Approximate t-designs in generic circuit architectures

PRX Quantum (2024)

 

In this research paper, scientists explore unitary t-designs, which are specific distributions of quantum operations (unitaries) that behave as if they are random, at least for the operations’ first few moments. These designs are useful for many tasks in quantum computing, such as simulating randomness or benchmarking.

The authors looked at random quantum circuits, which are sequences of random two-qubit operations. These circuits are known to approximate unitary t-designs after a certain number of operation layers.

They found that the time it takes for a random circuit to become an approximate t-design depends on how its operations are structured. Also, if a circuit’s structure ensures that a block of gates can connect all the sites it operates on within a reasonable number of layers, the circuit can form an approximate t-design in depth proportional to the number of qubits.

Unitary t-designs are critical for creating quantum states that look random, which is useful for quantum cryptography, benchmarking quantum devices, and understanding quantum chaos.

The paper’s authors are Daniel Belkin, James Allen, Soumik Ghosh, Christopher Kang, Sophia Lin, James Sud, Fred Chong, Bill Fefferman and Bryan K. Clark, conducting work at the University of Illinois Urbana-Champaign and the University of Chicago.