Abstract. In the distributed quantum computing paradigm, well-controlled few-qubit ‘nodes ’ are networked together by connections which are relatively noisy and failure prone. A practical scheme must offer high tolerance to errors while requiring only simple (i.e. few-qubit) nodes. Here we show that relatively modest, three-qubit nodes can support advanced purification techniques and so offer robust scalability: the infidelity in the entanglement channel may be permitted to approach 10 % if the infidelity in local operations is of order 0.1%. Our tolerance of network noise is therefore a order of magnitude beyond prior schemes, and our architecture remains robust even in the presence of considerable decoherence rates (memory errors). We compare the performance with that of schemes involving nodes of lower and higher complexity. Ion traps, and NV- centres in diamond, are two highly relevant emerging technologies. ar X iv
Abstract. In the distributed quantum computing paradigm, well-controlled few-qubit ‘nodes ’ are networked together by connections which are relatively noisy and failure prone. A practical scheme must offer high tolerance to errors while requiring only simple (i.e. few-qubit) nodes. Here we show that relatively modest, three-qubit nodes can support advanced purification techniques and so offer robust scalability: the infidelity in the entanglement channel may be permitted to approach 10 % if the infidelity in local operations is of order 0.1%. Our tolerance of network noise is therefore a order of magnitude beyond prior schemes, and our architecture remains robust even in the presence of considerable decoherence rates (memory errors). We compare the performance with that of schemes involving nodes of lower and higher complexity. Ion traps, and NV- centres in diamond, are two highly relevant emerging technologies. ar X iv
In the distributed quantum computing paradigm, well-controlled few-qubit 'nodes' are networked together by connections which are relatively noisy and failure prone. A practical scheme must offer high tolerance to errors while requiring only simple (i.e. few-qubit) nodes. Here we show that relatively modest, three-qubit nodes can support advanced purification techniques and so offer robust scalability: the infidelity in the entanglement channel may be permitted to approach 10% if the infidelity in local operations is of order 0.1%. Our tolerance of network noise is therefore an order of magnitude beyond prior schemes, and our architecture remains robust even in the presence of considerable decoherence rates (memory errors). We compare the performance with that of schemes involving nodes of lower and higher complexity. Ion traps, and NV-centres in diamond, are two highly relevant emerging technologies: they possess the requisite properties of good local control, rapid and reliable readout, and methods for entanglement-at-a-distance.
In certain approaches to quantum computing the operations between qubits are nondeterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components; operations between components should be assumed to be failure prone. In the ultimate limit of this architecture each component contains only one qubit. Here we derive thresholds for fault-tolerant quantum computation under this extreme paradigm. We find that computation is supported for remarkably high failure rates (exceeding 90%) providing that failures are heralded; meanwhile the rate of unknown errors should not exceed 2 in 10(4) operations.
Distributed quantum computing interconnects small, high-quality nodes through optical links, but this architecture carries a pronounced asymmetry: in-node gates and measurements are cheap and high-fidelity, whereas inter-node communication relies on a low-coherence communication qubit and faulty photonics. Previous approaches overcame the noisy link by placing several high-quality data qubits in each node and consuming them for Bell pair and GHZ state distillation. Here we show that distillation can be avoided altogether. The key observation is that we can engineer a communication error bias, where photonic Bell pairs suffer frequent phase errors but only rare bit-flip errors. We design the syndrome-extraction circuits so that this phase noise appears solely as a measurement error that does not propagate to the data qubits, and is therefore suppressed by simply repeating the measurement; letting the error-correcting code itself, rather than a dedicated distillation subroutine, to purify the link. This dramatically reduces the need for ancillary nuclei: Floquet codes require only a single data qubit per node, while general stabilizer codes require just one additional ancilla. We demonstrate high error-correction thresholds throughout this regime, and we identify lattice surgery as inherently robust for this setting, enabling logical operations at a threshold close to that of quantum memory. As a result, the performance of the quantum computer is limited by the high-quality data qubits, while the requirements on photon indistinguishability and coherence of the communication qubit are substantially relaxed.
