We present a framework for differentiable quantum transforms. Such transforms are metaprograms capable of manipulating quantum programs in a way that preserves their differentiability. We highlight their potential with a set of relevant examples across quantum computing (gradient computation, circuit compilation, and error mitigation), and implement them using the transform framework of PennyLane, a software library for differentiable quantum programming. In this framework, the transforms themselves are differentiable and can be parametrized and optimized, which opens up the possibility of improved quantum resource requirements across a spectrum of tasks.
We present a framework for differentiable quantum transforms. Such transforms are metaprograms capable of manipulating quantum programs in a way that preserves their differentiability. We highlight their potential with a set of relevant examples across quantum computing (gradient computation, circuit compilation, and error mitigation), and implement them using the transform framework of PennyLane, a software library for differentiable quantum programming. In this framework, the transforms themselves are differentiable and can be parametrized and optimized, which opens up the possibility of improved quantum resource requirements across a spectrum of tasks.
This work describes the theoretical foundation for all quantum chemistry functionality in PennyLane, a quantum computing software library specializing in quantum differentiable programming. We provide an overview of fundamental concepts in quantum chemistry, including the basic principles of the Hartree-Fock method. A flagship feature in PennyLane is the differentiable Hartree-Fock solver, allowing users to compute exact gradients of molecular Hamiltonians with respect to nuclear coordinates and basis set parameters. PennyLane provides specialized operations for quantum chemistry, including excitation gates as Givens rotations and templates for quantum chemistry circuits. Moreover, built-in simulators exploit sparse matrix techniques for representing molecular Hamiltonians that lead to fast simulation for quantum chemistry applications. In combination with PennyLane's existing methods for constructing, optimizing, and executing circuits, these methods allow users to implement a wide range of quantum algorithms for quantum chemistry. We discuss how PennyLane can be used to implement variational algorithms for calculating ground-state energies, excited-state energies, and energy derivatives, all of which can be differentiated with respect to both circuit and Hamiltonian parameters. We provide an example workflow describing how to jointly optimize circuit parameters, nuclear coordinates, and basis set parameters for quantum chemistry algorithms. We discuss a functionality for reducing the number of qubits by using symmetries and explain how PennyLane can be used to estimate quantum resources needed to implement several quantum algorithms. By combining insights from quantum computing, computational chemistry, and machine learning, PennyLane is the first library for differentiable quantum computational chemistry.
Designing high-fidelity quantum circuits remains challenging, and current paradigms often depend on heuristic, fixed-ansatz structures or rule-based compilers that can be suboptimal or lack generality. We introduce a neuro-symbolic framework that reframes quantum circuit design as a differentiable logic programming problem. Our model represents a scaffold of potential quantum gates and parameterized operations as a set of learnable, continuous ``truth values'' or ``switches,'' s∈[0,1]N. These switches are optimized via standard gradient descent to satisfy a user-defined set of differentiable, logical axioms (e.g., correctness, simplicity, robustness). We provide a theoretical formulation bridging continuous logic (via T-norms) and unitary evolution (via geodesic interpolation), while addressing the barren plateau problem through biased initialization. We illustrate the approach on tasks including discovery of a 4-qubit Quantum Fourier Transform (QFT) from a scaffold of 21 candidate gates. We also report hardware-aware adaptation experiments on the 156-qubit IBM Fez processor, where the method autonomously adapted to both gradual noise drift (24.2~pp over static baseline) and catastrophic hardware failure (46.7~pp post-failure improvement), using only measurement-driven gradient updates with no hardwired bias or prior path preference
PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for hardware providers including the Xanadu Cloud, Amazon Braket, and IBM Quantum, allowing PennyLane optimizations to be run on publicly accessible quantum devices. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, JAX, and Autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.
Differentiable quantum dynamics require automatic differentiation of a complex-valued initial value problem, which numerically integrates a system of ordinary differential equations from a specified initial condition, as well as the eigendecomposition of a matrix. This work is a survey of existing differentiable programming frameworks for these tasks, finding that no framework natively supports our application requirements fully. We therefore demonstrate a need for broader support of complex-valued, differentiable numerical integration in scientific computing libraries. We further demonstrate that the derivatives of our quantum dynamics application can be computed through a combination of differentiable programming frameworks and handcoding.
This paper introduces a novel approach to optimizing quantum circuits by directly calculating and applying gradients. Traditional quantum algorithm optimization relies heavily on simulating the quantum circuit on classical computers, which is computationally expensive and limits the scalability of these algorithms. Our work proposes a framework for differentiable quantum circuit optimization, treating quantum circuits as differentiable functions and employing gradient-based optimization techniques. We outline a methodology for computing gradients of the expectation values of quantum circuits with respect to their adjustable parameters. This allows for the direct optimization of quantum circuits using algorithms such as gradient descent, potentially leading to significant improvements in the efficiency and accuracy of quantum algorithms. The core contribution lies in providing a mathematically rigorous foundation for this differentiable approach, paving the way for automated quantum algorithm design and enhancement. The presented method offers a viable alternative to classical simulation, addressing a key bottleneck in the practical implementation of quantum algorithms.
Quantum computing (QC) introduces a novel mode of computation with the possibility of greater computational power that remains to be exploitedpresenting exciting opportunities for high-performance computing (HPC) applications. However, recent advancements in the field have made clear that QC does not supplant conventional HPC, but can rather be incorporated into current heterogeneous HPC infrastructures as an additional accelerator, thereby enabling the optimal utilization of both paradigms. The desire for such integration significantly affects the development of software for quantum computers, which in turn influences the necessary software infrastructure. To date, previous review articles have investigated various quantum programming tools (QPTs) (such as languages, libraries, frameworks) in their ability to program, compile, and execute quantum circuits. However, the integration effort with classical HPC frameworks or systems has not been addressed. This study aims to characterize existing QPTs from an HPC perspective, investigating if existing QPTs have the potential to be efficiently integrated with classical computing models and determining where work is still required. This work structures a set of criteria into an analysis blueprint that enables HPC scientists to assess whether a QPT is suitable for a high-performance computing quantum computing (HPCQC) environment.