Efficient classical simulation of random shallow 2D quantum circuits

  title={Efficient classical simulation of random shallow 2D quantum circuits},
  author={John Napp and Rolando L. La Placa and Alexander M. Dalzell and Fernando G. S. L. Brand{\~a}o and Aram Wettroth Harrow},
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random gates, approximate simulation of typical instances is almost as hard as exact simulation. We prove that this is not the case by exhibiting a shallow circuit family with uniformly random gates that cannot be efficiently classically simulated near-exactly under… 

Improved robustness of quantum supremacy for random circuit sampling

It is proved under the complexity theoretical assumption of the non-collapse of the polynomial hierarchy that approximating the output probabilities of random quantum circuits to within exp(−Ω(m logm)) additive error is hard for any classical computer, where m is the number of gates in the quantum computation.

Random Quantum Circuits Anticoncentrate in Log Depth

The definition of anti-concentration is that the expected collision probability, that is, the probability that two independently drawn outcomes will agree, is only a constant factor larger than if the distribution were uniform, and it is shown that when the 2-local gates are each drawn from the Haar measure, at least $\Omega(n \log(n)$ gates are needed for this condition to be met on an qudit circuit.

Quantum supremacy and random circuits.

It is proved that estimating the output probabilities of random quantum circuits is formidably hard for any classical computer, implying that there is an exponential hardness barrier for the classical simulation of most quantum circuits.

Computational power of one- and two-dimensional dual-unitary quantum circuits

This research presents a probabilistic simulation of the response of the immune system to quantum fluctuations in a proton-proton collisions and shows clear patterns of decline in the presence of EMTs.

Efficient classical simulation of noisy random quantum circuits in one dimension

It is numerically demonstrated that for the two-qubit gate error rates the authors considered, there exists a characteristic system size above which adding more qubits does not bring about an exponential growth of the cost of classical MPO simulation of 1D noisy systems, possibly making classical simulation practically not feasible even with state-of-the-art supercomputers.

Quantum supremacy and hardness of estimating output probabilities of quantum circuits

It is proved under the complexity theoretical assumption of the non-collapse of the polynomial hierarchy that approximating the output probabilities of random quantum circuits to within $\exp(-\Omega(m\log m))$ additive error is hard for any classical computer, where $m$ is the number of gates in the quantum computation.

Average-case hardness of estimating probabilities of random quantum circuits with a linear scaling in the error exponent

  • H. Krovi
  • Computer Science, Mathematics
  • 2022
The hardness of computing additive approximations to output probabilities of random quantum circuits is considered and it is shown that approximating the Ising partition function with imaginary couplings to an additive error of 2 − O ( n ) is hard even in the average-case, which extends prior work on worst-case hardness of multiplicative approximation toIsing partition functions.

Classical simulation of bosonic linear-optical random circuits beyond linear light cone

Sampling from probability distributions of quantum circuits is a fundamentally and practically important task which can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum

Boundaries of quantum supremacy via random circuit sampling

The constraints of the observed quantum runtime advantage in an analytical extrapolation to circuits with a larger number of qubits and gates are examined, suggesting the boundaries of quantum supremacy via random circuit sampling may fortuitously coincide with the advent of scalable, error corrected quantum computing in the near term.

Quantum Coding with Low-Depth Random Circuits

It is found that for any rate beneath the capacity, high-performing codes with thousands of logical qubits are achievable with depth 4-8 expurgated random circuits in $D=2$ dimensions.



Achieving quantum supremacy with sparse and noisy commuting quantum computations

It is shown that purely classical error-correction techniques can be used to design IQP circuits which remain hard to simulate classically, even in the presence of arbitrary amounts of noise of this form.

On the complexity and verification of quantum random circuit sampling

Evidence is provided that quantum random circuit sampling, a near-term quantum computational task, is classically hard but verifiable, making it a leading proposal for achieving quantum supremacy.

Efficient classical simulation of noisy quantum computation

It is proved that under general conditions most of the quantum circuits at any constant level of noise per gate can be efficiently simulated classically with the cost increasing only polynomially with the size of the circuits.

Unitary designs from statistical mechanics in random quantum circuits.

It is argued that random circuits form approximate unitary $k$-designs in O(nk) depth and are thus essentially optimal in both £n and $k, and can be shown in the limit of large local dimension.

Polynomial simulations of decohered quantum computers

  • D. AharonovM. Ben-Or
  • Physics, Computer Science
    Proceedings of 37th Conference on Foundations of Computer Science
  • 1996
This work presents a simulation of decohered sequential quantum computers, on a classical probabilistic Turing machine, and proves that the expected slowdown of this simulation is polynomial in time and space of the quantum computation, for any non zero decoherence rate.

Classical simulability, entanglement breaking, and quantum computation thresholds (11 pages)

We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modeled classically. This question is useful for providing upper bounds on

Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy

  • M. BremnerR. JozsaD. Shepherd
  • Computer Science, Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2010
The class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection is introduced, and it is proved first that post- IQP equals the classical class PP, and that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, then the infinite tower of classical complexity classes known as the polynomial hierarchy would collapse to its third level.

Can Chaotic Quantum Circuits Maintain Quantum Supremacy under Noise

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

Classical algorithms for quantum mean values

It is shown that a classical approximation is possible when the quantum circuits are limited to constant depth, and sub-exponential time classical algorithms are developed for solving the quantum mean value problem for general classes of quantum observables and constant-depth quantum circuits.

Complexity-Theoretic Foundations of Quantum Supremacy Experiments

General theoretical foundations are laid for how to use special-purpose quantum computers with 40--50 high-quality qubits 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.