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arXiv:2109.13760

Switch networks for photonic fusion-based quantum computing

Sara Bartolucci, Patrick M. Birchall, Damien Bonneau, Hugo V. Cable, Mercedes Gimeno-Segovia, Konrad Kieling, Naomi Nickerson, Terry Rudolph, Chris Sparrow

Published Sep 28, 2021• 9 citations
arXivHTMLPDF

Abstract

Fusion-based quantum computing (FBQC) offers a powerful approach to building a fault-tolerant universal quantum computer using photonic components -- single-photon sources, linear-optical circuits, single-photon detectors, and optical switching with feedforward control. Both individual optical switches and sophisticated switch networks are needed where it is necessary to perform operations conditionally, using feedforward of previous photon-detection outcomes, within the lifetime of remaining photons. Most visibly, feedforward switching is required for fault-tolerant operations at the level of logical qubits, which are needed in turn for useful quantum algorithms. However, switch networks are also required for multiplexing ("muxing") stages that are needed for generating specific small entangled resource states, where it is used to boost the probabilities for allocating quantum states to fusion gates and other operations -- a task which dominates the footprint of photonic FBQC. Despite their importance, limited attention has been paid to exploring possible designs of switch networks in this setting. Here we present a wide range of new techniques and schemes which enable major improvements in terms of muxing efficiency and reductions in hardware requirements. Since the use of photonic switching heavily impacts qubit losses and errors, our schemes are constructed with low switch depth. They also exploit specific features of linear-optical circuits which are commonly used to generate entanglement in proposed quantum computing and quantum network schemes.

