Related papers: Quantum Approximate Counting with Additive Error: …
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
We present characterisations of "exact" gap-definable classes, in terms of indeterministic models of computation which slightly modify the standard model of quantum computation. This follows on work of Aaronson [arXiv:quant-ph/0412187], who…
Quantum computing is a new computational paradigm with the potential to solve certain computationally challenging problems much faster than traditional approaches. Civil engineering encompasses many computationally challenging problems,…
Quantum image processing (QIP) means the quantum based methods to speed up image processing algorithms. Many quantum image processing schemes claim that their efficiency are theoretically higher than their corresponding classical schemes.…
We analyze the complexity of quantum state verification in the context of solving systems of linear equations of the form $A \vec x = \vec b$. We show that any quantum operation that verifies whether a given quantum state is within a…
The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation…
Quantum computing is a game-changing technology for global academia, research centers and industries including computational science, mathematics, finance, pharmaceutical, materials science, chemistry and cryptography. Although it has seen…
Aaronson, Bouland, Fitzsimons and Lee introduced the complexity class PDQP (which was original labeled naCQP), an alteration of BQP enhanced with the ability to obtain non-collapsing measurements, samples of quantum states without…
The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the…
Quantization is a fundamental optimization for many machine-learning use cases, including compressing gradients, model weights and activations, and datasets. The most accurate form of quantization is \emph{adaptive}, where the error is…
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…
We investigate quantum computational complexity of calculating partition functions of Ising models. We construct a quantum algorithm for an additive approximation of Ising partition functions on square lattices. To this end, we utilize the…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…
This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…
We consider the following problem: estimate the size of a nonempty set $S\subseteq\left[ N\right] $, given both quantum queries to a membership oracle for $S$, and a device that generates equal superpositions $\left\vert S\right\rangle $…
Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and characterize their computational complexity. In the quantum setting,…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
Quantum compiling, a process that decomposes the quantum algorithm into a series of hardware-compatible commands or elementary gates, is of fundamental importance for quantum computing. We introduce an efficient algorithm based on deep…
Quantum capacities are fundamental quantities that are notoriously hard to compute and can exhibit surprising properties such as superadditivity. Thus, a vast amount of literature is devoted to finding tight and computable bounds on these…
With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…