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Exact holographic tensor networks for the Motzkin spin chain

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Rafael N. Alexander1,2, Glen Evenbly3, and Israel Klich4

1Centre for Quantum Computation and Communication Technology, School of Science, RMIT University, Melbourne, VIC 3000, Australia
2Center for Quantum Information and Control, University of New Mexico, Albuquerque, NM 87131, USA
3School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
4Department of Physics, University of Virginia, Charlottesville, Virginia 22903, USA

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Abstract

The study of low-dimensional quantum systems has proven to be a particularly fertile field for discovering novel types of quantum matter. When studied numerically, low-energy states of low-dimensional quantum systems are often approximated via a tensor-network description. The tensor network’s utility in studying short range correlated states in 1D have been thoroughly investigated, with numerous examples where the treatment is essentially exact. Yet, despite the large number of works investigating these networks and their relations to physical models, examples of exact correspondence between the ground state of a quantum critical system and an appropriate scale-invariant tensor network have eluded us so far. Here we show that the features of the quantum-critical Motzkin model can be faithfully captured by an analytic tensor network that exactly represents the ground state of the physical Hamiltonian. In particular, our network offers a two-dimensional representation of this state by a correspondence between walks and a type of tiling of a square lattice. We discuss connections to renormalization and holography.

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Cited by

[1] Thomas Schuster, Bryce Kobrin, Ping Gao, Iris Cong, Emil T. Khabiboulline, Norbert M. Linke, Mikhail D. Lukin, Christopher Monroe, Beni Yoshida, and Norman Y. Yao, “Many-body quantum teleportation via operator spreading in the traversable wormhole protocol”, arXiv:2102.00010.

[2] Rafael N. Alexander, Amr Ahmadain, Zhao Zhang, and Israel Klich, “Exact rainbow tensor networks for the colorful Motzkin and Fredkin spin chains”, Physical Review B 100 21, 214430 (2019).

[3] Glen Evenbly, “Number-State Preserving Tensor Networks as Classifiers for Supervised Learning”, arXiv:1905.06352.

[4] Jacob Miller, Guillaume Rabusseau, and John Terilla, “Tensor Networks for Probabilistic Sequence Modeling”, arXiv:2003.01039.

[5] A. Ahmadain and I. Klich, “Emergent geometry and path integral optimization for a Lifshitz action”, Physical Review D 103 10, 105013 (2021).

[6] Fumihiko Sugino, “Highly Entangled Spin Chains and 2D Quantum Gravity”, Symmetry 12 6, 916 (2020).

The above citations are from SAO/NASA ADS (last updated successfully 2021-09-21 15:40:03). The list may be incomplete as not all publishers provide suitable and complete citation data.

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Quantum

Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

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Julien Gacon1,2, Christa Zoufal1,3, Giuseppe Carleo2, and Stefan Woerner1

1IBM Quantum, IBM Research – Zurich, CH-8803 Rüschlikon, Switzerland
2Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
3Institute for Theoretical Physics, ETH Zurich, CH-8092 Zürich, Switzerland

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Abstract

The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFIM for a model with $d$ parameters, however, is computationally expensive and generally requires $mathcal{O}(d^2)$ function evaluations. To remedy these increasing costs in high-dimensional parameter spaces, we propose using simultaneous perturbation stochastic approximation techniques to approximate the QFIM at a constant cost. We present the resulting algorithm and successfully apply it to prepare Hamiltonian ground states and train Variational Quantum Boltzmann Machines.

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Cited by

[1] Tobias Haug, Kishor Bharti, and M. S. Kim, “Capacity and quantum geometry of parametrized quantum circuits”, arXiv:2102.01659.

[2] Johannes Jakob Meyer, “Fisher Information in Noisy Intermediate-Scale Quantum Applications”, arXiv:2103.15191.

[3] Tobias Haug and M. S. Kim, “Optimal training of variational quantum algorithms without barren plateaus”, arXiv:2104.14543.

[4] Tobias Haug and M. S. Kim, “Natural parameterized quantum circuit”, arXiv:2107.14063.

[5] Martin Larocca, Nathan Ju, Diego García-Martín, Patrick J. Coles, and M. Cerezo, “Theory of overparametrization in quantum neural networks”, arXiv:2109.11676.

[6] Christa Zoufal, David Sutter, and Stefan Woerner, “Error Bounds for Variational Quantum Time Evolution”, arXiv:2108.00022.

[7] Anna Lopatnikova and Minh-Ngoc Tran, “Quantum Natural Gradient for Variational Bayes”, arXiv:2106.05807.

The above citations are from SAO/NASA ADS (last updated successfully 2021-10-23 12:31:38). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2021-10-23 12:31:36).

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Quantum

Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation

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Patrick Rall

Quantum Information Center, University of Texas at Austin

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Abstract

We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum estimation algorithms make assumptions that make them unsuitable for this ‘coherent’ setting, leaving only the textbook approach. We present novel algorithms for phase, energy, and amplitude estimation that are both conceptually and computationally simpler than the textbook method, featuring both a smaller query complexity and ancilla footprint. They do not require a quantum Fourier transform, and they do not require a quantum sorting network to compute the median of several estimates. Instead, they use block-encoding techniques to compute the estimate one bit at a time, performing all amplification via singular value transformation. These improved subroutines accelerate the performance of quantum Metropolis sampling and quantum Bayesian inference.


