Quantum simulation is a promising application for quantum computing. Quantum simulation algorithms may require the ability to control the time evolution unitary. Naive techniques to control a unitary can substantially increase the required computational resources. A standard approach to controlling Trotterized time evolution doubles the number of single-qubit arbitrary rotations. Here, we describe a compilation scheme to control a symmetric Trotterization that does not increase the number of arbitrary rotations. This halves the number of arbitrary rotations required to implement controlled, Trotterized time evolution compared to the standard approach. Arbitrary rotations contribute significantly to $T$ cost in a fault-tolerant architecture due to the number of required magic states. Therefore, arbitrary rotations often dominate resource estimates for fault-tolerant implementations of quantum simulation algorithms. This construction reduces the number of arbitrary rotations for controlled Trotter evolution to that of uncontrolled Trotter evolution, thereby reducing the cost of fault-tolerant quantum simulation.

Close

PrevNext

View figure in article

• Quantum algorithms & computation
• Quantum algorithms for chemical calculations
• Quantum circuits
• Quantum gates
• Quantum information theory
• Quantum simulation
• Quantum software