Demonstrating robust simulation of driven-dissipative problems on near-term quantum computers

Abstract

Quantum computers are poised to revolutionize the simulation of quantum-mechanical systems in physics and chemistry. Current quantum computers execute their algorithms imperfectly, due to uncorrected noise, gate errors, and decoherence. This severely limits the size and scope of protocols which can be run on near-term quantum hardware. Much research has been focused on building more robust hardware to address this issue, however the advantages of more robust algorithms remains largely unexplored. Here we show that algorithms for solving the driven-dissipative many-body problem, among the hardest problems in quantum mechanics, are inherently robust against errors. We find it is possible to solve dissipative problems requiring deep circuits on current quantum devices due to the contractive nature of their time evolution maps. We simulate one thousand steps of time evolution for the non-interacting limit of the infinite driven-dissipative Hubbard model, calculate the current through the system and prepare a thermal state of the atomic limit of the Hubbard model. These problems were solved using circuits containing up to two thousand entangling gates on quantum computers made available by IBM, showing no signs of decreasing fidelity at long times. Our results demonstrate that algorithms for simulating dissipative problems are able to far out-perform similarly complex non-dissipative algorithms on noisy hardware. Our two algorithmic primitives are the basic building blocks of many condensedmatter-physics systems, and we anticipate their demonstrated robustness to hold when generalized to solve the full many-body driven-dissipative quantum problem. Building upon the algorithms presented here may prove to be the most promising approach to tackle important, classically intractable problems on quantum computers before error correction is available.

Variational Quantum Optimization of Nonlocality in Noisy Quantum Networks

“…In this regime, we may find practical simulation advantages. However, NISQ devices have yet to show a simulation advantage [90], [91], [92], [93], [94], [95]. Nevertheless, NISQ devices are predicted to provide simulation advantages in the near-term [96], [27] As an aside, we note that larger networks can be simulated using smaller quantum devices where an exponential increase in the number of circuit evaluations is accrued [97], [98].…”

Variational Quantum Optimization of Nonlocality in Noisy Quantum Networks

“…In this regime, we may find practical simulation advantages. However, NISQ devices have yet to show a simulation advantage [89][90][91][92][93][94]. Nevertheless, NISQ devices are predicted to provide simulation advantages in the near-term [32,95] As an aside, we note that larger networks can be simulated using smaller quantum devices where an exponential increase in the number of circuit evaluations is accrued [96,97].…”

Efficient method to simulate non-perturbative dynamics of an open quantum system using a quantum computer

“…Nevertheless, as quantum hardware and software improves, speedups relatively to classical simulation are expected to be observed (and some problems solved by quantum computing have been already shown to beat classical computing by a large factor [12,13]). In the context of quantum digital simulations of open quantum systems, several techniques have recently been proposed, such as using Kraus operators [14][15][16][17][18], solving the Lindblad equation with stochastic Schrödinger equations [19] or variationally [20], using the inherent decoherence of the quantum computer to implement the dissipative evolution [21,22], among others [23][24][25][26]. These techniques face some important issues, namely, the Kraus operators are hard to calculate in practice, Lindblad equations are restricted to Markovian environments and the natural decoherence of the quantum computer introduced by the qubits' environment is not fully controllable or its structure is not completely known, hence simulating arbitrary environments is hard.…”