DOI
10.48550/arxiv.2109.13760

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Fusion-based quantum computing (FBQC) offers a powerful approach to building a fault-tolerant universal quantum computer using photonic components -- single-photon sources, linear-optical circuits, single-photon detectors, and optical switching with feedforward control. Both individual optical switches and sophisticated switch networks are needed where it is necessary to perform operations conditionally, using feedforward of previous photon-detection outcomes, within the lifetime of remaining photons. Most visibly, feedforward switching is required for fault-tolerant operations at the level of logical qubits, which are needed in turn for useful quantum algorithms. However, switch networks are also required for multiplexing ("muxing") stages that are needed for generating specific small entangled resource states, where it is used to boost the probabilities for allocating quantum states to fusion gates and other operations -- a task which dominates the footprint of photonic FBQC. Despite their importance, limited attention has been paid to exploring possible designs of switch networks in this setting. Here we present a wide range of new techniques and schemes which enable major improvements in terms of muxing efficiency and reductions in hardware requirements. Since the use of photonic switching heavily impacts qubit losses and errors, our schemes are constructed with low switch depth. They also exploit specific features of linear-optical circuits which are commonly used to generate entanglement in proposed quantum computing and quantum network schemes.
Bell state measurements (BSMs) play a significant role in quantum information and quantum computing, in particular in fusion-based quantum computing (FBQC). The FBQC model is a framework for universal quantum computing, provided that we are able to perform entangling measurements, called fusions, on qubits within small entangled resource states. Here, we analyze the usage of different linear-optical BSM circuits as fusions in the FBQC schemes and numerically evaluate hardware requirements for fault-tolerance in this framework. We examine and compare the performance of several BSM circuits with varying additional resources and estimate the requirements on losses for every component of the linear-optical realization of fusions under which errors in fusion networks caused by these losses can be corrected. Our results show that fault-tolerant quantum computing in the FBQC model is possible with currently achievable levels of optical losses in an integrated photonic implementation, provided that we can create and detect single photons of the resource states with a total marginal efficiency higher than 0.973.
Fusion-based quantum computing is an attractive model for fault-tolerant computation based on photonics requiring only finite-sized entangled resource states followed by linear-optics operations and photon measurements. Large-scale implementations have so far been limited due to the access only to probabilistic photon sources, vulnerability to photon loss, and the need for massive multiplexing. Deterministic photon sources offer an alternative and resource-efficient route. By synergistically integrating deterministic photon emission, adaptive repeat-until-success fusions, and an optimised architectural design, we propose a complete blueprint for a photonic quantum computer using quantum dots and linear optics. It features time-bin qubit encoding, reconfigurable entangled-photon sources, and a fusion-based architecture with low optical connectivity, significantly reducing the required optical depth per photon and resource overheads. We present in detail the hardware required for resource-state generation and fusion networking, experimental pulse sequences, and exact resource estimates for preparing a logical qubit. We estimate that one logical clock cycle of error correction can be executed within microseconds, which scales linearly with the code distance. We also simulate error thresholds for fault-tolerance considering a full catalogue of intrinsic error sources found in real-world quantum dot devices. Our work establishes a practical blueprint for a low-optical-depth, emitter-based fault-tolerant photonic quantum computer.
Hybrid discrete- and continuous-variable (DV-CV) encodings have been developed to overcome operational drawbacks of each individual encoding, while fusion-based quantum computation (FBQC) has emerged to address the practical challenges of scalability toward fault-tolerant photonic quantum computation. Here we introduce hybrid FBQC using small optical DV-CV hybrid resource states connected through hybrid fusions, to combine the advantages of both approaches. We develop protocols for directly generating these resource states without requiring local hybrid logic such as the Hadamard gate, together with a tailored decoding strategy that exploits the error information contained in individual hybrid-fusion outcomes. We demonstrate that hybrid FBQC achieves a photon loss threshold of 2.231% while requiring only 12 hybrid fusions per surface-code unit cell, substantially improving upon the 0.89% threshold and 60-fusion requirement of previous hybrid measurement-based scheme. These results establish optical hybrid FBQC as a high-threshold resource-efficient route to scalable fault-tolerant photonic quantum computation.
The realisation of a fault-tolerant universal quantum computer requires the ability to implement and control large scale quantum systems while maintaining physical noise levels sufficiently low to avoid errors in the computation. Fusion-Based Quantum Computation (FBQC) – a framework in which entangling fusion measurements are performed between constant-size entangled resource states – has emerged as a promising approach to achieve this, especially in the context of Linear Optical Quantum Computing (LOQC). Most FBQC schemes proposed so far use physical fusions between two qubits. In this thesis, we study the impact of using multi-way fusions, which act on more physical qubits simultaneously, on the error tolerance and resource overhead of linear optical FBQC architectures. The main challenge of LOQC is that entangling operations are inherently non-deterministic, leading to large resource overheads. The success probability is known to decrease exponentially with the number of input qubits. We introduce novel fusion circuits which succeed at higher rates and/or entangle subsets of inputs upon failure. We present a framework to analyse the impact of noise on these circuits and describe the resulting errors as effective Pauli error channels on the input qubits. We also examine the application of multi-way fusion circuits within a linear optical FBQC architecture. We find that they can be used to generate resource states with significantly reduced Pauli error rates and footprint compared to two-way fusions alone, in turn resulting in linear optical FBQC architectures with higher error tolerance and lower resource overheads. We also investigate their use as primitives of the computation, applied between different resource states, and find evidence that two-way fusions remain preferable in this context due to their lower erasure rate.
Useful fault-tolerant quantum computers require very large numbers of physical qubits. Quantum computers are often designed as arrays of static qubits executing gates and measurements. Photonic qubits require a different approach. In photonic fusion-based quantum computing (FBQC), the main hardware components are resource-state generators (RSGs) and fusion devices connected via waveguides and switches. RSGs produce small entangled states of a few photonic qubits, whereas fusion devices perform entangling measurements between different resource states, thereby executing computations. In addition, low-loss photonic delays such as optical fiber can be used as fixed-time quantum memories simultaneously storing thousands of photonic qubits. Here, we present a modular architecture for FBQC in which these components are combined to form "interleaving modules" consisting of one RSG with its associated fusion devices and a few fiber delays. Exploiting the multiplicative power of delays, each module can add thousands of physical qubits to the computational Hilbert space. Networks of modules are universal fault-tolerant quantum computers, which we demonstrate using surface codes and lattice surgery as a guiding example. Our numerical analysis shows that in a network of modules containing 1-km-long fiber delays, each RSG can generate four logical distance-35 surface-code qubits while tolerating photon loss rates above 2% in addition to the fiber-delay loss. We illustrate how the combination of interleaving with further uses of non-local fiber connections can reduce the cost of logical operations and facilitate the implementation of unconventional geometries such as periodic boundaries or stellated surface codes. Interleaving applies beyond purely optical architectures, and can also turn many small disconnected matter-qubit devices with transduction to photons into a large-scale quantum computer.
Fusion-based quantum computing (FBQC) relies on a set of small, typically photonic, resource states that are fused together through Bell state measurements. The main bottleneck of FBQC is the low rate of generating the resource states, which stems from the probabilistic nature of photonic fusion gates. Previous work introduced a general algorithm for constructing circuits that deterministically generate photonic resource states from a minimal number of quantum emitters for a specified photon emission ordering. However, finding the minimal number of emitters and CNOT gates across all possible orderings is an NP-hard problem. Here, we exploit the symmetries present in FBQC resource states to dramatically simplify this optimization problem. We find that logically encoded 24-photon FBQC resource states can be produced using as few as 3 emitters and 11 CNOTs.