General-Purpose Quantum Circuit Simulator with Projected Entangled-Pair States and the Quantum Supremacy Frontier

Abstract

Recent advances on quantum computing hardware have pushed quantum computing to the verge of quantum supremacy. Here we bring together many-body quantum physics and quantum computing by using a method for strongly interacting two-dimensional systems, the Projected Entangled-Pair States, to realize an effective general-purpose simulator of quantum algorithms. We apply our method to study random quantum circuits, which are outstanding candidates to demonstrate quantum supremacy on quantum computers that supports nearest-neighbour gate operations on a two-dimensional configuration. Our approach allows to quantify precisely the memory usage and the time requirements of random quantum circuits, thus showing the frontier of quantum supremacy. Applying this general quantum circuit simulator we measured amplitudes for a 7 × 7 lattice of qubits with depth (1 + 40 + 1) and double-precision numbers in 31 minutes using less than 93 TB memory on the Tianhe-2 supercomputer. Our analytic complexity bounds also show that simulating a 8 × l circuit (l > 8) with depth (1 + 40 + 1), or a 10 × l (l > 10) circuit with depth (1 + 32 + 1) is within reach of current supercomputers.Quantum computers offer the promise of efficiently solving certain problems that are intractable for classical computers, most famously factorizing large numbers [1][2][3]. With the rapid progress of various quantum systems towards Noisy Intermediate-Scale Quantum computing devices [4][5][6][7][8][9][10][11], we are now on the verge of quantum supremacy [12], i.e. demonstrating that an actual quantum computer has the ability to do a computation that no classical computers can tackle, an important milestone in the field of computer science. Various candidates have been suggested to demonstrate quantum supremacy, such as BosonSampling [13,14], the instantaneous quantum polynomial protocol [15,16] and random quantum circuits (RQCs) [3,17] which demand less physical resources and are easier to implement compared to, for instance, factorization. The central aspect for all these near-term supremacy proof-of-principle computations, which poses fundamental limitations to classical computations, is that the quantum states produced, and from which we wish to sample configurations, live in a Hilbert space that grows exponentially with the system size.In view of recent progresses in quantum computing hardware, it is important to find effective ways to simulate accurately quantum algorithms on classical computers. While the quantum circuit simulator we present can tackle generic circuits, in the following we focus on RQCs. They consist of a series of single and two-qubit gates which are applied to different qubits in a particular order. A group of commuting gates which can be applied simultaneously constitute one layer of the circuit, and the more groups of operations that do not commute, the deeper the circuit is. The qualification of random circuit comes from the fact that the single-qubit gates applied are chosen at random from a small set of them (for more details about...

Sample caching Markov chain Monte Carlo approach to boson sampling simulation

“…Similar to MIS, SC-MCMC is also case independent. Besides boson sampling, SC-MCMC can be directly used as a general sampling framework for any sampling tasks as long as we can evaluate the probabilities for given events, for example the Gaussian boson sampling [26], IQP circuit sampling [27,28] and random quantum circuit sampling [29,30]. Meanwhile, SC-MCMC is particularly suitable for tasks where a large number of samples are taken.…”

“…Particularly, the SC-MCMC method can be used for quantum-enhanced applications based on boson sampling such as simulating the molecular vibronic spectra [23], finding dense subgraphs [24] or approximate optimization [25]. Moreover, Our method can also be directly applied on other quantum supremacy candidates, such as the Gaussian boson sampling [26], the IQP circuit sampling [27,28] and random quantum circuit (RQC) sampling [29,30], especially when a lot of samples are taken for validating the device [31]. (2) On the quantum side, our results suggest that the hardness of demonstrating quantum supremacy by boson sampling is increasing with the development of classical simulator.…”

Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design

“…Quantum circuits are special cases of tensor networks with the unitary constraints on the gates. Thus, tensor network algorithms developed in the quantum many-body community are potentially useful for simulating quantum circuits, especially the shallow ones with a large number of qubits where the state vector does not fit into memory [100][101][102]. In this sense, one can perform more efficient simulations at a larger scale by exploring low-rank structures in the tensor networks with a trade-off of almost negligible errors [103].…”

Global Investments

“…Although, it was Google which has succeeded in achieving quantum supremacy, but it needs to be highlighted that, this has become possible because of the groundwork done by various US governmental agencies like NIST, NASA, defence department and various other federal agencies and programmes. 18 The credit goes to goggle that they quickly grew beyond the traditional IT industry mind-set and have invested in the technology which is yet to practically succeed and there is no guaranty of its economic viability.…”

“…17 The discussion on NIST is based on "American Leadership in Quantum Technology", October 24, 2017, https://www.nist.gov/speech-testimony/american-leadership-quantum-technology, October 23, 2020. 18 Kratsios [6]. 19 Schoff [1].…”