A Method for Constructing Quasi-Random Peaked Quantum Circuits

TL;DR

This paper introduces a novel algorithm for constructing quasi-random peaked quantum circuits that concentrate probability on specific states, with applications in quantum state preparation and simulation.

Contribution

The paper presents a new algorithm for creating peaked quantum circuits with controlled probability distributions and introduces techniques to obscure final states and construct multi-peaked circuits.

Findings

Effective for shallow circuits using MPS simulation

High probability concentration on specific basis states

Ability to construct multi-peaked quantum circuits

Abstract

An algorithm is proposed for constructing quasi-random "peaked" quantum circuits, i.e., circuits whose final qubit state exhibits a high probability concentration on a specific computational basis state. These circuits consist of random gates arranged in a brick-wall architecture. While the multiqubit state in the middle of the circuit can exhibit significant entanglement, the final state is, with high probability, a predetermined pure bitstring. A technique is introduced to obscure the final bitstring in the structure of the quantum circuit. The algorithm allows precise control over the probability of the final peaked state. A modified version of the algorithm enables the construction of double- or multi-peaked quantum circuits. The matrix product state (MPS) method is evaluated for simulating such circuits; it performs effectively for shallow peaked circuits but offers no significant advantage for deeper ones.