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Low-Overhead Quantum Fault Tolerance
Low-Overhead Quantum Fault Tolerance
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202104752
- ISBN
- 9798290653907
- DDC
- 004
- 서명/저자
- Low-Overhead Quantum Fault Tolerance
- 발행사항
- [Sl] : California Institute of Technology, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 213 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-01, Section: A.
- 주기사항
- Advisor: Preskill, John.
- 학위논문주기
- Thesis (Ph.D.)--California Institute of Technology, 2025.
- 초록/해제
- 요약Fault tolerance is an essential property of future quantum computers where a quantum computation is mapped to a new one that is resilient to operational errors. This resilience comes at an additional time and space overhead. In this thesis, we study schemes that asymptotically reduce the overhead of quantum fault tolerance in various models of computation.In the first half, we construct a scheme for fault-tolerant quantum computation that requires nearly-logarithmic spacetime overhead assuming access to noiseless classical computation. This construction relies critically on the introduction of several new ingredients: we develop new qubit resource state distillation protocols with sub-logarithmic spacetime overhead used to perform teleported gates. We also construct a single-shot bit-flipping decoder to decode the almost-good quantum locally-testable codes of Dinur-Lin-Vidick where the quantum local testability is used crucially in order to prepare input states to the distillation. Finally, to assemble the substantial variety of gadgets, we introduce a new weight enumerator formalism that tracks the sets of jointly uncorrectable faulty spacetime locations using polynomials.In the second half, we construct a quantum memory which has a threshold using a geometrically-local syndrome extraction circuit and almost-optimal parameters: the number of encoded qubits is nearly linear in the number of physical qubits, while the sub-threshold error suppression is nearly exponential in the number of physical qubits. Our construction surpasses known no-go results on the parameters of geometrically-local quantum codes by instead considering geometrically-local quantum circuits. The syndrome extraction circuits simulate the required long-range connectivity by performing a polynomial-depth permutation routing circuit with each qubit replaced by logarithmically-sized surface codes to retain a threshold.
- 일반주제명
- Quantum computing
- 일반주제명
- Construction
- 일반주제명
- Spacetime
- 일반주제명
- Connectivity
- 일반주제명
- Failure
- 일반주제명
- Codes
- 일반주제명
- Fault tolerance
- 일반주제명
- Theorems
- 일반주제명
- Logic
- 기타저자
- California Institute of Technology Physics Mathematics and Astronomy
- 기본자료저록
- Dissertations Abstracts International. 87-01A.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520260202104752
■006m o d
■007cr#unu||||||||
■020 ▼a9798290653907
■035 ▼a(MiAaPQ)AAI32151354
■035 ▼a(MiAaPQ)Caltech17297
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a004
■1001 ▼aPattison, Christopher Anand.
■24510▼aLow-Overhead Quantum Fault Tolerance
■260 ▼a[Sl]▼bCalifornia Institute of Technology▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a213 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-01, Section: A.
■500 ▼aAdvisor: Preskill, John.
■5021 ▼aThesis (Ph.D.)--California Institute of Technology, 2025.
■520 ▼aFault tolerance is an essential property of future quantum computers where a quantum computation is mapped to a new one that is resilient to operational errors. This resilience comes at an additional time and space overhead. In this thesis, we study schemes that asymptotically reduce the overhead of quantum fault tolerance in various models of computation.In the first half, we construct a scheme for fault-tolerant quantum computation that requires nearly-logarithmic spacetime overhead assuming access to noiseless classical computation. This construction relies critically on the introduction of several new ingredients: we develop new qubit resource state distillation protocols with sub-logarithmic spacetime overhead used to perform teleported gates. We also construct a single-shot bit-flipping decoder to decode the almost-good quantum locally-testable codes of Dinur-Lin-Vidick where the quantum local testability is used crucially in order to prepare input states to the distillation. Finally, to assemble the substantial variety of gadgets, we introduce a new weight enumerator formalism that tracks the sets of jointly uncorrectable faulty spacetime locations using polynomials.In the second half, we construct a quantum memory which has a threshold using a geometrically-local syndrome extraction circuit and almost-optimal parameters: the number of encoded qubits is nearly linear in the number of physical qubits, while the sub-threshold error suppression is nearly exponential in the number of physical qubits. Our construction surpasses known no-go results on the parameters of geometrically-local quantum codes by instead considering geometrically-local quantum circuits. The syndrome extraction circuits simulate the required long-range connectivity by performing a polynomial-depth permutation routing circuit with each qubit replaced by logarithmically-sized surface codes to retain a threshold.
■590 ▼aSchool code: 0037.
■650 4▼aQuantum computing
■650 4▼aConstruction
■650 4▼aSpacetime
■650 4▼aConnectivity
■650 4▼aFailure
■650 4▼aCodes
■650 4▼aError correction & detection
■650 4▼aFault tolerance
■650 4▼aLow density parity check codes
■650 4▼aTheorems
■650 4▼aLogic
■690 ▼a0395
■71020▼aCalifornia Institute of Technology▼bPhysics, Mathematics and Astronomy.
■7730 ▼tDissertations Abstracts International▼g87-01A.
■790 ▼a0037
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17358792▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
