SU\G(𝔸)/K·U
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Logical Noise Bias in Magic State Injection

2024-01-01
Nicholas Fazio , Robin Harper , Stephen D. Bartlett
Fault-tolerant architectures aim to reduce the noise of a quantum computation. Despite such architectures being well studied a detailed understanding of how noise is transformed in a fault-tolerant primitive such … Fault-tolerant architectures aim to reduce the noise of a quantum computation. Despite such architectures being well studied a detailed understanding of how noise is transformed in a fault-tolerant primitive such as magic state injection is currently lacking. We use numerical simulations of logical process tomography on a fault-tolerant gadget that implements a logical T = $Z({\pi}/8)$ gate using magic state injection, to understand how noise characteristics at the physical level are transformed into noise characteristics at the logical level. We show how, in this gadget, a significant phase ($Z$) bias can arise in the logical noise, even with unbiased noise at the physical level. While the magic state injection gadget intrinsically induces biased noise, with extant phase bias being further amplified at the logical level, we identify noisy error correction circuits as a key limiting factor on the magnitude of this logical noise bias. Our approach provides a framework for assessing the detailed noise characteristics, as well as the overall performance, of fault-tolerant logical primitives.
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Low-overhead magic state distillation with color codes

2024-09-11
Seok-Hyung Lee , Felix Thomsen , Nicholas Fazio +2 more
Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but … Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but requires significant resources. Hence, it is crucial to tailor and optimize magic state distillation for specific codes from both logical- and physical-level perspectives. In this work, we perform such optimization for two-dimensional color codes, which are promising due to their higher encoding rates compared to surface codes, transversal implementation of Clifford gates, and efficient lattice surgery. We propose two distillation schemes based on the 15-to-1 distillation circuit and lattice surgery, which differ in their methods for handling faulty rotations. Our first scheme uses faulty T-measurement, offering resource efficiency when the target infidelity is above a certain threshold ($\sim 35p^3$ for physical error rate $p$). To achieve lower infidelities while maintaining resource efficiency, our second scheme exploits a distillation-free fault-tolerant magic state preparation protocol, achieving significantly lower infidelities (e.g., $\sim 10^{-19}$ for $p = 10^{-4}$) than the first scheme. Notably, our schemes outperform the best existing magic state distillation methods for color codes by up to about two orders of magnitude in resource costs for a given achievable target infidelity.
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Low-overhead Magic State Circuits with Transversal CNOTs

2025-01-17
Nicholas Fazio , Mark E. Webster , Zhenyu Cai
With the successful demonstration of transversal CNOTs in many recent experiments, it is the right moment to examine its implications on one of the most critical parts of fault-tolerant computation … With the successful demonstration of transversal CNOTs in many recent experiments, it is the right moment to examine its implications on one of the most critical parts of fault-tolerant computation -- magic state preparation. Using an algorithm that can recompile and simplify a circuit of consecutive multi-qubit phase rotations, we manage to construct fault-tolerant circuits for CCZ, CS and T states with minimal T-depth and also much lower CNOT depths and qubit counts than before. These circuits can play crucial roles in fault-tolerant computation with transversal CNOTs, and we hope that the algorithms and methods developed in this paper can be used to further simplify other protocols in similar contexts.
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Laser refractive surgery on TikTok: A DISCERN-based quality assessment

2025-05-21
Nicholas Fazio , Deborah M Li , Lauren R. Langman +3 more
Purpose To evaluate the quality of healthcare-related information on laser refractive surgery (LRS), including laser in situ keratomileusis (LASIK) and photorefractive keratectomy (PRK), among healthcare professionals (HCP) and non-healthcare professionals … Purpose To evaluate the quality of healthcare-related information on laser refractive surgery (LRS), including laser in situ keratomileusis (LASIK) and photorefractive keratectomy (PRK), among healthcare professionals (HCP) and non-healthcare professionals (NHCP) on TikTok using the DISCERN criteria. Materials and Methods In this study, searches of the top 100 results each of “LASIK” and “PRK” were conducted. The video results of 154 LASIK and PRK videos were evaluated for user engagement and content quality using the DISCERN criteria. Results The sources of LRS information were ophthalmologists (39.6%), optometrists (3.2%), and non-healthcare professionals (57.1%). User engagement had a combined 9.1 million likes, 79,000 comments, 187,000 shares, and 611,500 saves. DISCERN Criteria analysis revealed that videos by HCP had an average summation score of 34.03 (poor quality), with statistically significantly higher scores in 6 out of 15 categories, compared to 30.72 (poor quality) for videos by NHCP (p < 0.01). LASIK videos had higher viewership and user engagement than PRK videos. The PRK videos performed better in the additional treatment options category. Discussion The DISCERN criteria is useful for assessing the LRS video quality on TikTok. LRS is a popular topic on the platform, with LASIK topics being more popular than PRK topics. Although HCP scored higher in many DISCERN metrics, most videos among both HCP and NHCP were considered poor quality, and only a minority were considered fair or good quality. HCP should be cognizant of the quality of medical information produced and available to patients on social media platforms.

