Related papers: Optimal Short-Circuit Resilient Formulas
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
Using fault-tolerant constructions, computations performed with unreliable components can simulate their noiseless counterparts though the introduction of a modest amount of redundancy. Given the modest overhead required to achieve…
(Abridged.) This thesis investigates scalable fault-tolerant quantum computation through the development of bosonic quantum codes, quantum LDPC codes, and decoding protocols that connect continuous-variable and discrete-variable error…
We propose a method for exact circuit synthesis using a discrete gate set, as required for fault-tolerant quantum computing. Our approach translates the problem of synthesizing a gate specified by its unitary matrix into a boolean…
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…
High-connectivity circuits are a major roadblock for current quantum hardware. We propose a hybrid classical-quantum algorithm to simulate such circuits without swap-gate ladders. As main technical tool, we introduce…
I discuss how to perform fault-tolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when next-to-nearest-neighbor…
Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal have shown that an accuracy threshold exists for leakage faults using gadgets…
A pseudorandom code is a keyed error-correction scheme with the property that any polynomial number of encodings appear random to any computationally bounded adversary. We show that the pseudorandomness of any code tolerating a constant…
Recently, several groups have demonstrated two-qubit gate fidelities in semiconductor spin qubit systems above 99%. Achieving this regime of fault-tolerant compatible high fidelities is nontrivial and requires exquisite stability and…
Achieving scalable, fault-tolerant quantum computation requires quantum memory architectures that minimize error correction overhead while preserving coherence. This work presents a framework for high-dimensional qudit memory in…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
High-fidelity quantum gates are crucial for achieving fault-tolerant quantum computing; however, decoherence significantly reduces gate fidelities during long operation times. Although optimal control techniques can theoretically minimize…
Let $W$ be a binary-input memoryless symmetric (BMS) channel with Shannon capacity $I(W)$ and fix any $\alpha > 0$. We construct, for any sufficiently small $\delta > 0$, binary linear codes of block length $O(1/\delta^{2+\alpha})$ and rate…
In this paper we consider the variable-length lossless source coding for discrete memoryless sources. We proposes a new encryption framework for securely transmitting codewords over a noiseless channel. The proposed source encryption…
Three-dimensional (3D) topological codes offer the advantage of supporting fault-tolerant implementations of non-Clifford gates, yet their performance against realistic noise remains largely unexplored. In this work, we focus on the…
This work investigates the fundamental limits of communication over a noisy discrete memoryless channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless…
Quantum algorithms face significant challenges due to qubit susceptibility to environmental noise, and quantum error correction typically requires prohibitive resource overhead. This paper proposes that quantum algorithms may possess…
The design of codes for communicating reliably over a statistically well defined channel is an important endeavor involving deep mathematical research and wide-ranging practical applications. In this work, we present the first family of…
An $n$-bit boolean function is resilient to coalitions of size $q$ if any fixed set of $q$ bits is unlikely to influence the function when the other $n-q$ bits are chosen uniformly. We give explicit constructions of depth-$3$ circuits that…