Plane Wave Dual Basis for Quantum Simulation Making Molecular Simulations Tractable on Quantum Computers

This patent presents an advance in quantum computing – a method for representing the mathematics of quantum systems so that they can be simulated on quantum hardware using far fewer operations than conventional approaches demand.

The Problem

Simulating quantum systems on classical computers is hard. The resources required grow exponentially with the number of particles involved, so even modest systems (a few dozen electrons) quickly exceed what the world’s largest supercomputers can handle. This matters far beyond physics: accurate quantum simulation is what would let researchers design new catalysts, predict how candidate drugs bind to target proteins, or work out the properties of novel battery materials without a decade of laboratory trial and error.

Quantum computers are expected to change this. Because they operate under the same quantum rules as the systems being studied, they can in principle simulate them efficiently. But in practice the way a quantum system is mathematically described – its “Hamiltonian” – contains an enormous number of interacting terms. A naive quantum simulation has to process each term, and the total work scales steeply with system size. Without a more efficient representation, even a quantum computer struggles to handle the molecules and materials chemists actually want to model.

What This Invention Does

The invention is a method for rewriting a quantum system’s Hamiltonian into a more convenient form before simulating it. Specifically, it combines two complementary bases – a “plane wave” basis and a “plane wave dual” basis – and moves between them using a discrete Fourier transform. The kinetic-energy part of the problem is kept in the basis where it looks simplest (diagonal), and the potential-energy part is moved to the basis where it looks simplest (also diagonal). The result is a Hamiltonian whose terms scale only quadratically with the number of basis vectors, rather than the much steeper fourth-power scaling of conventional molecular-orbital representations.

Fewer terms means fewer operations on the quantum computer, which means shorter circuits, less noise accumulation, and more ambitious simulations within the reach of near-term hardware. The method is paired with a Trotter decomposition – a standard technique for turning a Hamiltonian into a sequence of time-evolution steps – and the authors show how the resulting circuit can be laid out on a planar lattice of qubits with linear depth.

Key Features

• Dual-basis representation. The Hamiltonian is split so that each piece is diagonal in its own basis, dramatically reducing the number of non-trivial terms that need to be simulated.
• Quadratic scaling. Whereas conventional electronic-structure Hamiltonians contain on the order of N⁴ terms, this representation contains on the order of N² – a fundamental improvement for large systems.
• Fast Fourier bridge. A discrete Fourier transform maps between the two bases. FFTs are extremely efficient operations on quantum hardware, so switching between representations during simulation is cheap.
• Planar-lattice friendly. The resulting circuits can be mapped onto a two-dimensional lattice of qubits with linear circuit depth, which matches the layout of most real quantum processors.
• Variational-algorithm ready. The decomposition is compatible with variational quantum algorithms such as VQE, letting the method plug into existing hybrid classical-quantum workflows for chemistry.

Who Is Behind It?

The applicant is Google LLC, with the invention credited to Ryan Babbush – a quantum computing researcher at Google well known for work on quantum chemistry algorithms. The Australian application is a divisional of earlier application 2024204635 and descends from a family of related filings at 2023201068, 2021215213, and 2018270115. The local patent agent is Pizzey’s Patent and Trade Mark Attorneys in Brisbane. The original priority filings are held by Google in the United States.

Why It Matters

Practical quantum simulation is one of the most anticipated applications of quantum computing, with implications for drug discovery, materials science, catalysis, and fundamental physics. The dominant bottleneck is not the hardware in isolation – it’s the efficiency of the algorithms that the hardware has to run. Work like this, which shaves entire factors of N off the problem size, is the kind of software progress that brings commercially useful quantum simulation closer without waiting for the next generation of qubits.

The broader context is worth noting: Google has been systematically building out a portfolio around near-term quantum chemistry, and this filing is another piece in that puzzle. Divisional applications like this one are often filed to protect specific algorithmic variants as the parent application moves toward grant.

AU 2026201656 was published in the Australian Official Journal of Patents on 26 March 2026 and is open for public inspection. Patent applications represent inventions that are sought to be protected and do not necessarily reflect commercially available products.