Evaluating low-depth quantum algorithms for time evolution on fermion-boson systems

Abstract

Simulating time evolution of quantum systems is one of the most promising applications of quantum computing and also appears as a subroutine in many applications such as Green's function methods. In the current era of NISQ machines we assess the state of algorithms for simulating time dynamics with limited resources. We propose the Jaynes-Cummings model and extensions to it as useful toy models to investigate time evolution algorithms on near-term quantum computers. Using these simple models, direct Trotterisation of the time evolution operator produces deep circuits, requiring coherence times out of reach on current NISQ hardware. Therefore we test two alternative responses to this problem: variational compilation of the time evolution operator, and variational quantum simulation of the wavefunction ansatz. We demonstrate numerically to what extent these methods are successful in time evolving this system. The costs in terms of circuit depth and number of measurements are compared quantitatively, along with other drawbacks and advantages of each method. We find that computational requirements for both methods make them suitable for performing time evolution simulations of our models on NISQ hardware. Our results also indicate that variational quantum compilation produces more accurate results than variational quantum simulation, at the cost of a larger number of measurements.

Digital quantum simulation of scalar Yukawa coupling: Dynamics following an interaction quench on IBM Q

“…Unlike their fermionic counterparts, quantum manybody systems involving bosonic constituents have infinite-dimensional Hilbert spaces that ought to be truncated if one aims to simulate such systems on either classical or quantum computers. Due to the inherently nontrivial problem of encoding bosonic states on qubit registers, digital simulators of systems involving bosonic particles have heretofore received comparatively modest at- * Electronic address: vladimir.stojanovic@physik.tu-darmstadt.de tention [20][21][22][23][24][25]. In particular, while a multitude of analog simulators of coupled fermion-boson models [20,26] have been proposed [27][28][29][30][31][32][33], only a handful of such models have as yet been addressed in the DQS context [21,34].…”

Recompilation-enhanced simulation of electron–phonon dynamics on IBM quantum computers

“…If the initial state is |0 ⊗n , as is convention for quantum algorithms, then the problem can be solved with ISL [34]. In ISL, the structure of V † is informed by incrementally adding gates that work to disentangle the original circuit back to the |0 ⊗n state, leading to significant gate count reductions [51] particularly for Trotterised time evolution circuits [52]. More details of ISL can be found in [34].…”

Recompilation-enhanced simulation of electron-phonon dynamics on IBM Quantum computers

“…If the initial state is 0⟩ ⊗ n , as is convention for quantum algorithms, then the problem can be solved with incremental structural learning (ISL) [35]. In ISL, the structure of V † is informed by incrementally adding gates that work to disentangle the original circuit back to the 0⟩ ⊗ n state, leading to significant gate count reductions [50] particularly for Trotterised time evolution circuits [51]. More details of ISL can be found in [35].…”

“…Overall, ISL can be considered as a method for substituting circuit depth for increased circuit evaluations, such that obtaining the population at a given time requires O(kn e ) rather than O(k) evaluations, where k is the number of shots and n e is the number of evaluations required for convergence of ISL. Analysis of how the value of n e changes for different systems is an ongoing effort [51,52], however across this work it ranges from ∼ 10 1 to ∼ 10 4 depending on the complexity and depth of the circuit.…”