In our latest Nature publication, we introduce a new quantum computational task measuring Out-of-Time-Order Correlators (OTOCs). This work demonstrates a verifiable quantum advantage and paves the way for solving real-world problems like Hamiltonian learning in Nuclear Magnetic Resonance (NMR).
Nature is brimming with chaos, a phenomenon characterized by the high sensitivity of a system toward small perturbations. In the macroscopic world, notable examples of chaotic systems include weather patterns, wherein a small change in initial conditions leads to vastly different outcomes over time (often dubbed “the butterfly effect”), and population dynamics, where small shifts in local populations may eventually affect the entire ecosystem. Chaos is similarly abundant in quantum systems, with examples including the dynamics of magnetization of atomic nuclei when subjected to a time-varying magnetic field, and the flow of electrons in high-temperature superconductors.
Simulating quantum-chaotic systems is challenging for classical computation due to exponentially scaling computational cost, making quantum computers ideal for achieving quantum advantage. In 2019, we demonstrated the first beyond-classical quantum computation by sampling bitstrings from a highly chaotic quantum state of qubits. However, this random circuit sampling approach has limited practical utility since the same bitstring never appears twice in a large quantum system, restricting its ability to reveal useful information.
In “Observation of constructive interference at the edge of quantum ergodicity”, featured on the cover of Nature, we introduce and experimentally demonstrate a quantum algorithm which we call Quantum Echoes. The heart of the algorithm is measuring the expectation value of a quantum observable, called the out-of-time-order correlator (OTOC). OTOC and its higher order generalizations are a new family of observables that describe how quantum dynamics become chaotic. Unlike bitstrings, quantum expectation values, e.g., current, velocity, magnetization and density, are verifiable computational outcomes that remain the same when run on different quantum computers. The wide relevance of expectation values combined with their verifiability indicates a direct path toward using OTOCs to solve real-world problems using quantum computers, which are not possible to solve on classical computers. Remarkably, we show that running the Quantum Echoes algorithm on the Willow quantum chip is already in the beyond-classical regime for a set of benchmarking quantum circuits.
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