Abstract High error-rates preclude the preparation of fully error-corrected logical qubit state on noisy intermediate scale quantum (NISQ) computers. When operand logical qubits inherit large state-preparation noise, it is difficult to show that subsequent logical gate fails less frequently than its physical (unprotected) version. We articulate a scheme of decoupling transversal logical gate errors from state-preparation noise and experimentally validate its use-case for IBM Q quantum processors. We find that in the absence of state preparation noise, the IBM Q processors significantly raise the likelihood of certain two-qubit errors in the operand(s) of [[7, 1, 3]] transversal gates. Yet, encoding can still be shown to improve the gate fidelity provided that the gate operands are strategically decoded/corrected for the likely two-qubit errors in lieu of their less likely single-qubit counterparts. This trade-off enables quantum CSS code to principally correct longer strings of errors without increasing the codeword size and paves new avenues of investigating fault-tolerance in NISQ computers.
Abstract High error-rates preclude the preparation of fully error-corrected logical qubit state on noisy intermediate scale quantum (NISQ) computers. When operand logical qubits inherit large state-preparation noise, it is difficult to show that subsequent logical gate fails less frequently than its physical (unprotected) version. We articulate a scheme of decoupling transversal logical gate errors from state-preparation noise and experimentally validate its use-case for IBM Q quantum processors. We find that in the absence of state preparation noise, the IBM Q processors significantly raise the likelihood of certain two-qubit errors in the operand(s) of [[7, 1, 3]] transversal gates. Yet, encoding can still be shown to improve the gate fidelity provided that the gate operands are strategically decoded/corrected for the likely two-qubit errors in lieu of their less likely single-qubit counterparts. This trade-off enables quantum CSS code to principally correct longer strings of errors without increasing the codeword size and paves new avenues of investigating fault-tolerance in NISQ computers.
Noisy Intermediate-Scale Quantum (NISQ) devices represent current quantum computing technology with 50-1000 qubits operating without comprehensive fault-tolerant error correction. The fundamental challenge lies in balancing error correction necessity against prohibitive resource overhead. Conventional quantum error correction codes require 10:1 to 1000:1 qubit ratios and syndrome extraction circuits exceeding 50 gates, consuming entire NISQ capacities. This work presents a comprehensive low-overhead quantum error correction framework specifically designed for NISQ constraints. Our approach combines three elements: optimised stabiliser codes which get qubit ratios of 3:1 to 10:1, adaptive syndrome extraction which works with circuits with less than 20 gates and machine learning-enhanced decoding which is specific to the noise profiles of the hardware. Experimental validation on IBM Quantum (127- qubit Eagle), IonQ trapped-ion systems, and Google Sycamore simulation demonstrates successful quantum state protection achieving 2.7× error suppression with 60% overhead reduction versus conventional surface codes. The proposed code achieves logical error rates of 0.0065 using only 10 physical qubits compared to 25 qubits for equivalent surface codes. Machine learning decoder attains 94.3% accuracy with 12-microsecond inference latency, enabling real-time error correction. Break-even performance achieved at 0.8% physical error rates establishes practical pathways for near-term quantum advantage in variational algorithms and quantum simulation applications.
Noisy Intermediate-Scale Quantum (NISQ) devices represent current quantum computing technology with 50-1000 qubits operating without comprehensive fault-tolerant error correction. The fundamental challenge lies in balancing error correction necessity against prohibitive resource overhead. Conventional quantum error correction codes require 10:1 to 1000:1 qubit ratios and syndrome extraction circuits exceeding 50 gates, consuming entire NISQ capacities. This work presents a comprehensive low-overhead quantum error correction framework specifically designed for NISQ constraints. Our approach combines three elements: optimised stabiliser codes which get qubit ratios of 3:1 to 10:1, adaptive syndrome extraction which works with circuits with less than 20 gates and machine learning-enhanced decoding which is specific to the noise profiles of the hardware. Experimental validation on IBM Quantum (127- qubit Eagle), IonQ trapped-ion systems, and Google Sycamore simulation demonstrates successful quantum state protection achieving 2.7× error suppression with 60% overhead reduction versus conventional surface codes. The proposed code achieves logical error rates of 0.0065 using only 10 physical qubits compared to 25 qubits for equivalent surface codes. Machine learning decoder attains 94.3% accuracy with 12-microsecond inference latency, enabling real-time error correction. Break-even performance achieved at 0.8% physical error rates establishes practical pathways for near-term quantum advantage in variational algorithms and quantum simulation applications.
