Constant Depth Digital-Analog Counterdiabatic Quantum Computing

TL;DR

This paper presents a digital-analog quantum computing framework that implements counterdiabatic protocols at constant circuit depth, enabling efficient and scalable quantum state preparation on current hardware.

Contribution

It introduces a novel digital-analog approach using commutator product formulas to realize higher-order counterdiabatic protocols with fixed resource overhead.

Findings

Enables constant-depth implementation of counterdiabatic protocols

Demonstrates application to two-dimensional spin models

Shows improved resource scaling for quantum control

Abstract

We introduce a digital-analog quantum computing framework that enables counterdiabatic protocols to be implemented at constant circuit depth, allowing fast and resource-efficient quantum state preparation on current quantum hardware. Counterdiabatic protocols suppress diabatic excitations in finite-time adiabatic evolution, but their practical application is limited by the non-local structure of the required Hamiltonians and the resource overhead of fully digital implementations. Counterdiabatic terms can be expressed as truncated expansions of nested commutators of the adiabatic Hamiltonian and its parametric derivative. Here, we show how this algebraic structure can be efficiently realized in a digital-analog setting using commutator product formulas. Using native multi-qubit analog interactions augmented by local single-qubit rotations, this approach enables higher-order counterdiabatic protocols whose implementation requires a constant number of analog blocks for any fixed truncation order, independent of system size. We demonstrate the method for two-dimensional spin models and analyze the associated approximation errors. These results show that digital-analog quantum computing enables a qualitatively new resource scaling for counterdiabatic protocols and related quantum control primitives, with direct implications for quantum simulation, optimization, and algorithmic state preparation on current quantum devices.