Variational Hamiltonian simulation for translational invariant systems via classical pre-processing

Abstract

The simulation of time evolution of large quantum systems is a classically challenging and in general intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation thereof, where a higher approximation accuracy can be traded for an increased gate count. In this work, we introduce a variational algorithm which uses solutions of classical optimizations to predict efficient quantum circuits for time evolution of translationally invariant quantum systems. Our strategy can improve upon the Trotter-Suzuki accuracy by several orders of magnitude. It translates into a reduction in gate count and hence gain in overall fidelity at the same algorithmic accuracy. This is important in NISQ-applications where the fidelity of the output state decays exponentially with the number of gates. The performance advantage of our classical assisted strategy can be extended to open boundaries with translational symmetry in the bulk. We can extrapolate our method to beyond classically simulatable system sizes, maintaining its total fidelity advantage over a Trotter-Suzuki approximation making it an interesting candidate for beyond classical time evolution.

Barren plateaus in quantum tensor network optimization

“…Our results show that exhausting the possibilities of classical optimization in the context of variational quantum algorithms can have significant advantages, similar to what was also found in other contexts of quantum computation, e.g. Hamiltonian simulation [80,81].…”

Optimal compression of quantum many-body time evolution operators into brickwall circuits

“…The implications are the same as those derived from Fig. 6: With a smaller amount of gates we essentially get the same performance, in this case even for a quantity that does not appear in the objective function (19). Finally, we check whether the refocussing that was observed for the infidelity ε in Fig.…”

“…Having studied the infidelity and its behavior under stacking in detail in Sec. 3.1, we now use the compressed circuits to determine the behavior of a quantity that does not enter the objective function (19), namely the OTOC (22). In Fig.…”

“…Due to the universal representation of the wave function, this is an attractive approach which is extremely flexible once a suitable mapping of the system of interest to qubits is devised. Recent applications include condensed matter systems [14][15][16][17][18][19], simulations from quantum chemistry [11,[20][21][22] and high-energy physics [23,24]. Digital quantum simulations were also used to realize exotic phases of matter like time crystals [25,26] and quantum spin liquids [27].…”

Large-scale simulations of Floquet physics on near-term quantum computers

“…Nonetheless, error rates are yet to reach the error correction threshold for moderate-sized devices and hence quantum simulation algorithms designed for fault-tolerant devices remain challenging for the near future [26][27][28][29][30]. This has prompted the search for quantum simulation algorithms suitable for implementation on near-term quantum devices [28,[31][32][33][34][35][36][37][38][39][40][41][42][43]. However, most of these studies focused on simulating time-independent systems and less attention has so far been paid to how to simulate periodically driven systems.…”