Related papers: Low Overhead Universal Quantum Computation with Tr…
In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation. First, we show how to simplify universal encoded computation by using only transversal gates and standard error…
A basic question in the theory of fault-tolerant quantum computation is to understand the fundamental resource costs for performing a universal logical set of gates on encoded qubits to arbitrary accuracy. Here we consider qubits encoded…
Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with…
A non-Clifford gate is required for universal quantum computation, and, typically, this is the most error-prone and resource intensive logical operation on an error-correcting code. Small, single-qubit rotations are popular choices for this…
Topological color codes are widely acknowledged as promising candidates for fault-tolerant quantum computing. Neither a two-dimensional nor a three-dimensional topology, however, can provide a universal gate set $\{$H, T, CNOT$\}$, with the…
While quantum low-density parity check (qLDPC) codes are a low-overhead means of quantum information storage, it is valuable for quantum codes to possess fault-tolerant features beyond this resource efficiency. In this work, we introduce…
Given any quantum error correcting code permitting universal fault-tolerant quantum computation and transversal measurement of logical X and Z, we describe how to perform time-optimal quantum computation, meaning the execution of an…
The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and…
We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic…
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…
Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to…
A long-standing challenge in quantum error correction is the infeasibility of universal transversal gates, as shown by the Eastin-Knill theorem. We obtain a necessary and sufficient condition for a quantum code to have universal transversal…
Transversal gates are the simplest form of fault-tolerant gates and are relatively easy to implement in practice. Yet designing codes that support useful transversal operations -- especially non-Clifford or addressable gates -- remains…
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…
Toponomic quantum computing (TQC) employs rotation sequences of anticoherent $k$-planes to construct noise-tolerant quantum gates. In this work, we demonstrate the implementation of generalized Toffoli gates, using $k$-planes of spin…
A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates…
A triorthogonal code is a binary quantum Calderbank-Shor-Steane (CSS) code defined by a triorthogonal matrix. Triorthogonal codes are a key ingredient in magic-state distillation, since they allow for transversal $\mathsf{T}$ gates, a…
The Eastin-Knill theorem states that no quantum error correcting code can have a universal set of transversal gates. For CSS codes that can implement Clifford gates transversally it suffices to provide one additional non-Clifford gate, such…
Error correction has long been suggested to extend the sensitivity of quantum sensors into the Heisenberg Limit. However, operations on logical qubits are only performed through universal gate sets consisting of finite-sized gates such as…
Magic states are a foundational resource for universal quantum computation. To survive in a realistic noisy environment, magic states must be prepared fault-tolerantly and protected by a quantum error-correcting code. The recent discovery…