Fault tolerant quantum computation with nondeterministic gates

Tailoring Fusion-Based Error Correction for High Thresholds to Biased Fusion Failures

We introduce fault-tolerant (FT) architectures for error correction with the XZZX cluster state based on performing measurements of two-qubit Pauli operators Z⊗Z and X⊗X, or fusions, on a collection of few-body entangled resource states. Our construction is tailored to effectively correct noise that predominantly causes faulty X⊗X measurements during fusions. This feature offers a practical advantage in linear optical quantum computing with dual-rail photonic qubits, where failed fusions only erase X⊗X measurement outcomes. By applying our construction to this platform, we find a record-high threshold to fusion failures exceeding 25% in the experimentally relevant regime of nonzero loss rate per photon, considerably simplifying hardware requirements.

Resource-Efficient Topological Fault-Tolerant Quantum Computation with Hybrid Entanglement of Light

We propose an all-linear-optical scheme to ballistically generate a cluster state for measurement-based topological fault-tolerant quantum computation using hybrid photonic qubits entangled in a continuous-discrete domain. Availability of near-deterministic Bell-state measurements on hybrid qubits is exploited for this purpose. In the presence of photon losses, we show that our scheme leads to a significant enhancement in both tolerable photon-loss rate and resource overheads. More specifically, we report a photon-loss threshold of ∼3.3×10^{-3}, which is higher than those of known optical schemes under a reasonable error model. Furthermore, resource overheads to achieve logical error rate of 10^{-6}(10^{-15}) is estimated to be ∼8.5×10^{5}(1.7×10^{7}), which is significantly less by multiple orders of magnitude compared to other reported values in the literature.

Foliated Quantum Error-Correcting Codes

We show how to construct a large class of quantum error-correcting codes, known as Calderbank-Steane-Shor codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger cluster state, implementing foliated quantum error correction. We exemplify this construction with several familiar quantum error-correction codes and propose a generic method for decoding foliated codes. We numerically evaluate the error-correction performance of a family of finite-rate Calderbank-Steane-Shor codes known as turbo codes, finding that they perform well over moderate depth foliations. Foliated codes have applications for quantum repeaters and fault-tolerant measurement-based quantum computation.

Computational quantum-classical boundary of noisy commuting quantum circuits

It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.

Ultrafast and fault-tolerant quantum communication across long distances

Quantum repeaters (QRs) provide a way of enabling long distance quantum communication by establishing entangled qubits between remote locations. In this Letter, we investigate a new approach to QRs in which quantum information can be faithfully transmitted via a noisy channel without the use of long distance teleportation, thus eliminating the need to establish remote entangled links. Our approach makes use of small encoding blocks to fault-tolerantly correct both operational and photon loss errors. We describe a way to optimize the resource requirement for these QRs with the aim of the generation of a secure key. Numerical calculations indicate that the number of quantum memory bits at each repeater station required for the generation of one secure key has favorable polylogarithmic scaling with the distance across which the communication is desired.

Robust-fidelity atom-photon entangling gates in the weak-coupling regime

We describe a simple entangling principle based on the scattering of photons off single emitters in one-dimensional waveguides (or extremely lossy cavities). The scheme can be applied to polarization- or time bin-encoded photonic qubits, and features a filtering mechanism that works effectively as a built-in error-correction directive. This automatically maps imperfections from the dominant sources of errors into heralded losses instead of infidelities, something highly advantageous, for instance, in quantum information applications. The scheme is thus adequate for high-fidelity maximally entangling gates even in the weak-coupling regime. These, in turn, can be directly used to store and retrieve photonic-qubit states, thereby completing an atom-photon interface toolbox, or applied to sequential measurement-based quantum computations with atomic memories.

Blind topological measurement-based quantum computation

Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf–Harrington–Goyal scheme. The error threshold of our scheme is 4.3×10⁻³, which is comparable to that (7.5×10⁻³) of non-blind topological quantum computation. As the error per gate of the order 10⁻³ was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach.

Blind quantum computation is a protocol that permits an algorithm, its input and output to be kept secret from the owner of the computational resource doing the calculation. Morimae and Fujii propose a strategy for topologically protected fault-tolerant blind quantum computation that is robust to environmental noise.

Thermal states as universal resources for quantum computation with always-on interactions

Measurement-based quantum computation utilizes an initial entangled resource state and proceeds with subsequent single-qubit measurements. It is implicitly assumed that the interactions between qubits can be switched off so that the dynamics of the measured qubits do not affect the computation. By proposing a model spin Hamiltonian, we demonstrate that measurement-based quantum computation can be achieved on a thermal state with always-on interactions. Moreover, computational errors induced by thermal fluctuations can be corrected and thus the computation can be executed fault tolerantly if the temperature is below a threshold value.

Fault-tolerant topological one-way quantum computation with probabilistic two-qubit gates

We propose a scalable way to construct a 3D cluster state for fault-tolerant topological one-way computation (TOWC) even if the entangling two-qubit gates succeed with a small probability. It is shown that fault-tolerant TOWC can be performed with the success probability of the two-qubit gate such as 0.5 (0.1) provided that the unheralded error probability of the two-qubit gate is less than 0.040% (0.016%). Furthermore, the resource usage is considerably suppressed compared to the conventional fault-tolerant schemes with probabilistic two-qubit gates.