It is crucial to efficiently implement the time-evolution operator as a quantum circuit to execute such simulations on near-term quantum computing devices with limited computational resources. However, standard approaches such as Trotterization sometimes require a deep quantum circuit, which is hard to implement on near-term quantum computers. Here, we propose a hybrid quantum-classical algorithm, called local subspace variational quantum compilation (LSVQC), for compiling the time-evolution operator of quantum many-body systems. The LSVQC performs a variational optimization to reproduce the action of the target time-evolution operator within a physically reasonable subspace. The optimization is performed for small local subsystems based on the Lieb-Robinson bound, which allows us to execute the cost function evaluation using small-scale quantum devices and/or classical computers. We demonstrate the validity of the LSVQC algorithm through numerical simulations of a simple spin-lattice model and an effective model of a parent compound of cuprate superconductors, Sr 2 CuO 3 , constructed by the downfolding method. It is shown that the LSVQC achieves a 95% reduction of the circuit depth for simulating quantum many-body dynamics compared to the Trotterization at best while maintaining the same computational accuracy. We also demonstrate that the restriction to a subspace leads to a substantial reduction of required resources and improved accuracy compared to the case of considering the entire Hilbert space. Furthermore, we estimate the gate count needed to execute the quantum simulations using the LSVQC on near-term quantum computing architectures in the noisy intermediate-scale or early fault-tolerant quantum computing era. Our estimation suggests that the acceptable physical gate error rate for the LSVQC can be about one order of magnitude larger than that for the Trotterization.
Variational quantum algorithms (VQAs) hold significant promise for solving complex problems across diverse fields. However, their practical implementation on near-term quantum devices is severely hampered by the pervasive effects of quantum noise. Traditional quantum circuit compilation techniques are largely static, failing to account for the unique noise profiles inherent in individual quantum hardware. This paper introduces a novel adaptive quantum circuit compilation framework designed to mitigate these limitations. The core concept centers around dynamically adjusting the circuit layout and gate decomposition in real-time, leveraging measurements of the quantum hardware's noise characteristics to optimize both the accuracy and circuit depth of the compiled quantum circuit. This approach represents a critical step towards unlocking the full potential of VQAs by enabling them to effectively operate within the constraints of noisy quantum computers. The framework incorporates feedback loops for continuous refinement, adapting to evolving noise conditions. The methodology is described, focusing on the key components: noise profiling, adaptive gate decomposition, and circuit re-optimization. Simulation results demonstrate the effectiveness of the adaptive approach in reducing circuit depth and improving the fidelity of VQA computations compared to static compilation methods. This work lays the foundation for robust and efficient VQA execution on future quantum hardware.
Quantum computers hold the promise of solving certain computational problems significantly faster than classical computers. Unlocking the full potential of quantum hardware depends on our ability to efficiently translate high-level quantum algorithms into executable sequences of quantum operations tailored to the specific constraints of a given device, a task known as quantum compilation. Among the most promising applications is the simulation of quantum systems, such as in quantum chemistry, where scalable, error resilient, and experimentally feasible Hamiltonian simulation techniques are essential. In the first part of this thesis, we present recent advances in the field of quantum compilation, emphasizing on efficient gate decomposition and circuit optimization. In particular, we analyze compilation techniques for Clifford circuits and general single-qubit rotations. Clifford operations play a central role in quantum error correction, the characterization of quantum devices and quantum cryptography. We explore asymptotically optimal decomposition methods, including constructions using either two-qubit gates or global entangling operations, the latter being especially well-suited for platforms like trapped ions. For single-qubit unitaries, we discuss approximation schemes that achieve the theoretically optimal scaling of gate count with respect to the desired precision. Beyond gate synthesis, we examine various hardware-aware optimization strategies aimed at reducing circuit depth and gate overhead. These include techniques for qubit routing in systems with limited connectivity, as well as methods for removing redundant operations. The second and primary, scientific contribution of this thesis focuses on implementation of effective many-body interactions on quantum hardware by combining the system’s native dynamics with control operations, which we call Hamiltonian engineering. Motivated by the central role of Hamiltonian simulation in quantum science, we introduce a general and efficient framework for synthesizing arbitrary target Hamiltonians under mild locality constraints. We propose a novel linear programming (LP) approach that computes pulse sequences consisting of single-qubit π or π/2 rotations applied at certain times during free evolution under the system’s native Hamiltonian. Our LP-based framework offers multiple advantages. First, its classical runtime depends only on the number and locality of the interactions in the system Hamiltonian, not directly on the overall system size. Second, we extend the method to include robustness against common error sources such as finite pulse time effects and systematic control errors, leveraging tools from average Hamiltonian theory and robust composite pulses. Our approach enables the efficient realization of high-fidelity Hamiltonian dynamics with minimal experimental overhead. The scalability of the approach are demonstrated through simulations, including the engineering of a random two-body Hamiltonian on a 225 qubit lattice in under a minute of classical preprocessing. In conclusion, this thesis contributes both theoretical insights and practical tools that bridge the gap between algorithm design and experimental implementation in quantum computing. The techniques developed here are directly applicable to a variety of platforms, including trapped ions, neutral atoms, and superconducting circuits. By advancing the frontiers of Hamiltonian engineering, this work enables more efficient, robust, and scalable quantum simulations on nearterm devices. Finally, it brings us closer to realizing quantum technologies, which are possibly capable of solving meaningful problems.
Optimizing quantum circuits by reducing circuit depth is essential for improving the efficiency and scalability of quantum algorithms, particularly as quantum hardware continues to evolve. This can be achieved by restructuring quantum algorithms to allow more parallelism. A compiler is needed to automatically detect and apply these optimizations. In this work, we focus on the optimization of two fundamental quantum subroutines: GHZ state creation and CNOT/CZ chain decomposition. Traditional implementations of these subroutines suffer from linearly increasing circuit depth, which limits scalability. We propose a compiler-driven approach that automatically detects and optimizes these two fundamental quantum subroutines. Our approach reduces circuit depth through constant-depth GHZ state creation, constant depth CZ chain decomposition, and logarithmic depth recursive CNOT chain decomposition, which enhance parallel execution. Performance analysis of benchmarked algorithms shows significant reductions in depth. However, our solution also results in an increased gate count, which makes our optimization a trade-off. The gate count for the CNOT chains is doubled, where logarithmic depth reduction is achieved. The reduced circuit depth results in more efficient algorithms by reducing execution time.
Quantum circuit compilation is a crucial step in the process of executing quantum algorithms on near-term quantum hardware. The challenge lies in translating high-level quantum algorithms, often expressed using universal gate sets, into efficient, gate-level circuits that minimize gate count and circuit depth, thereby reducing error rates and improving execution times. Traditional compilation methods often rely on hand-crafted heuristics or limited search algorithms, failing to fully explore the exponentially large search space of possible circuit transformations. This work proposes an adaptive quantum circuit compilation framework leveraging Bayesian optimization. The system dynamically explores the space of potential circuit transformations, learning to identify optimal compilation strategies through a probabilistic modeling approach. The core claim is that Bayesian optimization can effectively adaptively compile quantum circuits, optimizing for performance and minimizing gate count. The system incorporates a compiler that utilizes Bayesian optimization to explore the vast space of possible quantum circuit transformations, learning to identify the most efficient compilation strategies. The results demonstrate the potential of this approach to significantly reduce the complexity of quantum circuits while maintaining algorithm fidelity.