Related papers: Quantum Hardcore Functions by Complexity-Theoretic…
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation…
Quantum computing is an emerging computational paradigm that leverages the laws of quantum mechanics to perform elementary logic operations. Existing programming models for quantum computing were designed with fault-tolerant hardware in…
Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the…
Randomized encoding is a powerful cryptographic primitive with various applications such as secure multiparty computation, verifiable computation, parallel cryptography, and complexity lower-bounds. Intuitively, randomized encoding…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
The conventional paradigm of quantum computing is discrete: it utilizes discrete sets of gates to realize bitstring-to-bitstring mappings, some of them arguably intractable for classical computers. In parameterized quantum approaches, the…
Cryptographic hash functions are fundamental primitives widely used in practice. For such a function $f:\{0, 1\}^n\to\{0, 1\}^m$, it is nearly impossible for an adversary to produce the hash $f(x)$ without knowing the secret message…
Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic…
Quantum computers promise to solve problems that are intractable for classical computers, but qubits are vulnerable to many sources of error, limiting the depth of the circuits that can be reliably executed on today's quantum hardware.…
We introduce a new graphical framework for designing quantum error correction codes based on classical principles. A key feature of this graphical language, over previous approaches, is that it is closely related to that of factor graphs or…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
We formalize and study the notion of a quantum trapdoor function. This is an efficiently computable unitary that takes as input a "public" quantum state and a classical string $x$, and outputs a quantum state. This map is such that (i) it…
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
Extensive quantum error correction is necessary in order to scale quantum hardware to the regime of practical applications. As a result, a significant amount of decoding hardware is necessary to process the colossal amount of data required…
Quantum computers have advanced rapidly in qubit count and gate fidelity. However, large-scale fault-tolerant quantum computing still relies on quantum error correction code (QECC) to suppress noise. Manually or experimentally verifying the…
Complex quantum circuits are constituted by combinations of quantum subroutines. The computation is possible as long as the quantum data encoding is consistent throughout the circuit. Despite its fundamental importance, the formalization of…
As the scale of quantum programs grows to match that of classical software, the nascent field of quantum software engineering must mature and tools such as debuggers will become increasingly important. However, developing a quantum debugger…