Universal Parity Quantum Computing

Fellner, Michael; Messinger, Anette; Ender, Kilian; Lechner, Wolfgang

doi:10.1103/physrevlett.129.180503

Cited by 14 publications

(13 citation statements)

References 53 publications

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“…. , K) for the case of K = 7 [36][37][38]. Without this row, the layout of the physical spins is reduced to the original LHZ layout that is fully consistent with the Hamiltonian H phys (z) [5].…”

Section: Parity Encodingmentioning

confidence: 99%

“…Let us examine how the PE spin network is described in the quantum-mechanical context. We introduce the concept of logical lines Q i , or constraint-preserving driver lines [37], which define the subsets of the physical operators that preserve the space of the code state and have one-to-one correspondence with the Pauli operators on the logical spins [36][37][38][39][40][41]. Consider the Pauli-z operators ẑij that are associated with the physical spins in the PE spin network.…”

Section: Parity Encodingmentioning

confidence: 99%

“…The stabilizer operator Ŝi k (ẑ) commutes with Ĥphys (ẑ) and anti-commutes with the spin-flip errors for the physical spins involved in Eq. ( 37) or (38).…”

Section: Qacmentioning

confidence: 99%

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Error correction of parity-encoding-based annealing through post-readout decoding

Nambu

2024

Preprint

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Lechner, Hauke, and Zoller proposed a parity-encoded spin-embedding scheme for quantum annealing (QA) with all-to-all connectivity to avoid the issue of limited connectivity in near-term QA hardware and to enable the implementation thereof using only geometrically local interactions between spins fabricated on the planar substrate. Nevertheless, the redundant encoding of logical information, i.e., using a large number of spins to embed the logical information, increases the computational cost and reduces the efficiency. In this study, we show through Monte Carlo simulation that this redundant encoding may be exploited to solve the problems of the inefficiency and computational cost of the parity-encoded scheme by incorporating appropriate decoding, namely classical post-processing, of the spins to retrieve the logical information. Our findings open up the possibility of parity-encoded schemes for realizing the QA with near-term quantum technologies.

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Section: Parity Encodingmentioning

confidence: 99%

Section: Parity Encodingmentioning

confidence: 99%

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Error correction of parity-encoding-based annealing through post-readout decoding

Nambu

2024

Preprint

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“…In the previous section we studied the performance of parity QAOA using different amounts M of random spanning trees. Now we fix the decoding to a special set of spanning trees in the parity architecture: the logical lines [35,37], denoted by…”

Section: Logical Linesmentioning

confidence: 99%

“…The parity architecture was initially designed to tackle the issue of limited connectivity in quantum annealing hardware. However, when combined with digital hardware, the parity architecture provides the benefit of full parallelization of quantum gates [34], and universal quantum computing [35]. In addition, Ref.…”

Section: Introductionmentioning

confidence: 99%

Error Mitigation for Quantum Approximate Optimization

Weidinger¹,

Mbeng²,

Lechner³

2023

Preprint

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Solving optimization problems on near term quantum devices requires developing error mitigation techniques to cope with hardware decoherence and dephasing processes. We propose a mitigation technique based on the LHZ architecture. This architecture uses a redundant encoding of logical variables to solve optimization problems on fully programmable planar quantum chips. We discuss how this redundancy can be exploited to mitigate errors in quantum optimization algorithms. In the specific context of the quantum approximate optimization algorithm (QAOA), we show that errors can be significantly mitigated by appropriately modifying the objective cost function.

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Rewriting the quantum-computer blueprint

Cartlidge¹

2023

Nature

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Universal Parity Quantum Computing

Cited by 14 publications

References 53 publications

Error correction of parity-encoding-based annealing through post-readout decoding

Error correction of parity-encoding-based annealing through post-readout decoding

Error Mitigation for Quantum Approximate Optimization

Rewriting the quantum-computer blueprint

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