17 results for "Theodore J. Yoder"
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Journal Article
The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems
Qudits with local dimension $d \gt 2$ can have unique structure and uses that qubits ($d=2$) cannot. Qudit Pauli operators provide a very useful basis of the space of qudit states and operators. We study the structure of the qudit Pauli group for any, including composite, $d$ in several ways. To…
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Journal Article
A graph-based formalism for surface codes and twists
Twist defects in surface codes can be used to encode more logical qubits, improve the code rate, and implement logical gates. In this work we provide a rigorous formalism for constructing surface codes with twists generalizing the well-defined homological formalism introduced by Kitaev for…
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Journal Article
The surface code with a twist
The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new variety called twists have made it possible to implement the…
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Journal Article
Four-dimensional toric code with non-Clifford transversal gates
The design of a four-dimensional toric code is explored with the goal of finding a lattice capable of implementing a logical CCCZ gate transversally. The established lattice is the octaplex tessellation, which is a regular tessellation of four-dimensional Euclidean space whose underlying 4-cell is…
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Journal Article
Homomorphic Logical Measurements
Shor and Steane ancillae are two well-known methods for fault-tolerant logical measurements, which are successful on small codes and their concatenations. On large quantum low-density-parity-check codes, however, Shor and Steane measurements have impractical time and space overhead, respectively…
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Journal Article
Universal Fault-Tolerant Gates on Concatenated Stabilizer Codes
It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked…
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Journal Article
Disjointness of Stabilizer Codes and Limitations on Fault-Tolerant Logical Gates
Stabilizer codes are among the most successful quantum error-correcting codes, yet they have important limitations on their ability to fault tolerantly compute. Here, we introduce a new quantity, the disjointness of the stabilizer code, which, roughly speaking, is the number of mostly…
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Journal Article
Universal Adapters between Quantum Low-Density Parity Check Codes
We propose the repetition code adapter as a way to perform joint logical Pauli measurements within a quantum low-density parity check (LDPC) codeblock or between separate such codeblocks, thus providing a flexible tool for fault-tolerant computation with quantum LDPC codes. This adapter is…
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Journal Article
Methodology of Resonant Equiangular Composite Quantum Gates
The creation of composite quantum gates that implement quantum response functions U[over ^](θ) dependent on some parameter of interest θ is often more of an art than a science. Through inspired design, a sequence of L primitive gates also depending on θ can engineer a highly nontrivial U[over ^](θ)…
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Journal Article
Triangular color codes on trivalent graphs with flag qubits
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available superconducting hardware despite constrained qubit connectivity. To…
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Journal Article
Parallel Logical Measurements via Quantum Code Surgery
Quantum code surgery is a flexible and low-overhead technique for performing logical measurements on quantum error-correcting codes, which generalizes lattice surgery. In this work, we present a code surgery scheme, applicable to any qubit stabilizer low-density parity check (LDPC) code, that…
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Journal Article Full text
High-threshold and low-overhead fault-tolerant quantum memory
Abstract The accumulation of physical errors 1–3 prevents the execution of large-scale algorithms in current quantum computers. Quantum error correction 4 promises a solution by encoding k logical qubits onto a larger number n of physical qubits, such that the physical errors are suppressed enough…
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Journal Article
Topological and Subsystem Codes on Low-Degree Graphs with Flag Qubits
In this work we introduce two code families, which we call the heavy-hexagon code and the heavy-square code. Both code families are implemented by assigning physical data and ancilla qubits to both vertices and edges of low-degree graphs. Such a layout is particularly suitable for superconducting…
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Journal Article
Hamiltonian simulation with optimal sample complexity
Quantum Software from Quantum States One of the hallmarks of quantum computation is the storage and extraction of information within quantum systems. Recently, Lloyd, Mohseni and Rebentrost created a protocol to treat multiple identical copies of a quantum state as “quantum software”, specifying a…
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Journal Article Full text
Harmonic radar tracking of individual melon flies, Zeugodacus cucurbitae, in Hawaii: Determining movement parameters in cage and field settings.
Tephritid fruit flies, such as the melon fly, Zeugodacus cucurbitae, are major horticultural pests worldwide and pose invasion risks due primarily to international trade. Determining movement parameters for fruit flies is critical to effective surveillance and control strategies, from setting…
Also available at: PLOS
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Journal Article
Demonstrating multi-round subsystem quantum error correction using matching and maximum likelihood decoders
Abstract Quantum error correction offers a promising path for performing high fidelity quantum computations. Although fully fault-tolerant executions of algorithms remain unrealized, recent improvements in control electronics and quantum hardware enable increasingly advanced demonstrations of the…