We propose a general tensor network method for simulating quantum circuits. The method is massively more efficient in computing a large number of correlated bitstring amplitudes and probabilities than existing methods. As an application, we study the sampling problem of Google's Sycamore circuits, which are believed to be beyond the reach of classical supercomputers and have been used to demonstrate quantum supremacy. Using our method, employing a small computational cluster containing 60 graphical processing units (GPUs), we have generated one million correlated bitstrings with some entries fixed, from the Sycamore circuit with 53 qubits and 20 cycles, with linear cross-entropy benchmark (XEB) fidelity equals 0.739, which is much higher than those in Google's quantum supremacy experiments.
We study the problem of generating independent samples from the output distribution of Google's Sycamore quantum circuits with a target fidelity, which is believed to be beyond the reach of classical supercomputers and has been used to demonstrate quantum supremacy. We propose a new method to classically solve this problem by contracting the corresponding tensor network just once, and is massively more efficient than existing methods in obtaining a large number of uncorrelated samples with a target fidelity. For the Sycamore quantum supremacy circuit with $53$ qubits and $20$ cycles, we have g…
A major milestone in the era of noisy intermediate scale quantum computers is \textit{quantum supremacy} [Nature \textbf{574}, 505 (2019)] claimed on the Sycamore quantum processor of $53$ qubits, which can perform a random circuit sampling task within $200$ seconds while the same task is estimated to require a runtime of $10,000$ years on Summit. This record has been renewed with two recent experiments on the Zuchongzhi $2.0$ ($56$ qubits) and Zuchongzhi $2.1$ ($60$ qubits) quantum processors. On the other front of quantum supremacy comparison, there has also been continuous improvements on b…
Even if Google AI's Sycamore processor is efficient for the particular task it has been designed for it fails to deliver universal computational capacity. Furthermore, even classical devices implementing transverse homoclinic orbits realize exponential speedups with respect to universal classical as well as quantum computations. Moreover, relative to the validity of quantum mechanics, there already exist quantum oracles which violate the Church-Turing thesis.
It is believed that random quantum circuits are difficult to simulate classically. These have been used to demonstrate quantum supremacy: the execution of a computational task on a quantum computer that is infeasible for any classical computer. The task underlying the assertion of quantum supremacy by Arute et al. (Nature, 574, 505--510 (2019)) was initially estimated to require Summit, the world's most powerful supercomputer today, approximately 10,000 years. The same task was performed on the Sycamore quantum processor in only 200 seconds. In this work, we present a tensor network-based clas…
We introduce a new open-source software library Jet, which uses task-based parallelism to obtain speed-ups in classical tensor-network simulations of quantum circuits. These speed-ups result from i) the increased parallelism introduced by mapping the tensor-network simulation to a task-based framework, ii) a novel method of reusing shared work between tensor-network contraction tasks, and iii) the concurrent contraction of tensor networks on all available hardware. We demonstrate the advantages of our method by benchmarking our code on several Sycamore-53 and Gaussian boson sampling (GBS) supr…
Simulating complex molecules and materials is an anticipated application of quantum devices. With strong quantum advantage demonstrated in artificial tasks, we examine how such advantage translates into modeling physical problems of correlated electronic structure. We simulate static and dynamical electronic structure on a superconducting quantum processor derived from Google's Sycamore architecture for two representative correlated electron problems: the nitrogenase iron-sulfur molecular clusters, and $α$-ruthenium trichloride, a proximate spin-liquid material. To do so, we simplify the elect…
The computational advantage of noisy quantum computers has been demonstrated by sampling the bitstrings of quantum random circuits. An important issue is how the performance of quantum devices could be quantified in the so-called "supremacy regime". The standard approach is through the linear cross entropy benchmark (XEB), where the theoretical value of the probability is required for each bitstring. However, the computational cost of XEB grows exponentially. So far, random circuits of the 53-qubit Sycamore chip were verified up to 10 cycles of gates only; the XEB fidelities of deeper circuits…
We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being non-universal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses. Equipped with the intrinsic single-instance-hardness property, a single fixed unitary evolution in our model is sufficient to produce classically intractable results, compared to several other models that rely on implementation of an ensemble of different unitaries (instances). We propose a feasible experimental scheme to implement our Hamiltonian model using c…
We develop a high-performance tensor-based simulator for random quantum circuits(RQCs) on the new Sunway supercomputer. Our major innovations include: (1) a near-optimal slicing scheme, and a path-optimization strategy that considers both complexity and compute density; (2) a three-level parallelization scheme that scales to about 42 million cores; (3) a fused permutation and multiplication design that improves the compute efficiency for a wide range of tensor contraction scenarios; and (4) a mixed-precision scheme to further improve the performance. Our simulator effectively expands the scope…
Although the emergence of a fully-functional quantum computer may still be far away from today, in the near future, it is possible to have medium-size, special-purpose, quantum devices that can perform computational tasks not efficiently simulable with any classical computer. This status is known as quantum supremacy (or quantum advantage), where one of the promising approaches is through the sampling of chaotic quantum circuits. Sampling of ideal chaotic quantum circuits has been argued to require an exponential time for classical devices. A major question is whether quantum supremacy can be …
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear quantum speedup for some task, motivated by the goal of overturning the Extended Church-Turing Thesis as confidently as possible. First, we study the hardness of sampling the output distribution of a random quantum circuit, along the lines of a recent proposal by the the Quantum AI group at Google. We show that there's a natural hardness assumption, which has no…
