Quantum Computational Advantage via High-Dimensional Gaussian Boson Sampling

Abstract

Photonics is a promising platform for demonstrating quantum computational supremacy (QCS), the task of convincingly outperforming the most powerful classical supercomputers. Despite this promise, existing photonics proposals and demonstrations face significant hurdles. Experimentally, current implementations of Gaussian boson sampling lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make significant progress in improving both the theoretical evidence and experimental prospects. On the theory side, we provide strong evidence for the hardness of Gaussian boson sampling, placing it on a par with the strongest theoretical proposals for QCS. On the experimental side, we propose a new QCS architecture, high-dimensional Gaussian boson sampling, which is programmable and can be implemented with low loss rates using few optical components. We show that particular classical algorithms for simulating GBS are vastly outperformed by high-dimensional Gaussian boson sampling experiments at modest system sizes. This work thus opens the path to demonstrating QCS with programmable photonic processors.

Jet: Fast quantum circuit simulations with parallel task-based tensor-network contraction

“…The alterations to the Gray and Kourtis methodology introduced by Huang et al were later incorporated into the software library of Gray and Kourtis, CoTenGra [37]. In collaboration with NVIDIA, CoTenGra contracted a Sycamore-53 m = 20 sample in 558 seconds on the Selene GPU cluster [38] In [8] a three-dimensional random GBS quantum circuit containing 216 modes (6 modes per dimension of the circuit architecture) and a single cycle was proposed to showcase quantum advantage. In order to map the threedimensional random GBS circuit to a tensor-network simulation, a truncated Fock space corresponding to a qudit size of 4 was assumed.…”

“…In order to map the threedimensional random GBS circuit to a tensor-network simulation, a truncated Fock space corresponding to a qudit size of 4 was assumed. Using the theoretical compute performance of the Fugaku supercomputer, and the CoTen-Gra contraction path finder [3,37], Deshpande et al [8] found that the 6x6x6 circuit could be computed in ≈ 10 14 seconds assuming access to memory well beyond that of all the nodes of Fugaku together, let alone a single node of Fugaku. Slicing the circuit down to sizes that could fit in the 32GB RAM of a Fugaku node would come with a slicing overhead that was astronomical, making this circuit infeasible on current or future supercomputers.…”

“…However, it was argued shortly thereafter that the classical simulation benchmarks used in [6] were overestimates and could be greatly improved upon by using secondary storage of the Summit supercomputer [7]. Deshpande et al [8] have proposed a quantum advantage experiment using Gaussian boson sampling (GBS) and a three-dimensional RQC. It appears these circuits could be much harder to simulate classically than Sycamore-53, with some simulations showing it would take ≈ 10 14 seconds on the top supercomputer in the most idealized scenario where unlimited memory was available.…”

Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series

“…Quantum computers operate in a multidimensional state space and are intrinsically probabilistic. They offer computational advantage for sampling tasks [28][29][30][31]. This was demonstrated experimentally with superconducting [32] and optical [33] quantum devices.…”

Polynomial speedup in Torontonian calculation by a scalable recursive algorithm

“…Among the different approaches for demonstrating quantum advantage [4,5,6,7,8,9], photonics provides a promising track as it enables fast gate operations, room-temperature functioning and significant potential for scalability [10,11,12]. The most well-known and feasible photonic advantage scheme is Boson Sampling formulated by Aaronson and Arkhipov [4] and its extended variant known as Gaussian Boson Sampling (GBS) [13,14,15], which are shown to be classically intractable under certain assumptions [4,16]. However, it should also be mentioned that high loss rates, partial photon indistinguishably and other issues could make such systems classically simulable [17,18,19,20,21,22].…”