Presentation at TQC 2021

A fundamental objective of quantum computing is to help study physical systems. One of the earliest results in the area was a fast quantum algorithm for measuring the energy of a system, which can serve as a building block for other quantum algorithms. However this algorithm is very complicated and hard to analyze. In this paper we present a simpler method based on applying polynomials to the Hamiltonian that extract each of the bits of the estimate. This technique is up to 20x faster than the prior state of the art.

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Cited by

[1] Yuan Su, Hsin-Yuan Huang, and Earl T. Campbell, “Nearly tight Trotterization of interacting electrons”, arXiv:2012.09194.

[2] John M. Martyn, Zane M. Rossi, Andrew K. Tan, and Isaac L. Chuang, “A Grand Unification of Quantum Algorithms”, arXiv:2105.02859.

The above citations are from SAO/NASA ADS (last updated successfully 2021-10-23 15:14:11). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2021-10-23 15:14:09).

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Quantum

Multidimensional cluster states using a single spin-photon interface coupled strongly to an intrinsic nuclear register

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Cathryn P. Michaels, Jesús Arjona Martínez, Romain Debroux, Ryan A. Parker, Alexander M. Stramma, Luca I. Huber, Carola M. Purser, Mete Atatüre, and Dorian A. Gangloff

Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, UK

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Abstract

Photonic cluster states are a powerful resource for measurement-based quantum computing and loss-tolerant quantum communication. Proposals to generate multi-dimensional lattice cluster states have identified coupled spin-photon interfaces, spin-ancilla systems, and optical feedback mechanisms as potential schemes. Following these, we propose the generation of multi-dimensional lattice cluster states using a single, efficient spin-photon interface coupled strongly to a nuclear register. Our scheme makes use of the contact hyperfine interaction to enable universal quantum gates between the interface spin and a local nuclear register and funnels the resulting entanglement to photons via the spin-photon interface. Among several quantum emitters, we identify the silicon-29 vacancy centre in diamond, coupled to a nanophotonic structure, as possessing the right combination of optical quality and spin coherence for this scheme. We show numerically that using this system a 2×5-sized cluster state with a lower-bound fidelity of 0.5 and repetition rate of 65 kHz is achievable under currently realised experimental performances and with feasible technical overhead. Realistic gate improvements put 100-photon cluster states within experimental reach.

Quantum states composed of multiple entangled photons are a key resource in quantum computing networks, both for robust communication and for implementing computational tasks. Photonic cluster states whose entanglement is multidimensional are required for universal quantum protocols. Such cluster states can be obtained from a highly efficient single-photon source, together with entangling gates between distinct emitters or between local spins. We propose to use the multidimensional entanglement naturally available to a single diamond colour center strongly coupled to an intrinsic nuclear spin to create multi-dimensional cluster states of photons. Our simulations show that 100-photon cluster states are realisable within achievable experimental parameters.

► BibTeX data

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Cited by

[1] Bikun Li, Sophia E. Economou, and Edwin Barnes, “Entangled photon factory: How to generate quantum resource states from a minimal number of quantum emitters”, arXiv:2108.12466.

The above citations are from SAO/NASA ADS (last updated successfully 2021-10-23 14:31:01). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2021-10-23 14:31:00).

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Quantum

Dynamically Generated Logical Qubits

Published

on

Matthew B. Hastings1,2 and Jeongwan Haah2

1Station Q, Microsoft Quantum, Santa Barbara, CA 93106-6105, USA
2Microsoft Quantum and Microsoft Research, Redmond, WA 98052, USA

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We present a quantum error correcting code with $textit{dynamically generated logical qubits}$. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement patterns generate logical qubits, allowing the code to act as a fault-tolerant quantum memory. Our particular code gives a model very similar to the two-dimensional toric code, but each measurement is a $two$-qubit Pauli measurement.

► BibTeX data

► References

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Cited by

[1] Craig Gidney, Michael Newman, Austin Fowler, and Michael Broughton, “A Fault-Tolerant Honeycomb Memory”, arXiv:2108.10457.

[2] James R. Wootton, “Hexagonal matching codes with 2-body measurements”, arXiv:2109.13308.

[3] Yaodong Li and Matthew P. A. Fisher, “Robust decoding in monitored dynamics of open quantum systems with Z_2 symmetry”, arXiv:2108.04274.

[4] Edward H. Chen, Theodore J. Yoder, Youngseok Kim, Neereja Sundaresan, Srikanth Srinivasan, Muyuan Li, Antonio D. Córcoles, Andrew W. Cross, and Maika Takita, “Calibrated decoders for experimental quantum error correction”, arXiv:2110.04285.

[5] Christopher A. Pattison, Michael E. Beverland, Marcus P. da Silva, and Nicolas Delfosse, “Improved quantum error correction using soft information”, arXiv:2107.13589.

[6] Christophe Vuillot, “Planar Floquet Codes”, arXiv:2110.05348.

[7] Julia Wildeboer, Thomas Iadecola, and Dominic J. Williamson, “Symmetry-Protected Infinite-Temperature Quantum Memory from Subsystem Codes”, arXiv:2110.05710.

[8] Andrew J. Landahl and Benjamin C. A. Morrison, “Logical Majorana fermions for fault-tolerant quantum simulation”, arXiv:2110.10280.

[9] Jeongwan Haah and Matthew B. Hastings, “Boundaries for the Honeycomb Code”, arXiv:2110.09545.

The above citations are from SAO/NASA ADS (last updated successfully 2021-10-23 13:49:03). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2021-10-23 13:49:01).

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Source: https://quantum-journal.org/papers/q-2021-10-19-564/

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