Achieving fault tolerance on capped color codes with few ancillas

• URL: http://arxiv.org/abs/2106.02649v4
• Date: Tue, 24 May 2022 16:47:40 GMT
• Title: Achieving fault tolerance on capped color codes with few ancillas
• Authors: Theerapat Tansuwannont, Debbie Leung
• Abstract summary: We develop a notion of distinguishable fault set which captures both concepts of flags and weight parities. We also develop fault-tolerant protocols for error correction, measurement, state preparation, and logical T gate implementation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits. One major technique that can overcome this problem is the flag technique, in which high-weight errors arising from a few faults can be detected by a few ancillas and distinguished using subsequent syndrome measurements. The technique can be further improved using the fact that for some families of codes, errors of any weight are logically equivalent if they have the same syndrome and weight parity, as previously shown in [Phys. Rev. A 104, 042410 (2021)]. In this work, we develop a notion of distinguishable fault set which captures both concepts of flags and weight parities, and extend the use of weight parities in error correction from [Phys. Rev. A 104, 042410 (2021)] to families of capped and recursive capped color codes. We also develop fault-tolerant protocols for error correction, measurement, state preparation, and logical T gate implementation via code switching, which are sufficient for performing fault-tolerant Clifford computation on a capped color code, and performing fault-tolerant universal quantum computation on a recursive capped color code. Our protocols for a capped or a recursive capped color code of any distance require only 2 ancillas, assuming that the ancillas can be reused. The concept of distinguishable fault set also leads to a generalization of the definitions of fault-tolerant gadgets proposed by Aliferis, Gottesman, and Preskill.

