Hierarchical qubit maps and hierarchically implemented quantum error correction

Klco, Natalie; Savage, Martin J.

doi:10.1103/physreva.104.062425

Cited by 14 publications

(4 citation statements)

References 57 publications

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“…Explorations of such mappings, and their relative quantum resource efficiency for gauge-invariant HEP problems of interest remain an open, but important first step. There have been several successful HEP problem implementations, generally focusing on how to truncate gauge degrees of freedom while simultaneously satisfying gauge constraints efficiently [42,119]. This has paved the way, similarly to fermionic mappings, for methods of how to actually embed HEP simulations natively in error detection and correction schemes [41,120].…”

Section: Encodingsmentioning

confidence: 99%

Snowmass White Paper: Quantum Computing Systems and Software for High-energy Physics Research

Humble¹,

Delgado²,

Pooser³

et al. 2022

Preprint

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Quantum computing offers a new paradigm for advancing high-energy physics research by enabling novel methods for representing and reasoning about fundamental quantum mechanical phenomena. Realizing these ideals will require the development of novel computational tools for modeling and simulation, detection and classification, data analysis, and forecasting of high-energy physics (HEP) experiments. While the emerging hardware, software, and applications of quantum computing are exciting opportunities, significant gaps remain in integrating such techniques into the HEP community research programs. Here we identify both the challenges and opportunities for developing quantum computing systems and software to advance HEP discovery science. We describe opportunities for the focused development of algorithms, applications, software, hardware, and infrastructure to support both practical and theoretical applications of quantum computing to HEP problems within the next 10 years. I.MOTIVATION

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Section: Encodingsmentioning

confidence: 99%

Snowmass White Paper: Quantum Computing Systems and Software for High-energy Physics Research

Humble¹,

Delgado²,

Pooser³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Furthermore, performing scale setting classically can reduce quantum resources [57][58][59]. Lattice field theory specific error correction or mitigation could also potentially decrease quantum costs [60,61].…”

Section: Kks =mentioning

confidence: 99%

Improved Hamiltonians for Quantum Simulations

Carena,

Lamm,

et al. 2022

Preprint

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The quantum simulation of lattice gauge theories for the foreseeable future will be hampered by limited resources. The historical success of Symanzik-improved lattice actions in classical simulations strongly suggests that improved Hamiltonians will reduce quantum resources for fixed discretization errors. In this work, we consider Symanzik-improved lattice Hamiltonians for pure gauge theories and design quantum circuits for O(a 2 )-improved Hamiltonians in terms of primitive group gates. An explicit demonstration for Z2 is presented including exploratory tests using the ibm perth device.

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“…With the long-time goal of performing quantum simulation of LGT on fault-tolerant protocols, an intriguing possibility is to tailor general purpose error correction schemes to best exploit the structural properties of these theories in order to reduce the resource requirements for early explorations (see e.g., 18 for a recent attempt in this direction using the surface code). The physical intuition behind the approach followed in this work is that error correcting codes can be seen as artificial gauge theories where the logical Hilbert space is determined by states that satisfy a suitable local symmetry.…”

Section: Introductionmentioning

confidence: 99%

Quantum error correction with gauge symmetries

2023

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Quantum simulations of lattice gauge theories (LGTs) are often formulated on an enlarged Hilbert space containing both physical and unphysical sectors in order to retain a local Hamiltonian. We provide simple fault-tolerant procedures that exploit such redundancy by combining a phase flip error correction code with the Gauss’ law constraint to correct one-qubit errors for a $${{\mathbb{Z}}}_{2}$$ Z 2 or truncated U(1) LGT in 1+1 and 2+1 dimensions with a link flux cutoff of 1. Unlike existing work on detecting violations of Gauss’ law, our circuits are fault tolerant and the overall error correction scheme outperforms a naïve application of the [5, 1, 3] code. The constructions outlined can be extended to LGT systems with larger cutoffs and may be of use in understanding how to hybridize error correction and quantum simulation for LGTs in higher space-time dimensions and with different symmetry groups.

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Hierarchical qubit maps and hierarchically implemented quantum error correction

Cited by 14 publications

References 57 publications

Snowmass White Paper: Quantum Computing Systems and Software for High-energy Physics Research

Snowmass White Paper: Quantum Computing Systems and Software for High-energy Physics Research

Improved Hamiltonians for Quantum Simulations

Quantum error correction with gauge symmetries

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