Shallow shadows: Expectation estimation using low-depth random Clifford circuits

• URL: http://arxiv.org/abs/2209.12924v2
• Date: Tue, 11 Apr 2023 08:06:59 GMT
• Title: Shallow shadows: Expectation estimation using low-depth random Clifford circuits
• Authors: Christian Bertoni, Jonas Haferkamp, Marcel Hinsche, Marios Ioannou, Jens Eisert, Hakop Pashayan
• Abstract summary: We present a depth-modulated randomized measurement scheme that interpolates between two known classical shadows schemes. We focus on the regime where depth scales logarithmically in n and provide evidence that this retains the desirable properties of both extremal schemes. We present methods for two key tasks; estimating expectation values of certain observables from generated classical shadows and, computing upper bounds on the depth-modulated shadow norm.
• Score: 0.8481798330936976
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We provide practical and powerful schemes for learning many properties of an unknown n-qubit quantum state using a sparing number of copies of the state. Specifically, we present a depth-modulated randomized measurement scheme that interpolates between two known classical shadows schemes based on random Pauli measurements and random Clifford measurements. These can be seen within our scheme as the special cases of zero and infinite depth, respectively. We focus on the regime where depth scales logarithmically in n and provide evidence that this retains the desirable properties of both extremal schemes whilst, in contrast to the random Clifford scheme, also being experimentally feasible. We present methods for two key tasks; estimating expectation values of certain observables from generated classical shadows and, computing upper bounds on the depth-modulated shadow norm, thus providing rigorous guarantees on the accuracy of the output estimates. We consider observables that can be written as a linear combination of poly(n) Paulis and observables that can be written as a low bond dimension matrix product operator. For the former class of observables both tasks are solved efficiently in n. For the latter class, we do not guarantee efficiency but present a method that works in practice; by variationally computing a heralded approximate inverses of a tensor network that can then be used for efficiently executing both these tasks.

Related papers

• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Optimization for expectation value estimation with shallow quantum circuits [1.5733643545082079]
  Estimating linear properties of quantum states is a fundamental task in quantum information science. We propose a framework that optimize sample complexity for estimating the expectation value of any observable using a shallow parameterized quantum circuit. We numerically demonstrate the performance of our algorithm by estimating the ground energy of a sparse Hamiltonian and the inner product of two pure states.
  arXiv  Detail & Related papers  (2024-07-28T14:04:33Z)
• Quantization of Large Language Models with an Overdetermined Basis [73.79368761182998]
  We introduce an algorithm for data quantization based on the principles of Kashin representation. Our findings demonstrate that Kashin Quantization achieves competitive or superior quality in model performance.
  arXiv  Detail & Related papers  (2024-04-15T12:38:46Z)
• Adversarial Likelihood Estimation With One-Way Flows [44.684952377918904]
  Generative Adversarial Networks (GANs) can produce high-quality samples, but do not provide an estimate of the probability density around the samples. We show that our method converges faster, produces comparable sample quality to GANs with similar architecture, successfully avoids over-fitting to commonly used datasets and produces smooth low-dimensional latent representations of the training data.
  arXiv  Detail & Related papers  (2023-07-19T10:26:29Z)
• Operator relaxation and the optimal depth of classical shadows [0.0]
  We study the sample complexity of learning the expectation value of Pauli operators via shallow shadows'' We show that the shadow norm is expressed in terms of properties of the Heisenberg time evolution of operators under the randomizing circuit.
  arXiv  Detail & Related papers  (2022-12-22T18:46:46Z)
• Thrifty shadow estimation: re-using quantum circuits and bounding tails [1.6814343144960449]
  We propose a more practical variant of the protocol, thrifty shadow estimation, in which quantum circuits are reused many times. We show that reuse is maximally effective when sampling Haar random unitaries, and maximally ineffective when sampling from the Clifford group.
  arXiv  Detail & Related papers  (2022-12-12T20:50:41Z)
• Closed-form analytic expressions for shadow estimation with brickwork circuits [0.4997673761305335]
  Properties of quantum systems can be estimated using classical shadows. We derive analytical expressions for shadow estimation using brickwork circuits. We find improved sample complexity in the estimation of observables supported on sufficiently many qubits.
  arXiv  Detail & Related papers  (2022-11-17T19:01:15Z)
• Estimating Quantum Hamiltonians via Joint Measurements of Noisy Non-Commuting Observables [0.0]
  We introduce a method for performing a single joint measurement that can be implemented locally. We derive bounds on the number of experimental repetitions required to estimate energies up to a certain precision. We adapt the joint measurement strategy to minimise the sample complexity when the implementation of measurements is assumed noisy.
  arXiv  Detail & Related papers  (2022-06-17T17:42:54Z)
• Generalization Metrics for Practical Quantum Advantage in Generative Models [68.8204255655161]
  Generative modeling is a widely accepted natural use case for quantum computers. We construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Our simulation results show that our quantum-inspired models have up to a $68 times$ enhancement in generating unseen unique and valid samples.
  arXiv  Detail & Related papers  (2022-01-21T16:35:35Z)
• Learnability of the output distributions of local quantum circuits [53.17490581210575]
  We investigate, within two different oracle models, the learnability of quantum circuit Born machines. We first show a negative result, that the output distributions of super-logarithmic depth Clifford circuits are not sample-efficiently learnable. We show that in a more powerful oracle model, namely when directly given access to samples, the output distributions of local Clifford circuits are computationally efficiently PAC learnable.
  arXiv  Detail & Related papers  (2021-10-11T18:00:20Z)
• High Probability Complexity Bounds for Non-Smooth Stochastic Optimization with Heavy-Tailed Noise [51.31435087414348]
  It is essential to theoretically guarantee that algorithms provide small objective residual with high probability. Existing methods for non-smooth convex optimization have complexity bounds with dependence on confidence level. We propose novel stepsize rules for two methods with gradient clipping.
  arXiv  Detail & Related papers  (2021-06-10T17:54:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.