This paper introduces Fermihedral, a compiler framework focusing on discovering the optimal Fermion-to-qubit encoding for targeted Fermionic Hamiltonians. Fermion-to-qubit encoding is a crucial step in harnessing quantum computing for efficient simulation of Fermionic quantum systems. Utilizing Pauli algebra, Fermihedral redefines complex constraints and objectives of Fermion-to-qubit encoding into a Boolean Satisfiability problem which can then be solved with high-performance solvers. To accommodate larger-scale scenarios, this paper proposed two new strategies that yield approximate optimal solutions mitigating the overhead from the exponentially large number of clauses. Evaluation across diverse Fermionic systems highlights the superiority of Fermihedral, showcasing substantial reductions in implementation costs, gate counts, and circuit depth in the compiled circuits. Real-system experiments on IonQ's device affirm its effectiveness, notably enhancing simulation accuracy.
This paper introduces Fermihedral, a compiler framework focusing on discovering the optimal Fermion-to-qubit encoding for targeted Fermionic Hamiltonians. Fermion-to-qubit encoding is a crucial step in harnessing quantum computing for efficient simulation of Fermionic quantum systems. Utilizing Pauli algebra, Fermihedral redefines complex constraints and objectives of Fermion-to-qubit encoding into a Boolean Satisfiability problem which can then be solved with high-performance solvers. To accommodate larger-scale scenarios, this paper proposed two new strategies that yield approximate optimal solutions mitigating the overhead from the exponentially large number of clauses. Evaluation across diverse Fermionic systems highlights the superiority of Fermihedral, showcasing substantial reductions in implementation costs, gate counts, and circuit depth in the compiled circuits. Real-system experiments on IonQ's device affirm its effectiveness, notably enhancing simulation accuracy.
This paper introduces the Hamiltonian-Adaptive Ternary Tree (HATT) framework to compile optimized Fermion-to-qubit mapping for specific Fermionic Hamiltonians. In the simulation of Fermionic quantum systems, efficient Fermion-toqubit mapping plays a critical role in transforming the Fermionic system into a qubit system. HATT utilizes ternary tree mapping and a bottom-up construction procedure to generate Hamiltonian aware Fermion-to-qubit mapping to reduce the Pauli weight of the qubit Hamiltonian, resulting in lower quantum simulation circuit overhead. Additionally, our optimizations retain the important vacuum state preservation property in our Fermion-toqubit mapping and reduce the complexity of our algorithm from O(N4) to O(N3). Evaluations on various Fermionic systems demonstrate 5∼25% reduction in Pauli weight, gate count, and circuit depth, alongside excellent scalability to larger systems. Experiments on the Ionq device also show the advantages of HATT in noise resistance in quantum simulations.
Compiling quantum algorithms for real devices involves hard optimization problems that can decide whether an algorithm runs at scale. We present a general method for solving such problems with AI agents, with every result certified. It builds on autoresearch loops, in which agents iteratively improve programs against a fixed evaluator and which have recently improved quantum cryptanalysis circuits, and adds two elements: a frozen, exact verifier certifies every result, and this verifier, together with the challenge around it, is built by an agent that formulates the problem with a researcher and validates the verifier against a solved case, deliberately broken solutions and published results before any solution exists. The method applies to any optimization problem whose solutions can be verified exactly and efficiently. We apply it to three compilation problems in quantum simulation, namely fermion-to-qubit encoding, Hamiltonian layout and unitary synthesis. In each, the agents improved substantially on published or standard constructions, reducing the cost being optimized by up to 73% at the largest sizes tested and outperforming a state-of-the-art optimizer for fermion-to-qubit encodings. Every submission is a program accompanied by its agent's notes, so the ideas behind each improvement are recorded in human-readable form; later agents built on them, and we describe them here. These results open the way to automated, certified discovery across quantum circuit design and beyond.
Quantum computing, leveraging the principles of superposition and entanglement, holds the potential to revolutionize computational problem-solving across a wide array of fields, from cryptography to complex system simulations. However, unlocking the full power of quantum computing requires the development of advanced quantum compilation techniques that can efficiently map high-level algorithms onto physical quantum hardware. This paper delves into state-of-the-art optimization strategies within quantum compilers, with a particular focus on methods such as Relaxed Peephole Optimization (RPO), gate reordering techniques for the Quantum Approximate Optimization Algorithm (QAOA), and reinforcement learning (RL)-driven frameworks. It also explores innovative approaches like distributed quantum compilation, parity quantum optimization, and the Paulihedral framework, all designed to minimize gate counts, reduce circuit depth, and optimize overall resource utilization. A key contribution of this work is the introduction of error mitigation techniques that enhance the fidelity and scalability of quantum circuits, particularly on noisy intermediate-scale quantum (NISQ) devices. Through comprehensive empirical evaluations across a variety of quantum algorithms, the paper demonstrates significant improvements in critical performance metrics such as circuit depth, gate count, and execution efficiency, providing a promising direction for optimizing quantum circuit design tailored to diverse quantum hardware platforms.
Quantum computers hold great promise for efficiently simulating Fermionic systems, benefiting fields like quantum chemistry and materials science. To achieve this, algorithms typically begin by choosing a Fermion-to-qubit mapping to encode the Fermionic problem in the qubits of a quantum computer. In this work, we introduce ‘Treespilation,’ a technique for efficiently mapping Fermionic systems using a large family of favourable tree-based mappings while minimising a generic cost function to reduce quantum simulation overhead. We use this technique to minimise the number of CNOT gates required to simulate approximate chemical groundstate circuits and observe significant reductions, up to 74%, in CNOT counts on full connectivity. For devices with limited qubit connectivity, we observe similar reductions in CNOT counts, often surpassing the full connectivity CNOT count for circuits encoded with the Jordan-Wigner mapping. We observed similar reductions when applied to reducing the Pauli weight of Hubbard model Hamiltonians.
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.
Recent advancements in quantum computing have enabled practical use of quantum error detecting and correcting codes. However, current architectures and future proposals of quantum computer design suffer from limited qubit counts, necessitating the use of high-rate codes. Such codes, with their code parameters denoted as [[n,k,d]], have more than 1 logical qubit per code (i.e., k>1). This leads to reduced error tolerance of the code, since ⌈(d−1)/2⌉ errors on any of the n physical qubits can affect the logical state of all k logical qubits. Therefore, it becomes critical to optimally map the input qubits of a quantum circuit to these codes, in such a way that the circuit fidelity is maximized. \par However, the problem of mapping program qubits to logical qubits for high-rate codes has not been studied in prior work. A brute force search to find the optimal mapping is super exponential (scaling as O(n!), where n is the number of input qubits), making exhaustive search infeasible past a small number of qubits. We propose a framework that addresses this problem on two fronts: (1) for any given mapping, it performs logical-to-physical compilation that translates input gates into efficiently encoded implementations utilizing Hadamard commutation and gate merging; and (2) it quickly searches the space of possible mappings through a merge-optimizing, noise-biased packing heuristic that identifies high-performing qubit assignments without exhaustive enumeration. To the best of our knowledge, our compiler is the first work to explore mapping and compilation for high-rate codes. Across 71 benchmark circuits, we reduce circuit depth by 34%, gate counts by up to 31% and 17% for one-qubit and two-qubit gates, and improve total variation distance by 1.75×, with logical selection rate improvements averaging 86% relative to naive compilation.