The Future of Quantum Computing

No quantum advantage (yet) in the world of tensor networks

Tensor networks pictographic scheme Each tensor is represented by an array of dimension N, that matches its number of indices. By joining the legs (indices) of each tensor, it is possible to encode the Hamiltonian or the state of a many-particle system. (Courtesy: Lucy Reading-Ikkanda/Simons Foundation)"> Tensor networks pictographic scheme Each tensor is represented by an array of dimension N, that matches its number of indices. By joining the legs (indices) of each tensor, it is possible to encode the Hamiltonian or the state of a many-particle system. (Courtesy: Lucy Reading-Ikkanda/Simons Foundation) Researchers at the Flatiron Institute in New York City have used a new tensor network (TN) scheme to simulate how Ising spin glasses evolve in time. In many cases, their classical method is more accurate than the latest quantum annealers running the same problem. The results scale in two and three dimensions and raise the bar in the ongoing competition between classical and quantum computers for simulating many-particle quantum systems. Classical versus quantum Quantum many-particle systems provide a good way of comparing computational techniques because their complexity grows exponentially with the number of particles. In theory, quantum computers hold an advantage rooted in entanglement and superposition. In a classical computer, the spin of a particle (up or down) is encoded in bit that is either zero (down) or one (up), but never both. In a quantum computer, the spin can be encoded in a qubit holding a quantum superposition of up and down. This is a much more natural way to represent what the simulated system is actually doing. Recently, a team of quantum computing researchers used the D-Wave’s Advantage2 quantum annealer to simulate Ising spin glass dynamics and claimed that classical computers could not match their results. But now, Joseph Tindall and colleagues at the Flatiron Institute have shown that a classical scheme can do just as well -and sometimes bet