Related papers

• Universal fault-tolerant logic with heterogeneous holographic codes [38.98035278249248]
  We introduce a new class of holographic codes that realize the ability to support universal fault-tolerant quantum logic. Unlike standard tunabled codes, we establish that the new codes can encode more than a single logical qubit per code block. Our work strengthens the case for the utility of holographic quantum codes for practical quantum computing.
  arXiv  Detail & Related papers  (2025-04-14T16:28:33Z)
• Universal quantum computation via scalable measurement-free error correction [45.29832252085144]
  We show that universal quantum computation can be made fault-tolerant in a scenario where the error-correction is implemented without mid-circuit measurements.<n>We introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical $mathitCCZ$ gate.<n>In particular, our findings support that below-breakeven logical performance is achievable with a circuit-level error rate below $10-3$.
  arXiv  Detail & Related papers  (2024-12-19T18:55:44Z)
• Scaling and logic in the color code on a superconducting quantum processor [109.61104855764401]
  We present a demonstration of the color code on a superconducting processor, achieving logical error suppression and performing logical operations. We inject magic states, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection. This work establishes the color code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors.
  arXiv  Detail & Related papers  (2024-12-18T19:00:05Z)
• Low-Overhead Transversal Fault Tolerance for Universal Quantum Computation [36.3664581543528]
  We show that logical operations can be performed fault-tolerantly with only a constant number of extraction rounds.<n>Our work sheds new light on the theory of quantum fault tolerance and has the potential to reduce the space-time cost of practical fault-tolerant quantum computation by over an order of magnitude.
  arXiv  Detail & Related papers  (2024-06-25T15:43:25Z)
• Orthogonal Causal Calibration [55.28164682911196]
  We prove generic upper bounds on the calibration error of any causal parameter estimate $theta$ with respect to any loss $ell$. We use our bound to analyze the convergence of two sample splitting algorithms for causal calibration.
  arXiv  Detail & Related papers  (2024-06-04T03:35:25Z)
• Experimental fault-tolerant code switching [1.9088985324817254]
  We present the first experimental implementation of fault-tolerant code switching between two codes. We construct logical circuits and prepare 12 different logical states which are not accessible in a fault-tolerant way within a single code. Our results experimentally open up a new route towards deterministic control over logical qubits with low auxiliary qubit overhead.
  arXiv  Detail & Related papers  (2024-03-20T16:40:57Z)
• Analysis of Maximum Threshold and Quantum Security for Fault-Tolerant Encoding and Decoding Scheme Base on Steane Code [10.853582091917236]
  The original Steane code is not fault-tolerant because the CNOT gates in an encoded block may cause error propagation. We first propose a fault-tolerant encoding and decoding scheme, which analyzes all possible errors caused by each quantum gate in an error-correction period. We then provide the fault-tolerant scheme of the universal quantum gate set, including fault-tolerant preparation and verification of ancillary states.
  arXiv  Detail & Related papers  (2024-03-07T07:46:03Z)
• Improving threshold for fault-tolerant color code quantum computing by flagged weight optimization [0.9002260638342727]
  thresholds of color codes under circuit-level noise are relatively low because of their high-weight stabilizer generators. We propose a method to suppress the impact of such errors using conditional error probabilities conditioned on the measurement outcomes of flag qubits. This method can also be applied to other weight-based decoders, making the color codes more promising for the candidate of experimental implementation of QEC.
  arXiv  Detail & Related papers  (2024-02-21T17:40:51Z)
• Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code [2.5553228515450765]
  We implement a small quantum algorithm, one-qubit addition, fault-tolerantly on the Quantinuum H1-1 quantum computer. We observe arithmetic errors with a rate of $sim 1.1 times 10-3$ for the fault-tolerant circuit and $sim 9.5 times 10-3$ for the unencoded circuit.
  arXiv  Detail & Related papers  (2023-09-18T15:56:14Z)
• Fault-Tolerant Computing with Single Qudit Encoding [49.89725935672549]
  We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit. These codes can be customized to the specific physical errors on the qudit, effectively suppressing them. We demonstrate a Fault-Tolerant implementation on molecular spin qudits, showcasing nearly exponential error suppression with only linear qudit size growth.
  arXiv  Detail & Related papers  (2023-07-20T10:51:23Z)
• Deep Quantum Error Correction [73.54643419792453]
  Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. In this work, we efficiently train novel emphend-to-end deep quantum error decoders. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy.
  arXiv  Detail & Related papers  (2023-01-27T08:16:26Z)
• Transversal Injection: A method for direct encoding of ancilla states for non-Clifford gates using stabiliser codes [55.90903601048249]
  We introduce a protocol to potentially reduce this overhead for non-Clifford gates. Preliminary results hint at high quality fidelities at larger distances.
  arXiv  Detail & Related papers  (2022-11-18T06:03:10Z)
• Overcoming leakage in scalable quantum error correction [128.39402546769284]
  Leakage of quantum information out of computational states into higher energy states represents a major challenge in the pursuit of quantum error correction (QEC) Here, we demonstrate the execution of a distance-3 surface code and distance-21 bit-flip code on a Sycamore quantum processor where leakage is removed from all qubits in each cycle. We report a ten-fold reduction in steady-state leakage population on the data qubits encoding the logical state and an average leakage population of less than $1 times 10-3$ throughout the entire device.
  arXiv  Detail & Related papers  (2022-11-09T07:54:35Z)
• Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code [0.0]
  We compare two implementations of fault-tolerant entangling gates on logical qubits. Fault-tolerant operation achieves higher fidelities than the average physical qubit SPAM fidelities.
  arXiv  Detail & Related papers  (2022-08-03T06:20:13Z)
• Fault-tolerant parity readout on a shuttling-based trapped-ion quantum computer [64.47265213752996]
  We experimentally demonstrate a fault-tolerant weight-4 parity check measurement scheme. We achieve a flag-conditioned parity measurement single-shot fidelity of 93.2(2)%. The scheme is an essential building block in a broad class of stabilizer quantum error correction protocols.
  arXiv  Detail & Related papers  (2021-07-13T20:08:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.