For the first time in history, we are seeing a branching point in computing paradigms with the emergence of quantum processing units (QPUs). Extracting the full potential of computation and realizing quantum algorithms with a super-polynomial speedup will most likely require major advances in quantum error correction technology. Meanwhile, achieving a computational advantage in the near term may be possible by combining multiple QPUs through circuit knitting techniques, improving the quality of solutions through error suppression and mitigation, and focusing on heuristic versions of quantum algorithms with asymptotic speedups. For this to happen, the performance of quantum computing hardware needs to improve and software needs to seamlessly integrate quantum and classical processors together to form a new architecture that we are calling quantum-centric supercomputing. In the long term, we see hardware that exploits qubit connectivity in higher than 2D topologies to realize more efficient quantum error correcting codes, modular architectures for scaling QPUs and parallelizing workloads, and software that evolves to make the intricacies of the technology invisible to the users and realize the goal of ubiquitous, frictionless quantum computing.

https://aip.scitation.org/doi/pdf/10.1063/5.0082975

The future of quantum computing with superconducting qubits

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. 

/pdf/erasure-conversion-for-fault-tolerant-quantum-computing-in-u1a9jdqs.pdf

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

We construct a new explicit family of good quantum low-density parity-check codes which additionally have linear time decoders. Our codes are based on a three-term chain (2m× m)V   →δ0  (2m)E →δ1  2F where V (X-checks) are the vertices, E (qubits) are the edges, and F (Z-checks) are the squares of a left-right Cayley complex, and where the maps are defined based on a pair of constant-size random codes CA,CB:2m→2Δ where Δ is the regularity of the underlying Cayley graphs. One of the main ingredients in the analysis is a proof of an essentially-optimal robustness property for the tensor product of two random codes.

/pdf/good-quantum-ldpc-codes-with-linear-time-decoders-3k13qv50.pdf

Good Quantum LDPC Codes with Linear Time Decoders

Tanner codes are long error correcting codes obtained from short codes and a graph, with bits on the edges and parity-check constraints from the short codes enforced at the vertices of the graph. Combining good short codes together with a spectral expander graph yields the celebrated expander codes of Sipser and Spielman, which are asymptotically good classical LDPC codes. In this work we apply this prescription to the left-right Cayley complex that lies at the heart of the recent construction of a c3 locally testable code by Dinur et at. Specifically, we view this complex as two graphs that share the same set of edges. By defining a Tanner code on each of those graphs we obtain two classical codes that together define a quantum code. This construction can be seen as a simplified variant of the Panteleev and Kalachev asymptotically good quantum LDPC code, with improved estimates for its minimum distance. This quantum code is closely related to the Dinur et at. code in more than one sense: indeed, we prove a theorem that simultaneously gives a linearly growing minimum distance for the quantum code and recovers the local testability of the Dinur et at. code.

Quantum Tanner codes

Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, potentially enabling low-overhead fault-tolerant quantum computing. However, implementing qLDPC codes involves nonlocal operations that require long-range connectivity between qubits. This makes their physical realization challenging in comparison to geometrically local codes, such as the surface code. Here we propose a hardware-efficient scheme for fault-tolerant quantum computation with high-rate qLDPC codes that is compatible with the recently demonstrated capabilities of reconfigurable atom arrays. Our approach utilizes the product structure inherent in many qLDPC codes to implement the nonlocal syndrome extraction circuit through atom rearrangement, resulting in an effectively constant overhead. We prove the fault tolerance of these protocols, and our simulations show that the qLDPC-based architecture starts to outperform the surface code with as few as several hundred physical qubits. We further find that quantum algorithms involving thousands of logical qubits can be performed using less than 105 physical qubits. Our work suggests that low-overhead quantum computing with qLDPC codes is within reach using current experimental technologies. Quantum low-density parity-check codes are highly efficient in principle but challenging to implement in practice. This proposal shows that these codes could be implemented in the near term using recently demonstrated neutral-atom arrays.

Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays

This chapter is devoted to quantum LDPC codes, which have many advantages compared to other classes of quantum codes thanks to the sparseness of their quantum-check matrices. Both semi-random and structured quantum LDPC codes are described. The chapter begins with the introduction of classical LDPC codes, their design and decoding algorithms. Further, dual-containing quantum LDPC codes are described. Next section is devoted to the entanglement-assisted quantum LDPC codes. The final section of this chapter describes the probabilistic sum-product algorithm based on quantum-check matrix instead of classical parity-check matrix.

Quantum Low-Density Parity-Check Codes

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Quantum Low-Density Parity-Check Codes