The resource overhead required to achieve net computational benefits from quantum error correction (QEC) limits its utility while current systems remain constrained in size, despite exceptional progress in experimental demonstrations. In this paper, we demonstrate that the strategic application of QEC primitives without logical encoding can yield significant advantages on superconducting processors—relative to any alternative error-reduction strategy—while only requiring a modest overhead. We first present a novel protocol for implementing long-range gates that relies on a unitarily prepared Greenberger-Horne-Zeilinger (GHZ) state as well as a unitary disentangling step; the protocol natively introduces an error-detection process using the disentangled qubits as flags. We demonstrate that it achieves state-of-the-art gate fidelities of over 85% across up to 40 lattice sites, significantly and consistently outperforming the best alternative measurement-based protocol without introducing any additional ancilla qubits. We then apply sparse stabilizer measurements to generate large GHZ states by detecting bit-flip and amplitude-damping errors. Employing this technique in combination with deterministic error suppression, we generate a 75-qubit GHZ state exhibiting genuine multipartite entanglement, the largest reported to date. The generation requires no more than 9 ancilla qubits and the fraction of samples discarded due to errors grows no higher than 78%, far lower than previous discard fractions required for tests using comparable numbers of fully encoded qubits. This work in total represents compelling evidence that adopting QEC primitives on current-generation devices can deliver substantial net benefits.
The resource overhead required to achieve net computational benefits from quantum error correction (QEC) limits its utility while current systems remain constrained in size, despite exceptional progress in experimental demonstrations. In this paper, we demonstrate that the strategic application of QEC primitives without logical encoding can yield significant advantages on superconducting processors—relative to any alternative error-reduction strategy—while only requiring a modest overhead. We first present a novel protocol for implementing long-range gates that relies on a unitarily prepared Greenberger-Horne-Zeilinger (GHZ) state as well as a unitary disentangling step; the protocol natively introduces an error-detection process using the disentangled qubits as flags. We demonstrate that it achieves state-of-the-art gate fidelities of over 85% across up to 40 lattice sites, significantly and consistently outperforming the best alternative measurement-based protocol without introducing any additional ancilla qubits. We then apply sparse stabilizer measurements to generate large GHZ states by detecting bit-flip and amplitude-damping errors. Employing this technique in combination with deterministic error suppression, we generate a 75-qubit GHZ state exhibiting genuine multipartite entanglement, the largest reported to date. The generation requires no more than 9 ancilla qubits and the fraction of samples discarded due to errors grows no higher than 78%, far lower than previous discard fractions required for tests using comparable numbers of fully encoded qubits. This work in total represents compelling evidence that adopting QEC primitives on current-generation devices can deliver substantial net benefits.
Protecting quantum information through quantum error correction (QEC) is a cornerstone of future fault-tolerant quantum computation. However, current QEC-protected logical qubits have only achieved coherence times about twice those of their best physical constituents. Here, we show that the primary barrier to higher QEC gains is ancilla-induced operational errors rather than intrinsic cavity coherence. To overcome this bottleneck, we introduce error-detectable universal control of bosonic modes, wherein ancilla relaxation events are detected and the corresponding trajectories discarded, thereby suppressing operational errors on logical qubits. For binomial codes, we demonstrate universal gates with fidelities exceeding 99.6% and QEC gains of 8.33× beyond break-even. Our results establish that gains beyond 10× are achievable with state-of-the-art devices, establishing a path toward fault-tolerant bosonic quantum computing.
Dynamic circuits, which augment unitary operations with mid-circuit measurements and classical feedforward, can generate long-range entanglement in constant depth, enabling low-depth primitives ranging from nontrivial state preparation to many-qubit entangling gates. Escaping the light-cone constraints of unitary circuits, however, comes at a cost: these primitives typically require a number of mid-circuit measurements that scales with system size and that, together with feedforward latency, can introduce errors that degrade the long-range entanglement they rely on. Here, we alleviate this tension by showing that many such primitives, when cast into a common framework, admit an error-detection scheme that trades infidelity for postselection overhead with no additional ancillas. Our framework thus unifies and upgrades a broad class of primitives including fan-out gates, multi-qubit Pauli rotations, the preparation of W and higher-weight Dicke states, and certain non-normal matrix product states. We also introduce a reduced-depth, error-detected implementation of the Hadamard test, extending the use cases of dynamic circuits to a key algorithmic primitive. Finally, we establish the practical utility of our scheme through experiments on a superconducting quantum processor. We demonstrate the error-detected preparation of a long-range entangled Bell pair spanning a 100-qubit chain with fidelity F=0.59±0.02, surpassing the entanglement-certification threshold F>0.5 that the baseline dynamic-circuit implementation fails to reach (0.39±0.01). Separately, we demonstrate constant-depth preparation of W states of up to 20 qubits by consuming GHZ states of up to 40 qubits, finding absolute fidelity improvements of ΔF≈0.2 across the largest sizes studied. Altogether, these results bring low-depth dynamic-circuit primitives within practical reach on present-day hardware.