Quantum computing has the potential to transform information technology by offering algorithms for certain tasks, such as quantum simulation, that are vastly more efficient than what is possible with any classical device. But experimentally implementing practical quantum information processing is a very difficult task. Here we study two important, and closely related, aspects of this challenge: architectures for quantum computing, and quantum error correction Exquisite quantum control has now been achieved in small ion traps, in nitrogen-vacancy centres and in superconducting qubit clusters, but the challenge remains of how to scale these systems to build practical quantum devices. In Part I of this thesis we analyse one approach to building a scalable quantum computer by networking together many simple processor cells, thus avoiding the need to create a single complex structure. The difficulty is that realistic quantum links are very error prone. Here we describe a method by which even these error-prone cells can perform quantum error correction. Groups of cells generate and purify shared resource states, which then enable stabilization of topologically encoded data. Given a realistically noisy network (10% error rate) we find that our protocol can succeed provided that all intra-cell error rates are below 0.8%. Furthermore, we show that with some adjustments, the protocols we employ can be made robust also against high levels of loss in the network interconnects. We go on to analyse the potential running speed of such a device. Using levels of fidelity that are either already achievable in experimental systems, or will be in the near-future, we find that employing a surface code approach in a highly noisy and lossy network architecture can result in kilohertz computer clock speeds. In Part II we consider the question of quantum error correction beyond the surface code. We consider several families of topological codes, and determine the minimum requirements to demonstrate proof-of-principle error suppression in each type of code. A particularly promising code is the gauge color code, which admits a universal transversal gate set. Furthermore, a recent result of Bombin shows the gauge color code supports an error-correction protocol that achieves tolerance to noisy measurements without the need for repeated measurements, so called single-shot error correction. Here, we demonstrate the promise of single-shot error correction by designing a decoder and investigating its performance. We simulate fault-tolerant error correction with the gauge color code, and estimate a sustainable error rate, i.e. the threshold for the long time limit, of ~0.31% for a phenomenological noise model using a simple decoding algorithm.
Tremendous efforts have been paid for realization of fault-tolerant quantum computation so far. However, preexisting fault-tolerant schemes assume that a lot of qubits live together in a single quantum system, which is incompatible with actual situations of experiment. Here we propose a novel architecture for practically scalable quantum computation, where quantum computation is distributed over small-size (four-qubit) local systems, which are connected by quantum channels. We show that the proposed architecture works even with the error probability 0.1% of local operations, which breaks through the consensus by one order of magnitude. Furthermore, the fidelity of quantum channels can be very low ∼ 0.7, which substantially relaxes the difficulty of scaling-up the architecture. All key elements and their accuracy required for the present architecture are within reach of current technology. The present architecture allows us to achieve efficient scaling of quantum computer, as has been achieved in today's classical computer.
Recent constructions of quantum low-density parity-check (QLDPC) codes provide optimal scaling of the number of logical qubits and the minimum distance in terms of the code length, thereby opening the door to fault-tolerant quantum systems with minimal resource overhead. However, the hardware path from nearest-neighbor-connection-based topological codes to long-range-interaction-demanding QLDPC codes is likely a challenging one. Given the practical difficulty in building a monolithic architecture for quantum systems, such as computers, based on optimal QLDPC codes, it is worth considering a distributed implementation of such codes over a network of interconnected medium-sized quantum processors. In such a setting, all syndrome measurements and logical operations must be performed through the use of high-fidelity shared entangled states between the processing nodes. Since probabilistic many-to-1 distillation schemes for purifying entanglement are inefficient, we investigate quantum error correction based entanglement purification in this work. Specifically, we employ QLDPC codes to distill GHZ states, as the resulting high-fidelity logical GHZ states can interact directly with the code used to perform distributed quantum computing (DQC), e.g. for fault-tolerant Steane syndrome extraction. This protocol is applicable beyond the application of DQC since entanglement distribution and purification is a quintessential task of any quantum network. We use the min-sum algorithm (MSA) based iterative decoder with a sequential schedule for distilling 3 -qubit GHZ states using a rate 0.118 family of lifted product QLDPC codes and obtain an input fidelity threshold of ≈0.7974 under i.i.d. single-qubit depolarizing noise. This represents the best threshold for a yield of 0.118 for any GHZ purification protocol. Our results apply to larger size GHZ states as well, where we extend our technical result about a measurement property of 3 -qubit GHZ states to construct a scalable GHZ purification protocol.