Researchers at the Flatiron Institute and Boston University have demonstrated that a conventional laptop can solve a class of quantum problems once believed to require a quantum computer. By applying a 1980s algorithm to mathematical frameworks known as tensor networks, the team successfully simulated a highly complex quantum system, challenging earlier claims that such calculations were beyond the capabilities of classical computers.

Reported in Science, the breakthrough shows that innovative algorithms can significantly expand the power of classical computers, enabling them to tackle problems once thought to require quantum machines. The approach opens new possibilities for studying quantum dynamics and could provide an effective new strategy for solving complex optimization challenges.

Figure 1. Tensor Networks Power Quantum Simulations.

Why Quantum Bits are So Difficult to Simulate

The researchers tackled the challenge of simulating hundreds of interacting qubits—quantum bits that can exist in multiple states simultaneously—arranged in complex lattice structures. Because this behavior is extremely difficult for classical computers to model, a 2025 Science study had claimed that only a quantum computer could accurately simulate such a system. Skeptical of that conclusion, the Flatiron Institute team used the claim as a benchmark to test their own computational methods, ultimately demonstrating that the problem could, in fact, be solved using classical computing techniques. Figure 1 shows Tensor Networks Power Quantum Simulations.

A key challenge in simulating quantum systems is quantum entanglement, which links qubits so strongly that they cannot be treated as independent particles, even when separated by large distances. As the number of interacting qubits increases, the system’s wave function grows exponentially, quickly becoming too large for conventional computers to store directly. Overcoming this computational barrier requires sophisticated algorithms, making efficient simulation essential for understanding quantum materials such as superconductors and other complex quantum systems.

Tensor Networks Make Quantum Problems Manageable

The researchers overcame the computational challenge by using tensor networks, mathematical structures that efficiently compress a quantum system’s enormous wave function into a more manageable form. This approach enabled complex quantum simulations to run on classical computers, with many of the initial calculations performed on a standard laptop using the ITensor software library developed at the Flatiron Institute. By extending tensor network methods to three-dimensional systems, the team demonstrated a powerful new way to model complex quantum dynamics, while highlighting the advanced algorithms and software engineering needed to handle these highly sophisticated mathematical structures.

The team achieved state-of-the-art quantum simulations using relatively modest computing resources by combining tensor networks with belief propagation, a computational algorithm developed in the 1980s and recently adapted for quantum systems [1]. Despite its simplicity, the approach produced results that matched both theoretical predictions and previous quantum-computer simulations. The researchers emphasize that classical and quantum computing should be viewed as complementary rather than competing technologies, with advances in one helping to guide the other. Building on this success, they are now applying their methods to even more challenging problems involving mobile electrons and quantum materials, pushing the boundaries of what classical computers can simulate.

References:

1. https://scitechdaily.com/physicists-solve-a-quantum-only-problem-using-an-ordinary-laptop/

Cite this article:

Janani R (2026), Researchers Crack a “Quantum-Only” Problem Using a Standard Laptop, AnaTechMaz, pp.541.