Quantum computers will require encoding of quantum information to protect them from noise. Fault-tolerant quantum computing architectures illustrate how this might be done but have not yet shown a conclusive practical advantage. Here we demonstrate that a small but useful error detecting code improves the fidelity of the fault-tolerant gates implemented in the code space as compared to the fidelity of physically equivalent gates implemented on physical qubits. By running a randomized benchmarking protocol in the logical code space of the [4,2,2] code, we observe an order of magnitude improvement in the infidelity of the gates, with the two-qubit infidelity dropping from 5.8(2)% to 0.60(3)%. Our results are consistent with fault-tolerance theory and conclusively demonstrate the benefit of carrying out computation in a code space that can detect errors. Although the fault-tolerant gates offer an impressive improvement in fidelity, the computation as a whole is not below the fault-tolerance threshold because of noise associated with state preparation and measurement on this device.
Quantum computation promises to revolutionize information processing by exploiting superposition and entanglement, enabling applications such as quantum simulation, combinatorial optimization, and secure quantum communication. Beyond individual processors, the quantum internet aims to connect quantum nodes through entanglement distribution, enabling distributed computation. However, quantum states are fragile: environmental interactions, imperfect gate operations, and measurement errors can quickly degrade encoded information. Reliable quantum computation therefore requires carefully designed quantum error-correcting codes and fault-tolerant protocols. Unlike classical redundancy schemes, quantum error correction must preserve delicate phase relationships and relies on indirect error detection through syndrome extraction with ancillary qubits, enabling error identification without collapsing encoded states. Topological codes, in particular, emerged early as the preferred choice for many architectures due to their planar structure, local interactions, and natural support for fault-tolerant logical operations. Color codes, for instance, allow transversal implementation of all Clifford gates, whereas non-Clifford operations require magic-state injection. More recent constructions, including quantum low-density parity-check codes, offer higher encoding rates and reduced resource overhead, but require long-range qubit connectivity and more complex protocols. Despite experimental progress, several challenges remain. Many platforms exhibit biased noise, motivating codes that exploit channel asymmetry. Real-time decoding remains a critical bottleneck, as fault-tolerant computation requires low-latency processing of rapidly generated syndrome data. Fault-tolerant logical state initialization also remains resource-intensive and scales poorly with code distance. Addressing these challenges, this thesis develops a unified framework spanning theory and experiment. It provides precise performance analysis of quantum error-correcting codes in the low physical error-rate regime, introduces codes tailored to biased noise, develops fast low-complexity decoding algorithms for real-time operation, and presents modular and efficient protocols for fault-tolerant state preparation of CSS codes. The latter is demonstrated experimentally through the preparation of a logical zero state of the Golay code on the Quantinuum H2 trapped-ion quantum computer.
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while operating the logical qubit, and are essential for realizing error suppression in practice. While fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. In this work, we experimentally demonstrate fault-tolerant preparation, measurement, rotation, and stabilizer measurement of a Bacon-Shor logical qubit using 13 trapped ion qubits. When we compare these fault-tolerant protocols to non-fault tolerant protocols, we see significant reductions in the error rates of the logical primitives in the presence of noise. The result of fault-tolerant design is an average state preparation and measurement error of 0.6% and a Clifford gate error of 0.3% after error correction. Additionally, we prepare magic states with fidelities exceeding the distillation threshold, demonstrating all of the key single-qubit ingredients required for universal fault-tolerant operation. These results demonstrate that fault-tolerant circuits enable highly accurate logical primitives in current quantum systems. With improved two-qubit gates and the use of intermediate measurements, a stabilized logical qubit can be achieved.
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms. This can be remedied by protecting quantum information with a quantum error-correcting code, where the logical information of an algorithmic qubit is spread across multiple physical qubits. Individual quantum errors are then located and corrected by the fault-tolerant measurement of multi-qubit stabilizer operators (parity checks). Unfortunately, error correction and fault tolerance both impose large demands on the qubit overhead: hundreds to thousands of physical qubits per logical qubit.
We reduce the spacetime cost of fault tolerance by redesigning key building blocks of an error-corrected quantum computer. First, we develop a combinatorial proof with flag fault tolerance that exponentially reduces the extra qubits needed to measure a stabilizer of any size, while tolerating one fault. We leverage these proofs to then design state preparation circuits for the Steane and Golay codes with 100% yield. Next, we improve error correction on a planar layout by showing that a distance-four code encoding six logical qubits protects information as well as the distance-five surface code, using one-tenth as many physical qubits. Finally, we optimize the time overhead of logical gates in surface code quantum computers by protecting measurement results with a classical code, cutting computation time by a factor of two to six. Our hardware-agnostic optimizations of fault tolerance overheads thus suggest new routes to advance the timeline of error-free quantum computing.