The promise of quantum computing is closer to reality today than ever before, thanks to rapid progress in the development of quantum hardware. Even as qubit lifetimes and gate fidelities continue to improve, realizing robust, fault-tolerant quantum computers is contingent upon the successful implementation of quantum error correction (QEC). Conventional QEC schemes have rather high resource overheads and low threshold requirements, making them challenging to implement on present day hardware. Here, we use a recently developed noise-adapted 3-qubit QEC scheme to demonstrate break-even performance against native amplitude-damping (AD) noise on IBM quantum hardware. We use variational quantum circuits to construct hardware-efficient encoding and decoding circuits. This scheme is probabilistic due to the non-unitary nature of the recovery operators, which are implemented via the block-encoding technique. We demonstrate logical qubit lifetimes exceeding those of the physical qubits by performing multiple rounds of QEC. To further protect the qubits from dephasing due to crosstalk, we incorporate dynamical decoupling into our noise-adapted QEC scheme in a seamless fashion. To account for the post-selection overhead, we define a measure of gain, that allows for faithful performance benchmarking of the protocol. Our analysis suggests that the performance of our protocol is limited primarily by the measurement readout fidelity, and is bound to improve with successive generations of quantum processors.
Quantum error correction protects logical quantum information against environmental decoherence by encoding logical qubits into entangled states of physical qubits. One of the most important near-term challenges in building a scalable quantum computer is to reach the break-even point, where logical quantum circuits on error-corrected qubits achieve higher fidelity than equivalent circuits on uncorrected physical qubits. Using Quantinuum's H2 trapped-ion quantum processor, we encode the Greenberger-Horne-Zeilinger (GHZ) state in four logical qubits with fidelity 99.5±0.15%≤F≤99.7±0.1% (after postselecting on over 98% of outcomes). Using the same quantum processor, we can prepare an uncorrected GHZ state on four physical qubits with fidelity 97.8±0.2%≤F≤98.7±0.2%. The logical qubits are encoded in a ⟦25,4,3⟧ Tanner-transformed long-range-enhanced surface code. Logical entangling gates are implemented using simple swap operations. Our results are a first step toward realizing fault-tolerant quantum computation with logical qubits encoded in geometrically nonlocal quantum low-density parity check codes.
Quantum error detection is essential in realizing large-scale universal quantum computation, especially for quantum error correction (QEC). However, key elements for FTQC have yet to be realized in silicon qubits. Here, we demonstrate quantum error detection on a donor-based silicon quantum processor comprising four-nuclear spin qubits and one electron spin as an auxiliary qubit. The entanglement capability of this system is validated through the establishment of two-qubit Bell state entanglement between the nuclear spins and the generation of a four-qubit Greenberger-Horne-Zeilinger (GHZ) state, achieving a GHZ state fidelity of 88.5(2.3)%. Furthermore, by executing a four-qubit error detection circuit with the stabilizers, we successfully detect arbitrary single-qubit errors. The encoded Bell state entanglement information is recovered by performing the Pauli-frame update (PFU) via postprocessing. Based on the detected errors, we identify strongly biased noise in our system. Our results mark a significant advance toward FTQC in silicon spin qubits.
In this paper, we describe and experimentally demonstrate an error detection scheme that does not employ ancilla qubits or mid-circuit measurements. This is achieved by expanding the Hilbert space where a single logical qubit is encoded using several physical qubits. For example, one possible two qubit encoding identifies ∣0⟩L=∣01⟩ and ∣1⟩L=∣10⟩. If during the final measurement a ∣11⟩ or ∣00⟩ is observed an error is declared and the run is not included in subsequent analysis. We provide codewords for a simple bit-flip encoding, a way to encode the states, a way to implement logical U3 and logical Cx gates, and a description of which errors can be detected. We then run Greenberger-Horne-Zeilinger circuits on the transmon based IBM quantum computers, with an input space of N∈{2,3,4,5} logical qubits and Q∈{1,2,3,4,5} physical qubits per logical qubit. The results are compared relative to Q=1 with and without error detection and we find a significant improvement for Q∈{2,3,4}.