We propose a scheme for distributed quantum computation with small local systems connected via noisy quantum channels. We show that the proposed scheme tolerates errors with probabilities ∼30% and ∼ 0.1% in quantum channels and local operations, respectively, both of which are improved substantially compared to the previous works.
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.
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output to the quantum algorithm are classical. In contrast to stand-alone single-core quantum computers, in many distributed scenarios, quantum information might have to be passed on from one quantum information processing system to another one, possibly via noisy quantum communication channels with noise levels above fault-tolerant thresholds. In such situations, quantum information processing devices will have quantum inputs, quantum outputs or even both, which pass qubits among each other. Working in the fault-tolerant framework of [Kitaev, 1997], we show that any quantum circuit with quantum input and output can be transformed into a fault-tolerant circuit that produces the ideal circuit with some controlled noise applied at the input and output. The framework allows the direct composition of the statements, enabling versatile future applications. We illustrate this with a concrete application, namely, communication over a noisy channel with faulty encoding and decoding operations [Christandl and M{ü}ller-Hermes, 2024]. For communication codes with linear minimum distance, we construct fault-tolerant encoders and decoders for general noise (including coherent errors). For the weaker, but standard, model of local stochastic noise, we obtain fault-tolerant encoders and decoders for any communication code that can correct a constant fraction random errors.
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor’s algorithm for factoring. In particular, this means that input and output to the quantum algorithm are classical. In contrast to stand-alone single-core quantum computers, in many distributed scenarios, quantum information might have to be passed on from one quantum information processing system to another one, possibly via noisy quantum communication channels with noise levels above fault-tolerant thresholds. In such situations, quantum information processing devices will have quantum inputs, quantum outputs or even both, which pass qubits among each other. Working in the fault-tolerant framework of [Kitaev, 1997], we show that any quantum circuit with quantum input and output can be transformed into a fault-tolerant circuit that produces the ideal circuit with some controlled noise applied at the input and output. The framework allows the direct composition of the statements, enabling versatile future applications. We illustrate this with a concrete application, namely, communication over a noisy channel with faulty encoding and decoding operations [Christandl and Müller-Hermes, 2024]. For communication codes with linear minimum distance, we construct fault-tolerant encoders and decoders for general noise (including coherent errors). For the weaker, but standard model of local stochastic noise, we obtain fault-tolerant encoders and decoders for any communication code that can correct a constant fraction of random errors.
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error it is usually assumed that these circuits can be implemented using noise-free gates. While this assumption is satisfied for classical machines in many scenarios, it is not expected to be satisfied in the near term future for quantum machines where decoherence leads to faults in the quantum gates. As a result, fundamental questions regarding the practical relevance of quantum channel coding remain open. By combining techniques from fault-tolerant quantum computation with techniques from quantum communication, we initiate the study of these questions. We introduce fault-tolerant versions of quantum capacities quantifying the optimal communication rates achievable with asymptotically vanishing total error when the encoding and decoding circuits are affected by gate errors with small probability. Our main results are threshold theorems for the classical and quantum capacity: For every quantum channelTand everyϵ>0there exists a thresholdp(ϵ,T)for the gate error probability below which rates larger than$C-\epsilon arefault−tolerantlyachievablewithvanishingoverallcommunicationerror,whereC$denotes the usual capacity. Our results are not only relevant in communication over large distances, but also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise than affecting the local gates.
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than some constant threshold. The cost is polylogarithmic in time and space, and no measurements are used during the quantum computation. The result holds also for quantum circuits which operate on nearest neighbors only. To achieve this noise resistance, we use concatenated quantum error correcting codes. The scheme presented is general, and works with all quantum codes that satisfy some restrictions, namely that the code is ``proper''. We present two explicit classes of proper quantum codes. The first example of proper quantum codes generalizes classical secret sharing with polynomials. The second uses a known class of quantum codes and converts it to a proper code. This class is defined over a field with p elements, so the elementary quantum particle is not a qubit but a ``qupit''. With our codes, the threshold is about 10^(-6). Hopefully, this paper motivates a search for proper quantum codes with higher thresholds, at which point quantum computation becomes practical.
Practical fault-tolerant quantum computation requires a large number of physical qubits, posing a major challenge for scaling up individual quantum processors. Distributed architectures offer a promising solution by interconnecting multiple processors through quantum networks. However, remote Bell-pair generation remains technically demanding, making it essential to assess computational performance under limited communication resources. In this work, we present a comprehensive resource analysis of distributed fault-tolerant quantum computation using superconducting processors connected by microwave or optical links. We show that even a single physical communication channel per node can substantially reduce the physical-qubit requirements per node under experimentally motivated, forward-looking microwave-link assumptions of a 1 MHz physical Bell-pair generation rate and 90% fidelity, although at the cost of a roughly tenfold increase in execution time. Conversely, reducing the execution-time overhead requires substantially greater communication resources, including higher Bell-pair fidelities and extensive multiplexing. These results demonstrate the potential feasibility of distributed fault-tolerant quantum computation with limited communication resources and provide a quantitative basis for balancing quantum-link performance, processor size, and execution time.