Related papers: Asymptotically Efficient Quantum Karatsuba Multipl…
The multisilce method is an important algorithm for electron diffraction and image simulations in transmission electron microscopy. We have proposed a quantum algorithm of the multislice method based on quantum circuit model previously. In…
Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
We propose a new finding $k$-minima algorithm and prove that its query complexity is $\mathcal{O}(\sqrt{kN})$, where $N$ is the number of data indices. Though the complexity is equivalent to that of an existing method, the proposed is…
A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e.,…
In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices…
The synthesis approaches for quantum circuits typically aim at minimizing the number of lines or gates. Given the tight restrictions on those logical resources in physical implementations, we propose to view the problem fundamentally…
We present a method for quantum error mitigation on partially error-corrected quantum computers - i.e., computers with some logical qubits and some noisy qubits. Our method is inspired by the error cancellation method and is implemented via…
In this work we present a new structure for multiplication in finite fields. This structure is based on a digit-level LFSR (Linear Feedback Shift Register) multiplier in which the area of digit-multipliers are reduced using the Karatsuba…
Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with…
Quantum computers promise to outperform their classical counterparts at certain tasks. However, existing quantum devices are error-prone and restricted in size. Thus, effective compilation methods are crucial to exploit limited quantum…
This paper shows how to design efficient arithmetic elements out of quantum gates using "carry-save" techniques borrowed from classical computer design. This allows bit-parallel evaluation of all the arithmetic elements required for Shor's…
Existing numerical optimizers deployed in quantum compilers use expensive $\mathcal{O}(4^n)$ matrix-matrix operations. Inspired by recent advances in quantum machine learning (QML), QFactor-Sample replaces matrix-matrix operations with…
Let {\alpha} be the maximal value such that the product of an n x n^{\alpha} matrix by an n^{\alpha} x n matrix can be computed with n^{2+o(1)} arithmetic operations. In this paper we show that \alpha>0.30298, which improves the previous…
The ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer facilitates the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete…
Computational quantum technologies are entering a new phase in which noisy intermediate-scale quantum computers are available, but are still too small to benefit from active error correction. Even with a finite coherence budget to invest in…
The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the $\mathcal{O}(N^4)$ gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes…
The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…
A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…
Complex quantum simulation workflows are often hindered by incompatible wavefunction representations adopted across different algorithmic frameworks. In particular, the mismatch between the first- and second-quantization formalisms prevents…