Quantum Low-Density Parity-Check Codes

Breuckmann, Nikolas P.; Eberhardt, Jens Niklas

doi:10.1103/prxquantum.2.040101

Cited by 118 publications

(55 citation statements)

References 84 publications

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“…Fur-thermore, the ability to reconfigure and interlace our arrays will allow efficient, parallel execution of transversal entangling gates between many logical qubits [37,46]. In addition, these techniques also enable implementation of higher-dimensional or nonlocal error correcting codes with more favorable properties [47,48]. Together, these ingredients could enable a new approach to universal, fault-tolerant quantum computing with thousands of physical qubits.…”

Section: Discussion and Outlookmentioning

confidence: 99%

A quantum processor based on coherent transport of entangled atom arrays

Bluvstein,

Levine,

Semeghini

et al. 2021

Preprint

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The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is central for building scalable quantum information systems [1,2]. In most stateof-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here, we demonstrate a quantum processor with dynamic, nonlocal connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, in between layers of single-and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation [3][4][5]. We use this architecture to realize programmable generation of entangled graph states such as cluster states and a 7-qubit Steane code state [6,7]. Furthermore, we shuttle entangled ancilla arrays to realize a surface code with 19 qubits [8] and a toric code state on a torus with 24 qubits [9]. Finally, we use this architecture to realize a hybrid analog-digital evolution [2] and employ it for measuring entanglement entropy in quantum simulations [10][11][12], experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars [13,14]. Realizing a long-standing goal, these results pave the way toward scalable quantum processing and enable new applications ranging from simulation to metrology.

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Section: Discussion and Outlookmentioning

confidence: 99%

A quantum processor based on coherent transport of entangled atom arrays

Bluvstein,

Levine,

Semeghini

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…While we analyze the surface code in this work because of the availability of simple, accurate decoders, we expect erasure conversion to realize a similar benefit on any code. In combination with the flexible connectivity of neutral atom arrays enabled by dynamic rearrangement [58][59][60], this opens the door to implementing a wide range of efficient codes [61].…”

Section: Discussionmentioning

confidence: 99%

Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays

Wu,

Kolkowitz,

Puri

et al. 2022

Preprint

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Executing quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Recently, the development of error correcting codes tailored to particular physical noise models has helped relax these requirements. In this work, we propose a qubit encoding and gate protocol for 171 Yb neutral atom qubits that converts the dominant physical errors into erasures, that is, errors in known locations. The key idea is to encode qubits in a metastable electronic level, such that gate errors predominantly result in transitions to disjoint subspaces whose populations can be continuously monitored via fluorescence. We estimate that 98% of errors can be converted into erasures. We quantify the benefit of this approach via circuit-level simulations of the surface code, finding a threshold increase from 0.937% to 4.15%. We also observe a larger code distance near the threshold, leading to a faster decrease in the logical error rate for the same number of physical qubits, which is important for near-term implementations. Erasure conversion should benefit any error correcting code, and may also be applied to design new gates and encodings in other qubit platforms.

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“…As we have discussed above, the GKP qubit is a two-dimensional subspace of an infinite dimensional Hilbert space that is stabilized by the operators in Eq. (2). While the GKP analog information can be used to postselect some of the logical error events, it has been shown that concatenating GKP qubits with an outer stabilizer code provides substantial gains [18], [23].…”

Section: Gkp Concatenation Frameworkmentioning

confidence: 99%

Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound

Raveendran,

Rengaswamy,

Rozpędek

et al. 2021

Preprint

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Quantum error correction has recently been shown to benefit greatly from specific physical encodings of the code qubits. In particular, several researchers have considered the individual code qubits being encoded with the continuous variable Gottesman-Kitaev-Preskill (GKP) code, and then imposed an outer discrete-variable code such as the surface code on these GKP qubits. Under such a concatenation scheme, the analog information from the inner GKP error correction improves the noise threshold of the outer code. However, the surface code has vanishing rate and demands a lot of resources with growing distance. In this work, we concatenate the GKP code with generic quantum low-density parity-check (QLDPC) codes and demonstrate a natural way to exploit the GKP analog information in iterative decoding algorithms. We first show the noise thresholds for two lifted product QLDPC code families, and then show the improvements of noise thresholds when the iterative decoder -a hardwarefriendly min-sum algorithm (MSA) -utilizes the GKP analog information. We also show that, when the GKP analog information is combined with a sequential update schedule for MSA, the scheme surpasses the well-known CSS Hamming bound for these code families. Furthermore, we observe that the GKP analog information helps the iterative decoder in escaping harmful trapping sets in the Tanner graph of the QLDPC code, thereby eliminating or significantly lowering the error floor of the logical error rate curves. Finally, we discuss new fundamental and practical questions that arise from this work on channel capacity under GKP analog information, and on improving decoder design and analysis.N. Raveendran, N. Rengaswamy and B. Vasić are with the

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Quantum Low-Density Parity-Check Codes

Cited by 118 publications

References 84 publications

A quantum processor based on coherent transport of entangled atom arrays

A quantum processor based on coherent transport of entangled atom arrays

Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays

Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound

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