Related papers: On Asymptotic Gate Complexity and Depth of Reversi…
We extend Nielsen's formulation of quantum circuit complexity to include intrinsically non-invertible operations. Such gates arise from fusion with topological defect operators and remove a basic limitation of symmetry-based circuits: the…
Quantum squaring operation is a useful building block in implementing quantum algorithms such as linear regression, regularized least squares algorithm, order-finding algorithm, quantum search algorithm, Newton Raphson division, Euclidean…
The primary objective of quantum circuit synthesis is to efficiently and accurately realize specific quantum algorithms or operations utilizing a predefined set of quantum gates, while also optimizing the circuit size. It holds a pivotal…
Quantum computers promise great improvements in solving problems such as factoring large integers, simulating quantum systems, and database searching. Using a photon as a quantum bit (qubit) is one of the most promising ways to realize a…
Optical qubits uniquely combine information transfer in optical fibers with a good processing capability and are therefore attractive tools for quantum technologies. A large challenge, however, is to overcome the low efficiency of two-qubit…
We study pseudorandomness properties of permutations on $\{0,1\}^n$ computed by random circuits made from reversible $3$-bit gates (permutations on $\{0,1\}^3$). Our main result is that a random circuit of depth $n \cdot \tilde{O}(k^2)$,…
Mapping logical quantum circuits to Noisy Intermediate-Scale Quantum (NISQ) devices is a challenging problem which has attracted rapidly increasing interests from both quantum and classical computing communities. This paper proposes an…
In the paper, we consider quantum circuits for the Quantum Fourier Transform (QFT) algorithm. The QFT algorithm is a very popular technique used in many quantum algorithms. We present a generic method for constructing quantum circuits for…
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
In this paper we apply the canonical decomposition of two qubit unitaries to find pulse schemes to control the proposed Kane quantum computer. We explicitly find pulse sequences for the CNOT, swap, square root of swap and controlled Z…
The decomposition for controlled-$ZX$ gate in [Phys. Rev. A, 87, 062318 (2013)] has a shallow circuit depth $8n-20$ with no ancilla. Here we modify this decomposition to decompose $n$-qubit Toffoli gate with only $2n-3$ additional…
There is increasing interest in the development of gate-based quantum circuits for the training of machine learning models. Yet, little is understood concerning the parameters of circuit design, and the effects of noise and other…
Some physical implementation schemes of quantum computing can apply two-qubit gates only on certain pairs of qubits. These connectivity constraints are commonly viewed as a significant disadvantage. For example, compiling an unrestricted…
Works on quantum computing and cryptanalysis has increased significantly in the past few years. Various constructions of quantum arithmetic circuits, as one of the essential components in the field, has also been proposed. However, there…
We construct a polynomial-time classical algorithm that samples from the output distribution of noisy geometrically local Clifford circuits with any product-state input and single-qubit measurements in any basis. Our results apply to…
Current proposals for quantum compilers require the synthesis and optimization of linear reversible circuits and among them CNOT circuits. Since these circuits represent a significant part of the cost of running an entire quantum circuit,…
The current phase of quantum computing is in the Noisy Intermediate-Scale Quantum (NISQ) era. On NISQ devices, two-qubit gates such as CNOTs are much noisier than single-qubit gates, so it is essential to minimize their count. Quantum…
We present tools and methods to generalize parity compilation to digital quantum computing devices with arbitrary connectivity graphs and construct circuit implementations for the constraint Hamiltonian of higher-order constrained binary…
It is well known that most of the frequently used reversible logic gates (e.g., NOT, CNOT, SWAP, Toffoli, Fredkin) are self-inverse and are represented by square matrices that are unitary and Hermitian. However, with a simple minded…
One strategy to fit larger problems on NISQ devices is to exploit a tradeoff between circuit width and circuit depth. Unfortunately, this tradeoff still limits the size of tractable problems since the increased depth is often not realizable…