The XZZX surface code

Ataides, J. Pablo Bonilla; Tuckett, David K.; Bartlett, Stephen D.; Flammia, Steven T.; Brown, Benjamin J.

doi:10.1038/s41467-021-22274-1

Cited by 157 publications

(115 citation statements)

References 72 publications

(138 reference statements)

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“…As a result, we can prepare any state in the codespace of the surface code in step 2, and it does not matter if the Pauli correction R in step 3 acts non-trivially on the logical qubit. The problem of finding a suitable correction R in step 3 given the syndrome of each generator is essentially the same problem as decoding the XZZX surface code [3,53] under the quantum erasure channel (and where every qubit is erased). Therefore, any other suitable decoder could be used instead of using Equation ( 15), such as the variant of minimum-weight perfect matching used in Ref.…”

Section: Encoding Circuit For the Compact Mappingmentioning

confidence: 99%

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Optimal local unitary encoding circuits for the surface code

Higgott

Wilson

Hefford

et al. 2021

Quantum

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The surface code is a leading candidate quantum error correcting code, owing to its high threshold, and compatibility with existing experimental architectures. Bravyi et al. (2006) showed that encoding a state in the surface code using local unitary operations requires time at least linear in the lattice size L, however the most efficient known method for encoding an unknown state, introduced by Dennis et al. (2002), has O(L2) time complexity. Here, we present an optimal local unitary encoding circuit for the planar surface code that uses exactly 2L time steps to encode an unknown state in a distance L planar code. We further show how an O(L) complexity local unitary encoder for the toric code can be found by enforcing locality in the O(log⁡L)-depth non-local renormalisation encoder. We relate these techniques by providing an O(L) local unitary circuit to convert between a toric code and a planar code, and also provide optimal encoders for the rectangular, rotated and 3D surface codes. Furthermore, we show how our encoding circuit for the planar code can be used to prepare fermionic states in the compact mapping, a recently introduced fermion to qubit mapping that has a stabiliser structure similar to that of the surface code and is particularly efficient for simulating the Fermi-Hubbard model.

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Section: Encoding Circuit For the Compact Mappingmentioning

confidence: 99%

“…Therefore, any other suitable decoder could be used instead of using Equation ( 15), such as the variant of minimum-weight perfect matching used in Ref. [3], or an adaptation of the peeling decoder [17].…”

Section: Encoding Circuit For the Compact Mappingmentioning

confidence: 99%

Optimal local unitary encoding circuits for the surface code

Higgott

Wilson

Hefford

et al. 2021

Quantum

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show abstract

“…The enormous resource estimates mentioned above are all obtained using fault-tolerant architectures based on quantum error-correcting codes with local check operators [12][13][14][15][16]. These codes have a number of highly desirable features for quantum computation, including high thresholds and fast decoders [7,17].…”

Section: Introductionmentioning

confidence: 99%

Low-overhead fault-tolerant quantum computing using long-range connectivity

Cohen,

Kim,

Bartlett

et al. 2021

Preprint

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Vast numbers of qubits will be needed for large-scale quantum computing using today's faulttolerant architectures due to the overheads associated with quantum error correction. We present a scheme for low-overhead fault-tolerant quantum computation based on quantum low-density paritycheck (LDPC) codes, where the capability of performing long-range entangling interactions allows a large number of logical qubits to be encoded with a modest number of physical qubits. In our approach, quantum logic gates operate via logical Pauli measurements that preserve both the protection of the LDPC codes as well as the low overheads in terms of required number of additional ancilla qubits. Compared with the surface code architecture, resource estimates for our scheme indicate order-of-magnitude improvements in the overheads for encoding and processing around one hundred logical qubits, meaning fault-tolerant quantum computation at this scale may be achievable with a few thousand physical qubits at achievable error rates.

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“…Recently, error-biased qubits have been actively investigated for their promise of hardware-efficient and fault-tolerant universal quantum computation [8][9][10][11][12][13][14]. In particular, the bosonic cat qubit encoding [15] is showing potential thanks to its exponential error bias [16] inherited from a non-local encoding in the phase space of a harmonic oscillator.…”

Section: Introductionmentioning

confidence: 99%

Combined Dissipative and Hamiltonian Confinement of Cat Qubits

Gautier,

Sarlette,

Mirrahimi

2021

Preprint

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Quantum error correction with biased-noised qubits can drastically reduce the hardware overhead for universal and fault-tolerant quantum computation. Cat qubits are a promising realization of biased noise qubits as they feature an exponential error bias inherited from their non-local encoding in the phase space of a quantum harmonic oscillator. To confine the state of an oscillator to the cat qubit manifold, two main approaches have been considered so far: a Kerr-based Hamiltonian confinement with high gate performances, and a dissipative confinement with robust protection against a broad range of noise mechanisms. We introduce a new combined dissipative and Hamiltonian confinement scheme based on two-photon dissipation together with a Two-Photon Exchange (TPE) Hamiltonian. The TPE Hamiltonian is similar to Kerr nonlinearity, but unlike the Kerr it only induces a bounded distinction between even-and odd-photon eigenstates, a highly beneficial feature for protecting the cat qubits with dissipative mechanisms. Using this combined confinement scheme, we demonstrate fast and bias-preserving gates with drastically improved performance compared to dissipative or Hamiltonian schemes. In addition, this combined scheme can be implemented experimentally with only minor modifications of existing dissipative cat qubit experiments.

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The XZZX surface code

Cited by 157 publications

References 72 publications

Optimal local unitary encoding circuits for the surface code

Optimal local unitary encoding circuits for the surface code

Low-overhead fault-tolerant quantum computing using long-range connectivity

Combined Dissipative and Hamiltonian Confinement of Cat Qubits

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