Related papers: Parallel Quantum Computation and Quantum Codes
Executing a logical quantum circuit fault-tolerantly incurs a large spacetime overhead. Recent work has proposed and investigated phantom codes, defined by the property that every in-block logical $\mathrm{CNOT}$ circuit can be implemented…
Quantum signal processing (QSP), which enables systematic polynomial transformations on quantum data through sequences of qubit rotations, has emerged as a fundamental building block for quantum algorithms and data re-uploading quantum…
We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
In 2021, Broadbent and Kazmi developed a gate-teleportation-based protocol for computational indistinguishability obfuscation of quantum circuits. This protocol is efficient for Clifford+T circuits with logarithmically many T-gates, where…
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…
Despite the promise that fault-tolerant quantum computers can efficiently solve classically intractable problems, it remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy,…
This paper concerns the problem of checking if two shallow (i.e., constant-depth) quantum circuits perform equivalent computations. Equivalence checking is a fundamental correctness question -- needed, e.g., for ensuring that…
As an important branch of quantum secure multiparty computation, quantum private comparison (QPC) has attracted more and more attention recently. In this paper, according to the quantum implementation mechanism that these protocols used, we…
Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin--Knill theorem,…
Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
Verifying equivalence between two quantum circuits is a hard problem, that is nonetheless crucial in compiling and optimizing quantum algorithms for real-world devices. This paper gives a Turing reduction of the (universal) quantum circuits…
We present two protocols for classical verification of quantum depth. Our protocols allow a purely classical verifier to distinguish devices with different quantum circuit depths even in the presence of classical computation. We show that a…
Quantum Computing (QC) refers to an emerging paradigm that inherits and builds with the concepts and phenomena of Quantum Mechanic (QM) with the significant potential to unlock a remarkable opportunity to solve complex and computationally…
We propose a quantum circuit design for implementing coined quantum walks on complex networks. In complex networks, the coin and shift operators depend on the varying degrees of the nodes, which makes circuit construction more challenging…
The use of Quantum Neural Networks (QNN) that are analogous to classical neural networks, has greatly increased in the past decade owing to the growing interest in the field of Quantum Machine Learning (QML). A QNN consists of three major…
$\mathsf{QAC}^0$ is the class of constant-depth polynomial-size quantum circuits constructed from arbitrary single-qubit gates and generalized Toffoli gates. It is arguably the smallest natural class of constant-depth quantum computation…
In order to establish the computational equivalence between quantum Turing machines (QTMs) and quantum circuit families (QCFs) using Yao's quantum circuit simulation of QTMs, we previously introduced the class of uniform QCFs based on an…
Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC). This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes by…