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Fault tolerance in the IBM Q Experience

Robin Harper, Steven T. Flammia

Published Jun 6, 2018• 11 citations
OpenAlex

Abstract

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.

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Fault-Tolerant Logical Gates in the IBM Quantum Experience

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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.

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Fault-Tolerant Operation of a Quantum Error-Correction Code

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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.

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Fault-Tolerant Error Detection Above Break-Even for Multi-Qubit Gates

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A fully fault-tolerant implementation of the quantum error-detecting Iceberg $[[2m, 2m-2, 2]]$ code applied to a Toffoli circuit achieved beyond-break-even error detection on a leading trapped-ion quantum computer, where the effect of encoding a circuit with a quantum error-detection code enables increased fidelity compared to an unencoded circuit. This code was also applied to Bell state preparation circuits, where a lean non-fault-tolerant implementation of the Iceberg code enables a fidelity gain as well. This highlights the important point that, at least for small-scale circuits with a substantial portion of error-free runs, it can be effective simply to use error detection to filter out the runs with errors. Furthermore, experiments performed in this work highlight the necessity for judicious compilation of circuits not only for a given hardware but also within a quantum error detection code.

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Christophe Vuillot

Quantumcomputation is the modern version of Schrödinger’s cat experiment. It is backed up in principle by the theory and thinking about it can make people equally uncomfortable and excited. Besides, its practical realization seems so extremely challenging that some people even doubt it is possible. On the other hand, we are nowadays much closer to realizing quantum computation and in addition, it has much more implications than Schrödinger’s original cat experiment. One of the major difficulties in realizing quantum computation is the inevitable presence of noise in realistic quantum devices which makes the direct realization of quantum computers impossible. In order to protect quantum information and quantum processes against noise, quantum error correction and fault-tolerance have been devised. Although the gap between experiments and the requirements of fault-tolerance is still daunting, the field of quantum error correction and fault-tolerance extends and influences architectural decisions from the hardware to the ideal quantum programs that we want to run. That is why it has the potential to make or break the practicality of quantum computation and a lot of research effort goes into this field. In this thesis we investigate and improve several aspects of fault-tolerant schemes and quantum error correction. We implement an experiment which validates on a small device the usefulness of fault-tolerance for quantum computation. We investigate the advantages of harnessing quantum continuous degrees of freedom present in the lab to protect discrete quantum information in a scalable way. We establish a framework to analyze the fault-tolerant properties of code deformation techniques which are versatile techniques to process quantum information protected by an error correcting code. We also present some novel code deformation techniques with the potential to increase reliability. Finally we define a new class of quantum error correcting codes, quantum pin codes, with built in capabilities for fault-tolerant quantum gates. We give some practical constructions and show some protocols with interesting parameters. The roads towards universal and fault-tolerant quantum computation are still steep but research efforts are pushing in the right directions.

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Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale quantum (NISQ) computers and results in the inability to perform quantum algorithms at useful scales with near-term quantum processors. As a result, calculations are generally done without encoding. We propose a middle ground between these two approaches: constructions in the $[[n,n-2,2]]$ quantum error-detecting code that can detect any error from a single faulty gate by measuring the stabilizer generators of the code and additional ancillas at the end of the computation. This achieves weak fault tolerance. As we show, this yields a significant improvement over no error correction for small computations with low enough physical error probabilities and requires much less overhead than codes that achieve full fault tolerance. We give constructions for a set of gates that achieve universal quantum computation in this error-detecting code, while satisfying weak fault tolerance up to analog imprecision on the physical rotation gate.

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Lower overhead fault-tolerant building blocks for noisy quantum computers

Prithviraj Prabhu

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.

quant-pharXiv:2605.12385•May 13, 2026•0 citations
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 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 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.
A fully fault-tolerant implementation of the quantum error-detecting Iceberg [[2m,2m−2,2]][[2m, 2m-2, 2]][[2m,2m−2,2]] code applied to a Toffoli circuit achieved beyond-break-even error detection on a leading trapped-ion quantum computer, where the effect of encoding a circuit with a quantum error-detection code enables increased fidelity compared to an unencoded circuit. This code was also applied to Bell state preparation circuits, where a lean non-fault-tolerant implementation of the Iceberg code enables a fidelity gain as well. This highlights the important point that, at least for small-scale circuits with a substantial portion of error-free runs, it can be effective simply to use error detection to filter out the runs with errors. Furthermore, experiments performed in this work highlight the necessity for judicious compilation of circuits not only for a given hardware but also within a quantum error detection code.
Quantumcomputation is the modern version of Schrödinger’s cat experiment. It is backed up in principle by the theory and thinking about it can make people equally uncomfortable and excited. Besides, its practical realization seems so extremely challenging that some people even doubt it is possible. On the other hand, we are nowadays much closer to realizing quantum computation and in addition, it has much more implications than Schrödinger’s original cat experiment. One of the major difficulties in realizing quantum computation is the inevitable presence of noise in realistic quantum devices which makes the direct realization of quantum computers impossible. In order to protect quantum information and quantum processes against noise, quantum error correction and fault-tolerance have been devised. Although the gap between experiments and the requirements of fault-tolerance is still daunting, the field of quantum error correction and fault-tolerance extends and influences architectural decisions from the hardware to the ideal quantum programs that we want to run. That is why it has the potential to make or break the practicality of quantum computation and a lot of research effort goes into this field. In this thesis we investigate and improve several aspects of fault-tolerant schemes and quantum error correction. We implement an experiment which validates on a small device the usefulness of fault-tolerance for quantum computation. We investigate the advantages of harnessing quantum continuous degrees of freedom present in the lab to protect discrete quantum information in a scalable way. We establish a framework to analyze the fault-tolerant properties of code deformation techniques which are versatile techniques to process quantum information protected by an error correcting code. We also present some novel code deformation techniques with the potential to increase reliability. Finally we define a new class of quantum error correcting codes, quantum pin codes, with built in capabilities for fault-tolerant quantum gates. We give some practical constructions and show some protocols with interesting parameters. The roads towards universal and fault-tolerant quantum computation are still steep but research efforts are pushing in the right directions.
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale quantum (NISQ) computers and results in the inability to perform quantum algorithms at useful scales with near-term quantum processors. As a result, calculations are generally done without encoding. We propose a middle ground between these two approaches: constructions in the [[n,n−2,2]][[n,n-2,2]][[n,n−2,2]] quantum error-detecting code that can detect any error from a single faulty gate by measuring the stabilizer generators of the code and additional ancillas at the end of the computation. This achieves weak fault tolerance. As we show, this yields a significant improvement over no error correction for small computations with low enough physical error probabilities and requires much less overhead than codes that achieve full fault tolerance. We give constructions for a set of gates that achieve universal quantum computation in this error-detecting code, while satisfying weak fault tolerance up to analog imprecision on the physical rotation gate.
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.