Quobly and Hon Hai toolbox for QPE algorithm

QPE is widely regarded as a key algorithm for computing ground-state energies of molecular systems on future fault-tolerant quantum computers.

The toolbox is available on GitHub.

While its theoretical properties and asymptotic cost scalings are well understood, practical resource estimates and realistic performance trade-offs remain largely unexplored, due to the difficulty of simulating QPE beyond toy models.

The toolbox aims to bridge this gap by providing researchers with a practical environment to explore QPE implementations and their resource implications, with a strong focus on understanding algorithmic building blocks and their practical implementation constraints.

The Toolbox is designed to give quantum algorithm practitioners a hands-on, numerical understanding of the full QPE workflow, from chemistry preprocessing to phase estimation, in a regime that challenges classical simulation while remaining computationally tractable.

Built on advanced tensor network techniques, the toolbox enables users to:

• Prepare physically motivated initial states using DMRG and matrix product states,
• Encode molecular Hamiltonians into quantum circuits via trotterization or block-encoding / qubitization methods,
• Compare textbook QPE with single-ancilla Robust Phase Estimation (RPE),
• Analyze circuit depth, gate counts, and error sources without necessarily executing the circuit.

The toolbox relies on the open-source quimb library and interfaces with standard quantum chemistry tools such as PySCF, ensuring compatibility with established workflows.

The first release is designed as an educational and exploratory framework, enabling researchers to build intuition around the practical implementation of QPE and its variants.Rather than attempting to simulate early fault-tolerant quantum computers, which are by nature beyond classical reach, the QPE Toolbox focuses on practical, interpretable numerical experiments in regimes accessible to classical computation, where algorithmic choices, initialization fidelity, and Hamiltonian encoding strategies can be explored in detail.

Illustrative use cases enabled by the toolbox include (non-exhaustive):

• Full circuit executions for ~10–20 qubits and circuits ranging from <1,000 to ~100,000 gates,
• Ground state preparation for systems up to ~20–30 qubits,
• Hamiltonian encoding for systems up to ~20–30 qubits, typically within a few hours or less on a standard laptop.

These capabilities allow researchers to study trade-offs between precision, circuit depth, and resource requirements, and to build practical intuition about the behaviour of QPE building blocks.

The toolbox is therefore designed primarily as a pedagogical and exploratory platform, helping bridge the gap between theoretical proposals and their concrete implementation constraints.

The QPE Toolbox is released as open source and is intended to evolve with the community.

Future developments will include variational circuit synthesis, compressed fermionic encodings, and larger-scale tensor-network simulations.

Documentation and example workflows are provided to help researchers explore the different components of the QPE pipeline.

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