• Corpus ID: 238634707

Learnability of the output distributions of local quantum circuits

  title={Learnability of the output distributions of local quantum circuits},
  author={Marcel Hinsche and Marios Ioannou and A. Nietner and Jonas Haferkamp and Yihui Quek and Dominik Hangleiter and Jean-Pierre Seifert and Jens Eisert and Ryan Sweke},
M. Hinsche, M. Ioannou, A. Nietner, J. Haferkamp, 2 Y. Quek, 1 D. Hangleiter, 1 J.-P. Seifert, 6 J. Eisert, 2, 7 and R. Sweke Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany Information Systems Laboratory, Stanford University, Stanford, CA 94305, USA Joint Center for Quantum Information and Computer Science (QuICS), University of Maryland and NIST, College Park, MD 20742, USA… 

Figures from this paper

Complexity phase transitions in instantaneous quantum polynomial-time circuits
We study a subclass of the Instantaneous Quantum Polynomial-time (IQP) circuit with a varying density of two-qubit gates. We identify two phase transitions as a function of the gate density. At the
Equivariant Quantum Graph Circuits
This work proposes equivariant quantum graph circuits (EQGCs), as a class of parameterized quantum circuits with strong relational inductive bias for learning over graph-structured data, and proves that the subclasses of interest are universal approximators for functions over the bounded graph domain.
Learning Classical Readout Quantum PUFs based on single-qubit gates
This work formalizes the class of Classical Readout Quantum PUFs (CR-QPUFs) using the statistical query (SQ) model and explicitly shows insufficient security for CR-Q PUFs based on single qubit rotation gates, when the adversary has SQ access to the CR-ZPUF.
Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
It is proved that a wide class of variational quantum models—which are shallow, and exhibit no barren plateus—have only a superpolynomially small fraction of local minima within any constant energy from the global minimum, rendering these models untrainable if no good initial guess of the optimal parameters is known.
Evaluating Generalization in Classical and Quantum Generative Models
Using the sample-based generalization metrics proposed here, any generative model, from state-of-the-art classical generative models such as GANs to quantum models, can be evaluated on the same ground on a concrete well-defined framework and foresee these metrics as valuable tools for rigorously defining practical quantum advantage in the domain of generative modeling.


Stabiliser states are efficiently PAC-learnable
The results solve an open problem formulated by Aaronson (2007) and establish a connection between classical simulation of quantum systems and efficient learnability.
Local Random Quantum Circuits are Approximate Polynomial-Designs
We prove that local random quantum circuits acting on n qubits composed of O(t10n2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether
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.
The learnability of quantum states
  • S. Aaronson
  • Physics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2007
This theorem has the conceptual implication that quantum states, despite being exponentially long vectors, are nevertheless ‘reasonable’ in a learning theory sense and has two applications to quantum computing: first, a new simulation of quantum one-way communication protocols and second, the use of trusted classical advice to verify untrusted quantum advice.
Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
  • M. Bremner, R. Jozsa, D. 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.
Sample Complexity of Device-Independently Certified "Quantum Supremacy".
It is shown that any noninteractive certification from classical samples and a description of the target distribution requires exponentially many uses of the device, and that the sampling distributions, as random variables depending on the random unitaries defining the problem instances, have small second moments.
A quantum machine learning algorithm based on generative models
A general quantum algorithm for machine learning based on a quantum generative model that is more capable of representing probability distributions compared with classical generative models and has exponential speedup in learning and inference at least for some instances if a quantum computer cannot be efficiently simulated classically.
The Clifford group forms a unitary 3-design
  • Z. Webb
  • Mathematics
    Quantum Inf. Comput.
  • 2016
It is proved that the Clifford group is a 3-design, showing that it is a better approximation to Haar-random unitaries than previously expected and characterizing how well random Clifford elements approximateHaar- random unitaries.
Quantum generative adversarial learning in a superconducting quantum circuit
It is demonstrated that, after several rounds of adversarial learning, a quantum-state generator can be trained to replicate the statistics of the quantum data output from a quantum channel simulator, with a high fidelity so that the discriminator cannot distinguish between the true and the generated data.
A General Characterization of the Statistical Query Complexity
This work demonstrates that the complexity of solving general problems over distributions using SQ algorithms can be captured by a relatively simple notion of statistical dimension that is introduced, and is also the first to precisely characterize the necessary tolerance of queries.