New Krylov method reduces cost of the variational quantum phase estimation near term quantum algorithm

November 30, 2022

The research team behind Quantinuum's state-of-the-art quantum computational chemistry platform, InQuanto, has demonstrated a new method that makes more efficient use of today's "noisy" quantum computers, for simulating chemical systems.

In a new paper, “Variational Phase Estimation with Variational Fast Forwarding”, published on the arXiv, a team led by Nathan Fitzpatrick and co-authors Maria-Andreea Filip and David Muñoz Ramo, explored different methods and the trade-offs required to achieve results on near-term quantum hardware. The paper also assesses the hardware requirements for the proposed method.

Starting with the recently published Variational Quantum Phase Estimation (VQPE) algorithm, commonly used to calculate molecular ground-state and excited state energies, the team combined it with variational fast-forwarding (VFF) to reduce the quantum circuit depth required to achieve good results. 

The demonstration made use of a Krylov subspace diagonalization algorithm, which can be used as a low-cost alternative to the traditional quantum phase estimation algorithm to estimate both the ground and excited-state energies of a quantum many-body system. The Krylov method uses time evolution to generate the subspace used in the algorithm, which can be very expensive in terms of gate depth. The new method demonstrated is less expensive, making the circuit depth required to achieve good results manageable.

The team decreased the circuit depth by using VFF, a hybrid classical-quantum algorithm, which provides an approximation to time-evolution, allowing VQPE to be applied with linear cost in the number of time-evolved states. Introducing VFF allows the time evolved states to be expressed with a lower fixed depth therefore the quantum computing resources required to run the algorithm are drastically decreased.

This new approach resulted in a circuit with a depth of 57 gates for the H2 Molecule, of which 24 are CNOTs. This is a significant improvement from the original trotterized time-evolution implementation, particularly as the depth of this circuit remains constant for any number of steps. Whereas, the original trotterized circuit required 34 CNOTs per step, with a large number of steps required for high accuracy.

The techniques demonstrated in this paper will be of interest to quantum chemists seeking near-term results in fields such as, excited state quantum chemistry and strongly correlated materials.

The tradeoff involved in this use of VFF is that the results are more approximate. Improving this will be an area for future research.