Variational quantum algorithms (VQA) based on Hamiltonian simulation represent a specialized class of quantum programs well-suited for near-term quantum computing applications due to its modest resource requirements in terms of qubits and circuit depth. Unlike the conventional single-qubit (1 Q) and two-qubit (2 Q) gate sequence representation, Hamiltonian simulation programs are essentially composed of disciplined subroutines known as Pauli exponentiations (Pauli strings with coefficients) that are variably arranged. To capitalize on these distinct program features, this study introduces PHOENIX, a highly effective compilation framework that primarily operates at the high-level Pauli-based intermediate representation (IR) for generic Hamiltonian simulation programs. PHOENIX exploits global program optimization opportunities to the greatest extent, compared to existing SOTA methods despite some of them also utilizing similar IRs. PHOENIX employs the binary symplectic form (BSF) to formally describe Pauli strings and reformulates IR synthesis as reducing the column weights of BSF by appropriate Clifford transformations. It comes with a heuristic BSF simplification algorithm that searches for the most appropriate 2Q Clifford operators in sequence to maximally simplify the BSF at each step, until the BSF can be directly synthesized by basic 1 Q and 2Q gates. PHOENIX further performs a global ordering strategy in a TETRIS-like fashion for these simplified IR groups, carefully balancing optimization opportunities for gate cancellation, minimizing circuit depth, and managing qubit routing overhead. Experimental results demonstrate that PHOENIX outperforms SOTA VQA compilers across diverse program categories, backend ISAs, and hardware topologies.
Variational quantum algorithms (VQA) based on Hamiltonian simulation represent a specialized class of quantum programs well-suited for near-term quantum computing applications due to its modest resource requirements in terms of qubits and circuit depth. Unlike the conventional single-qubit (1 Q) and two-qubit (2 Q) gate sequence representation, Hamiltonian simulation programs are essentially composed of disciplined subroutines known as Pauli exponentiations (Pauli strings with coefficients) that are variably arranged. To capitalize on these distinct program features, this study introduces PHOENIX, a highly effective compilation framework that primarily operates at the high-level Pauli-based intermediate representation (IR) for generic Hamiltonian simulation programs. PHOENIX exploits global program optimization opportunities to the greatest extent, compared to existing SOTA methods despite some of them also utilizing similar IRs. PHOENIX employs the binary symplectic form (BSF) to formally describe Pauli strings and reformulates IR synthesis as reducing the column weights of BSF by appropriate Clifford transformations. It comes with a heuristic BSF simplification algorithm that searches for the most appropriate 2Q Clifford operators in sequence to maximally simplify the BSF at each step, until the BSF can be directly synthesized by basic 1 Q and 2Q gates. PHOENIX further performs a global ordering strategy in a TETRIS-like fashion for these simplified IR groups, carefully balancing optimization opportunities for gate cancellation, minimizing circuit depth, and managing qubit routing overhead. Experimental results demonstrate that PHOENIX outperforms SOTA VQA compilers across diverse program categories, backend ISAs, and hardware topologies.
Hamiltonian simulation is a core quantum workload, underpinning variational quantum algorithms and Trotterized time evolution. Such programs are expressed as Pauli exponential sequences, exhibiting structural patterns that are highly amenable to high-level synthesis and optimization. Existing compilers, however, fail to fully unlock the optimization potential of their global algebraic structure, even when employing advanced graph- or tableau-based methods.
We present Symphony, a holistic compilation approach built on the binary symplectic form (BSF) representation of Pauli strings. Unlike prior group-wise BSF simplification and path-based Pauli network synthesis, Symphony applies generalized controlled-Pauli Clifford transformations directly to a global BSF tableau, progressively reducing active Pauli rows while adaptively emitting eligible two-qubit blocks in addition to single-qubit rotations in a forward Clifford frame. Following algebraic simplification, Symphony performs a causality-preserving block rescheduling heuristic that respects frame-induced dependencies while exposing extensive two-qubit block parallelism opportunities. This streamlined compilation style comprehensively exploits simultaneous simplification and commutativity opportunities, achieving efficient global optimization without relying on computationally expensive heuristics or long-horizon searches. Across the generic Hamiltonian simulation benchmarks in HamLib, Symphony achieves average reductions of 59% in two-qubit gate count and 91% in circuit depth. It Pareto-dominates prior state-of-the-art compilers, requiring 1.17--1.58× fewer two-qubit gates and especially shrinking two-qubit circuit depth by a substantial factor of 1.87--5.67× on average.
The quantum simulation kernel is an important subroutine appearing as a very long gate sequence in many quantum programs. In this paper, we propose Paulihedral, a block-wise compiler framework that can deeply optimize this subroutine by exploiting high-level program structure and optimization opportunities. Paulihedral first employs a new Pauli intermediate representation that can maintain the high-level semantics and constraints in quantum simulation kernels. This naturally enables new large-scale optimizations that are hard to implement at the low gate-level. In particular, we propose two technology-independent instruction scheduling passes, and two technology-dependent code optimization passes which reconcile the circuit synthesis, gate cancellation, and qubit mapping stages of the compiler. Experimental results show that Paulihedral can outperform state-of-the-art compiler infrastructures in a wide-range of applications on both near-term superconducting quantum processors and future fault-tolerant quantum computers.
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 42.6% 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.
The quantum simulation kernel is an important subroutine appearing as a very long gate sequence in many quantum programs. In this paper, we propose Paulihedral, a block-wise compiler framework that can deeply optimize this subroutine by exploiting high-level program structure and optimization opportunities. Paulihedral first employs a new Pauli intermediate representation that can maintain the high-level semantics and constraints in quantum simulation kernels. This naturally enables new large-scale optimizations that are hard to implement at the low gate-level. In particular, we propose two technology-independent instruction scheduling passes, and two technology-dependent code optimization passes which reconcile the circuit synthesis, gate cancellation, and qubit mapping stages of the compiler. Experimental results show that Paulihedral can outperform state-of-the-art compiler infrastructures in a wide-range of applications on both near-term superconducting quantum processors and future fault-tolerant quantum computers.
Abstract Quantum simulation on noisy intermediate-scale quantum (NISQ) hardware is limited by short coherence time and gate errors. We present a universal variational compilation optimization method (VCOM) that directly leverages the native gate set of trapped-ion processors, namely single-qubit rotations and global Ising-type XX interactions, to construct shallow circuits for simulating molecular Hamiltonians. Specifically, VCOM employs a hybrid optimization strategy combining genetic algorithms with gradient-based refinement to compile Pauli string evolution operators e −i Pt , thereby substantially reducing circuit depth and multi-qubit gate overhead in Hamiltonian simulation. Applied to hydrogen chains, the compiled circuits achieve fidelities comparable to standard decompositions while reducing the proportion of two-qubit operations to only 1.9%–4.6% of the total native gates, a significant improvement over the standard second-order Trotter–Suzuki product formula. Under experimentally motivated laser-intensity and phase-noise models, the proposed scheme maintains high fidelity and exhibits significantly slower degradation than direct native gate decompositions of conventional circuits. These results establish native-gate-based variational compilation as a scalable and practical approach for digital quantum simulation on trapped-ion platforms, with potential extensions to strongly correlated systems and non-equilibrium dynamics.
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.