Laser refractive surgery on TikTok: A DISCERN-based quality assessment

2025-05-21
Nicholas Fazio , Deborah M Li , Lauren R. Langman +3 more
Purpose To evaluate the quality of healthcare-related information on laser refractive surgery (LRS), including laser in situ keratomileusis (LASIK) and photorefractive keratectomy (PRK), among healthcare professionals (HCP) and non-healthcare professionals … Purpose To evaluate the quality of healthcare-related information on laser refractive surgery (LRS), including laser in situ keratomileusis (LASIK) and photorefractive keratectomy (PRK), among healthcare professionals (HCP) and non-healthcare professionals (NHCP) on TikTok using the DISCERN criteria. Materials and Methods In this study, searches of the top 100 results each of “LASIK” and “PRK” were conducted. The video results of 154 LASIK and PRK videos were evaluated for user engagement and content quality using the DISCERN criteria. Results The sources of LRS information were ophthalmologists (39.6%), optometrists (3.2%), and non-healthcare professionals (57.1%). User engagement had a combined 9.1 million likes, 79,000 comments, 187,000 shares, and 611,500 saves. DISCERN Criteria analysis revealed that videos by HCP had an average summation score of 34.03 (poor quality), with statistically significantly higher scores in 6 out of 15 categories, compared to 30.72 (poor quality) for videos by NHCP (p < 0.01). LASIK videos had higher viewership and user engagement than PRK videos. The PRK videos performed better in the additional treatment options category. Discussion The DISCERN criteria is useful for assessing the LRS video quality on TikTok. LRS is a popular topic on the platform, with LASIK topics being more popular than PRK topics. Although HCP scored higher in many DISCERN metrics, most videos among both HCP and NHCP were considered poor quality, and only a minority were considered fair or good quality. HCP should be cognizant of the quality of medical information produced and available to patients on social media platforms.

Low-overhead Magic State Circuits with Transversal CNOTs

2025-01-17
Nicholas Fazio , Mark E. Webster , Zhenyu Cai
With the successful demonstration of transversal CNOTs in many recent experiments, it is the right moment to examine its implications on one of the most critical parts of fault-tolerant computation … With the successful demonstration of transversal CNOTs in many recent experiments, it is the right moment to examine its implications on one of the most critical parts of fault-tolerant computation -- magic state preparation. Using an algorithm that can recompile and simplify a circuit of consecutive multi-qubit phase rotations, we manage to construct fault-tolerant circuits for CCZ, CS and T states with minimal T-depth and also much lower CNOT depths and qubit counts than before. These circuits can play crucial roles in fault-tolerant computation with transversal CNOTs, and we hope that the algorithms and methods developed in this paper can be used to further simplify other protocols in similar contexts.
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Low-overhead magic state distillation with color codes

2024-09-11
Seok-Hyung Lee , Felix Thomsen , Nicholas Fazio +2 more
Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but … Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but requires significant resources. Hence, it is crucial to tailor and optimize magic state distillation for specific codes from both logical- and physical-level perspectives. In this work, we perform such optimization for two-dimensional color codes, which are promising due to their higher encoding rates compared to surface codes, transversal implementation of Clifford gates, and efficient lattice surgery. We propose two distillation schemes based on the 15-to-1 distillation circuit and lattice surgery, which differ in their methods for handling faulty rotations. Our first scheme uses faulty T-measurement, offering resource efficiency when the target infidelity is above a certain threshold ($\sim 35p^3$ for physical error rate $p$). To achieve lower infidelities while maintaining resource efficiency, our second scheme exploits a distillation-free fault-tolerant magic state preparation protocol, achieving significantly lower infidelities (e.g., $\sim 10^{-19}$ for $p = 10^{-4}$) than the first scheme. Notably, our schemes outperform the best existing magic state distillation methods for color codes by up to about two orders of magnitude in resource costs for a given achievable target infidelity.
View PDF Chat

Logical Noise Bias in Magic State Injection

2024-01-01
Nicholas Fazio , Robin Harper , Stephen D. Bartlett
Fault-tolerant architectures aim to reduce the noise of a quantum computation. Despite such architectures being well studied a detailed understanding of how noise is transformed in a fault-tolerant primitive such … Fault-tolerant architectures aim to reduce the noise of a quantum computation. Despite such architectures being well studied a detailed understanding of how noise is transformed in a fault-tolerant primitive such as magic state injection is currently lacking. We use numerical simulations of logical process tomography on a fault-tolerant gadget that implements a logical T = $Z({\pi}/8)$ gate using magic state injection, to understand how noise characteristics at the physical level are transformed into noise characteristics at the logical level. We show how, in this gadget, a significant phase ($Z$) bias can arise in the logical noise, even with unbiased noise at the physical level. While the magic state injection gadget intrinsically induces biased noise, with extant phase bias being further amplified at the logical level, we identify noisy error correction circuits as a key limiting factor on the magnitude of this logical noise bias. Our approach provides a framework for assessing the detailed noise characteristics, as well as the overall performance, of fault-tolerant logical primitives.
View PDF Chat
Coauthor Papers Together
Stephen D. Bartlett 2
Benjamin J. Brown 1
Mark E. Webster 1
Robin Harper 1
Seok-Hyung Lee 1
Deborah M Li 1
Andre Galenchik-Chan 1
Lauren R. Langman 1
Zhenyu Cai 1
Felix Thomsen 1
Sarah B. Weissbart 1
Diane Chernoff 1