As various quantum computing technologies continue to compete for quantum supremacy, several parameters have emerged as benchmarks for the quality of qubits. These include fidelity, coherence times, connectivity, and a few others. In this paper, we aim to study the importance of these parameters and their impact on quantum algorithms. We propose a realistic connectivity geometry and form quantum circuits for the Bernstein-Vazirani, QFT, and Grover Algorithms based on the limitations of the chosen geometry. We then simulate these algorithms using error models to study the impact of gate fidelit…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to tensor networks with irregular geometries. Finding the best possible contraction path for such networks is a central problem, with an exponential effect on computation time and memory footprint. In this work, we implement new randomized protocols that find very high quality contraction paths for arbitrary and large tensor networks. We test our methods on a vari…
In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the build…
Quantum supremacy is the ability of quantum processors to outperform classical computers at certain tasks. In digital random quantum circuit approaches for supremacy, the output distribution produced is described by the Porter-Thomas (PT) distribution. In this regime, the system uniformly explores its entire Hilbert space, which makes simulating such quantum dynamics with classical computational resources impossible for large systems. However, the latter has no direct application so far in solving a specific problem. In this work, we show that the same sampling complexity can be achieved from …
The numerical simulation of quantum circuits is an indispensable tool for development, verification and validation of hybrid quantum-classical algorithms on near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulation. We present a modernized version of the Tensor Network Quantum Virtual Machine (TNQVM) which serves as a quantum circuit simulation backend in the eXtreme-scale ACCelerator (XACC) framework. The new version is based on the general purpose, scalable tensor n…
BosonSampling is a well-defined scheme for demonstrating quantum supremacy with photons in near term. Although relying only on multi-photon interference in nonadaptive linear-optical networks, it is hard to simulate classically. Here we study BosonSampling using matrix product states, a powerful method from quantum many-body physics. This method stores the instantaneous quantum state during the evolution of photons in the optical quantum circuit, which allows us to reveal the dynamical features of single photons in BosonSampling devices, such as entanglement entropy growth. We show the flexibl…
We introduce a distributed classical simulation algorithm for general quantum circuits, and present numerical results for calculating the output probabilities of universal random circuits. We find that we can simulate more qubits to greater depth than previously reported using the cluster supported by the Data Infrastructure and Search Technology Division of the Alibaba Group. For example, computing a single amplitude of an $8\times 8$ qubit circuit with depth $40$ was previously beyond the reach of supercomputers. Our algorithm can compute this within $2$ minutes using a small portion ($\appr…
High-performance classical simulator for quantum circuits, in particular the tensor network contraction algorithm, has become an important tool for the validation of noisy quantum computing. In order to address the memory limitations, the slicing technique is used to reduce the tensor dimensions, but it could also lead to additional computation overhead that greatly slows down the overall performance. This paper proposes novel lifetime-based methods to reduce the slicing overhead and improve the computing efficiency, including an interpretation method to deal with slicing overhead, an in-place…
We propose a classical simulation method for quantum circuits based on decomposing unitary gates into a sum of stabilizer projectors. By only decomposing the non-Clifford gates, we take advantage of the Gottesman-Knill theorem and build a bridge between stabilizer-based simulation and Feynman-path-type simulation. We give two variants of this method: stabilizer-based path-integral recursion (SPIR) and stabilizer projector contraction (SPC). We also analyze further advantages and disadvantages of our method compared to the Bravyi-Gosset algorithm and recursive Feynman path-integral algorithms. …
Classical simulations of quantum circuits are limited in both space and time when the qubit count is above 50, the realm where quantum supremacy reigns. However, recently, for the low depth circuit with more than 50 qubits, there are several methods of simulation proposed by teams at Google and IBM. Here, we present a scheme of simulation which can extract a large amount of measurement outcomes within a short time, achieving a 64-qubit simulation of a universal random circuit of depth 22 using a 128-node cluster, and 56- and 42-qubit circuits on a single PC. We also estimate that a 72-qubit ci…
Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of 1-D integrable spin chains with nearest neighbor interactions. We show how the quantum Yang-Baxter equation can be exploited to compress and produce a shallow quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and only depends on the number of spins. We show that the compressed circuit scales quadr…
Simulating quantum systems is one of the most important potential applications of quantum computers. The high-level circuit defining the simulation needs to be compiled into one that complies with hardware limitations such as qubit architecture (connectivity) and instruction (gate) set. General-purpose quantum compilers work at the gate level and have little knowledge of the mathematical properties of quantum applications, missing further optimization opportunities. Existing application-specific compilers only apply advanced optimizations in the scheduling procedure and are restricted to the C…
To ensure a long-term quantum computational advantage, the quantum hardware should be upgraded to withstand the competition of continuously improved classical algorithms and hardwares. Here, we demonstrate a superconducting quantum computing systems \textit{Zuchongzhi} 2.1, which has 66 qubits in a two-dimensional array in a tunable coupler architecture. The readout fidelity of \textit{Zuchongzhi} 2.1 is considerably improved to an average of 97.74\%. The more powerful quantum processor enables us to achieve larger-scale random quantum circuit sampling, with a system scale of up to 60 qubits a…
The circuit model of quantum computation is reformulated as a multilayer network theory [3] called a Quantum Multiverse Network (QuMvN). The QuMvN formulation allows us to interpret the quantum wave function as a combination of ergodic Markov Chains where each Markov Chain occupies a different layer in the QuMvN structure. Layers of a QuMvN are separable components of the corresponding wave function. Single qubit measurement is defined as a state transition of the Markov Chain that emits either a $0$ or $1$ making each layer of the QuMvN a Discrete Information Source. A message is equivalent t…
