Dynamically Generated Logical Qubits

Hastings, Matthew B.; Haah, Jeongwan

doi:10.22331/q-2021-10-19-564

Cited by 80 publications

(27 citation statements)

References 13 publications

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“…Moreover, it will be interesting to modify our proposal for other topological codes. Our protocol adapts readily to other variations of the surface code with an equivalent boundary theory [28,[50][51][52], but we may also find that generalisations of our protocol using general topological codes [13,[53][54][55] with richer boundary theories [56][57][58][59][60][61] can outperform our surface code protocol. This future work will determine how best to nullify the harmful effects of fabrication defects in modern qubit architectures.…”

Section: Discussionmentioning

confidence: 85%

Quantum computing is scalable on a planar array of qubits with fabrication defects

Strikis¹,

Benjamin²,

Brown³

2021

Preprint

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To successfully execute large-scale algorithms, a quantum computer will need to perform its elementary operations near perfectly. This is a fundamental challenge since all physical qubits suffer a considerable level of noise. Moreover, real systems are likely to have a finite yield, i.e. some non-zero proportion of the components in a complex device may be irredeemably broken at the fabrication stage. We present a threshold theorem showing that an arbitrarily large quantum computation can be completed with a vanishing probability of failure using a two-dimensional array of noisy qubits with a finite density of fabrication defects. To complete our proof we introduce a robust protocol to measure high-weight stabilizers to compensate for large regions of inactive qubits. We obtain our result using a surface code architecture. Our approach is therefore readily compatible with ongoing experimental efforts to build a large-scale quantum computer.

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Section: Discussionmentioning

confidence: 85%

Quantum computing is scalable on a planar array of qubits with fabrication defects

Strikis¹,

Benjamin²,

Brown³

2021

Preprint

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“…Finally, it would be interesting to see if the quantum error-correcting properties of the volume-law phase, which have provided a useful lens on the phenomenology [37-39, 60, 178], could be put to practical use in quantum computers. While the hybrid dynamics encode quantum information, and a decoder is known to exist in the volume-law phase [60], it is not clear whether in general a 'good' decoder exists which could efficiently detect and correct errors [61].…”

Section: Discussionmentioning

confidence: 99%

“…Many questions related to the nature of the phase transitions between these two phases continue to be actively investigated [50][51][52][53][54][55][56][57][58][59]. The entanglement preserving phase can have error correcting properties and is being considered for stabilizing novel many-body states with multipartite entanglement by monitoring local degrees of freedom [60][61][62].…”

Section: Introductionmentioning

confidence: 99%

Quantum simulation using noisy unitary circuits and measurements

Lunt¹,

Richter²,

Pal³

2021

Preprint

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Many-body quantum systems are notoriously hard to study theoretically due to the exponential growth of their Hilbert space. It is also challenging to probe the quantum correlations in many-body states in experiments due to their sensitivity to external noise. Using synthetic quantum matter to simulate quantum systems has opened new ways of probing quantum many-body systems with unprecedented control, and of engineering phases of matter which are otherwise hard to find in nature. Noisy quantum circuits have become an important cornerstone of our understanding of quantum many-body dynamics. In particular, random circuits act as minimally structured toy models for chaotic nonintegrable quantum systems, faithfully reproducing some of their universal properties. Crucially, in contrast to the full microscopic model, random circuits can be analytically tractable under a reasonable set of assumptions, thereby providing invaluable insights into questions which might be out of reach even for state-of-the-art numerical techniques. Here, we give an overview of two classes of dynamics studied using random-circuit models, with a particular focus on the dynamics of quantum entanglement. We will especially pay attention to potential near-term applications of random-circuit models on noisy-intermediate scale quantum (NISQ) devices. In this context, we cover hybrid circuits consisting of unitary gates interspersed with nonunitary projective measurements, hosting an entanglement phase transition from a volume-law to an area-law phase of the steadystate entanglement. Moreover, we consider random-circuit sampling experiments and discuss the usefulness of random quantum states for simulating quantum many-body dynamics on NISQ devices by leveraging the concept of quantum typicality. We highlight how emergent hydrodynamics can be studied by utilizing random quantum states generated by chaotic circuits.

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“…Examples of fault-tolerant channels that are included within this model are transversal gates, code deformations, gauge fixing, and lattice surgeries [4,5,17,18,20,24,64,65]. While such operations are traditionally understood as a series of instructions on a set of static physical qubits, several recent works have introduced new approaches to fault-tolerant memories beyond the setting of static codes [7,66,67]. Here we want to generalize and extend these concepts to have a global view of logical operations rather than as operations on an underlying code.…”

Section: Fault-tolerant Channelsmentioning

confidence: 99%

Logical blocks for fault-tolerant topological quantum computation

Bombin¹,

Dawson²,

Mishmash³

et al. 2021

Preprint

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Logical gates constitute the building blocks of fault-tolerant quantum computation. While quantum errorcorrected memories have been extensively studied in the literature, explicit constructions and detailed analyses of thresholds and resource overheads of universal logical gate sets have so far been limited. In this paper, we present a comprehensive framework for universal fault-tolerant logic motivated by the combined need for (i) platformindependent logical gate definitions, (ii) flexible and scalable tools for numerical analysis, and (iii) exploration of novel schemes for universal logic that improve resource overheads. We first introduce the theory of faulttolerant logical channels for describing logical gates holistically in space-time. Focusing on channels based on surface codes, we introduce explicit, but platform-independent representations of topological logic gates-called logical blocks-and generate new, overhead-efficient methods for universal quantum computation. As a specific example, we propose fault-tolerant schemes based on surface codes concatenated with more general low-density parity check (LDPC) codes, suggesting an alternative path toward LDPC-based quantum computation. The logical blocks framework enables a convenient software-based mapping from an abstract description of the logical gate to a precise set of physical instructions for executing both circuit-based and fusion-based quantum computation (FBQC). Using this, we numerically simulate a surface-code-based universal gate set implemented with FBQC, and verify that the threshold for fault-tolerant gates is consistent with the bulk threshold for memory. We find, however, that boundaries, defects, and twists can significantly impact the logical error rate scaling, with periodic boundary conditions potentially halving the memory resource requirements. Motivated by the favorable logical error rate suppression for boundaryless computation, we introduce a novel computational scheme based on the teleportation of twists that may offer further resource reductions.

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Dynamically Generated Logical Qubits

Cited by 80 publications

References 13 publications

Quantum computing is scalable on a planar array of qubits with fabrication defects

Quantum computing is scalable on a planar array of qubits with fabrication defects

Quantum simulation using noisy unitary circuits and measurements

Logical blocks for fault-tolerant topological quantum computation

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