Related papers: Quantum Shift Register Circuits
Finding gradients is a crucial step in training machine learning models. For quantum neural networks, computing gradients using the parameter-shift rule requires calculating the cost function twice for each adjustable parameter in the…
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…
Quantum algorithms claim significant speedup over their classical counterparts for solving many problems. An important aspect of many of these algorithms is the existence of a quantum oracle, which needs to be implemented efficiently in…
Image processing is one of the most promising applications for quantum machine learning (QML). Quanvolutional Neural Networks with non-trainable parameters are the preferred solution to run on current and near future quantum devices. The…
Given an output wavefunction of a monitored quantum circuit consisting of both unitary gates and projective measurements, we ask whether two complementary subsystems are entangled or not. For Clifford circuits, we find that this question…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…
We introduce a block encoding method for mapping discrete subgroups to qubits on a quantum computer. This method is applicable to general discrete groups, including crystal-like subgroups such as $\mathbb{BI}$ of $SU(2)$ and $\mathbb{V}$ of…
Singular value thresholding (SVT) operation is a fundamental core module in many mathematical models in computer vision and machine learning, particularly for many nuclear norm minimizing-based problems. We presented a quantum SVT (QSVT)…
As the width and depth of quantum circuits implemented by state-of-the-art quantum processors rapidly increase, circuit analysis and assessment via classical simulation are becoming unfeasible. It is crucial, therefore, to develop new…
A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum…
Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the…
Satisfiability Testing (SAT) techniques are well-established in classical computing where they are used to solve a broad variety of problems, e.g., in the design of classical circuits and systems. Analogous to the classical realm, quantum…
We briefly review what a quantum computer is, what it promises to do for us, and why it is so hard to build one. Among the first applications anticipated to bear fruit is quantum simulation of quantum systems. While most quantum computation…
The Quantum Fourier Transform (QFT) is a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum…
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…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
The work proposes an extension of the quantum circuit formalism where qubits (wires) are circular instead of linear. The left-to-right interpretation of a quantum circuit is replaced by a circular representation which allows to select the…
The realization of quantum algorithms relies on specific quantum compilations according to the underlying quantum processors. However, there are various ways to physically implement qubits in different physical devices and manipulate those…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
We show how to explicitly construct an $O(nd)$ size and constant quantum depth circuit which encodes any given $n$-qubit stabilizer code with $d$ generators. Our construction is derived using the graphic description for stabilizer codes and…