Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Abstract

The phenomena of quantum criticality underlie many novel collective phenomena found in condensed matter systems. They present a challenge for classical and quantum simulation, in part because of diverging correlation lengths and consequently strong finite-size effects. Tensor network techniques that work directly in the thermodynamic limit can negotiate some of these difficulties. Here, we optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states.

Optimised Trotter Decompositions for Classical and Quantum Computing

“…The Taylor expansion outperforms all the polynomial decompositions by many orders of magnitude, practically over the complete range of time steps that yield any kind of useful results. The only exception from the behaviour predicted by the theoretical efficiency is that Verlet (24) and Omelyan (26) have practically identical errors. Again, this is explained by the more favourable error accumulation of Verlet's decomposition as 55) of the difference between the exact time evolution operator and the respective decomposition as a function of computational cost, i.e.…”

“…Quantum devices suffer from physical errors in addition to the algorithmic errors introduced through the decomposition. The physical errors are mostly determined by the number of operations performed, requiring a trade off between physical (as few gates as possible) and algorithmic errors (as many gates as possible) [9,26]. This implies that optimised decompositions necessitating less cycles for a given precision are even more advantageous for simulations on real quantum devices.…”

Optimised Trotter decompositions for classical and quantum computing

“…Quantum devices suffer from physical errors in addition to the algorithmic errors introduced through the decomposition. The physical errors are mostly determined by the number of operations performed, requiring a trade off between physical (as few gates as possible) and algorithmic errors (as many gates as possible) [9,28]. This implies that optimised decompositions necessitating less cycles for a given precision are even more advantageous for simulations on real quantum devices.…”

“…Eff 2 = 10.7 (28) is well known as Verlet decomposition [36] or Leapfrog algorithm. Taking into account its simplicity, it performs surprisingly well and is a valid choice when programming time is more important than performance or a high precision is explicitly not desired.…”

Variational Quantum Time Evolution without the Quantum Geometric Tensor

“…Quantum time evolution is a central task in physics. Real-time evolution provides detailed insight into properties of quantum mechanical systems, such as phase transitions [1][2][3] or thermalization [4,5]. Imaginary-time evolution is an important tool that enables the preparation of ground states or thermal states [6,7].…”