A verifiable quantum advantage (opens in new tab)

Google Quantum AI researchers have introduced "Quantum Echoes," a new algorithm designed to measure Out-of-Time-Order Correlators (OTOCs) to characterize quantum chaos. By demonstrating this task on the 103-qubit Willow chip, the team has achieved a verifiable quantum advantage that surpasses the limitations of previous random circuit sampling techniques. This work establishes a direct path toward solving practical problems in physics and chemistry, such as Hamiltonian learning, through the use of stable and reproducible quantum expectation values.

Limitations of Random Circuit Sampling

• While the 2019 "quantum supremacy" milestone proved quantum computers could outperform classical ones, the bitstring sampling method used was difficult to verify and lacked practical utility.
• In large-scale quantum systems, specific bitstrings rarely repeat, which restricts the ability to extract useful, actionable information from the computation.
• The Quantum Echoes approach shifts focus to quantum expectation values—such as magnetization, density, and velocity—which remain consistent across different quantum computers and are computationally verifiable.

The Quantum Echoes Algorithm and OTOCs

• The algorithm measures OTOCs, which represent the state of a single qubit after a series of "forward" ($U$) and "backward" ($U^\dagger$) evolutions.
• In the experiment, 103 qubits on the Willow processor underwent evolution through random quantum circuits to reach a highly chaotic state.
• A perturbation (gate $B$) is applied between the forward and backward evolutions; if the system is chaotic, this small change triggers a "butterfly effect," resulting in a final state significantly different from the initial one.
• Higher-order OTOCs involve multiple "round trips" of these evolutions, increasing the system's sensitivity to the perturbation and allowing for a more detailed characterization of the quantum dynamics.

Many-Body Interference and Signal Amplification

• The researchers discovered that higher-order OTOCs function like many-body interferometers, where the quantum states of many particles interfere with one another.
• The perturbation gates ($B$ and $M$) act as mirrors; when a resonance condition is met (where $U^\dagger$ is the exact inverse of $U$), constructive interference occurs.
• This constructive interference amplifies specific quantum correlations, allowing the OTOC signal magnitude to scale as a negative power of the system size, rather than the exponential decay typically seen in chaotic systems.
• This amplification makes the OTOC a sensitive instrument for identifying the specific correlations generated between two different qubits during the evolution of the circuit.

Practical Applications and Future Research

The success of the Quantum Echoes algorithm on the Willow chip marks a transition toward using quantum computers for tasks that are both beyond-classical and physically relevant. This method is particularly well-suited for Hamiltonian learning in Nuclear Magnetic Resonance (NMR) and studying the flow of electrons in high-temperature superconductors. Moving forward, the ability to measure verifiable expectation values in the chaotic regime will be essential for researchers looking to simulate complex quantum materials that are impossible to model on classical hardware.