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Many quantum algorithms for ground-state preparation and energy estimation require the implementation of high-degree polynomials of a Hamiltonian to achieve better convergence rates. Their circuit implementation typically relies on quantum…
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…
A basic problem of approximation theory, the approximation of functions from the Sobolev space W_p^r([0,1]^d) in the norm of L_q([0,1]^d), is considered from the point of view of quantum computation. We determine the quantum query…
A mathematical proposition with a trainable pair, operator and quantum circuit, are introduced to approximate functions expressed as cubic Taylor polynomials, numerical simulations illustrate three cases.
Many promising applications of quantum computing with a provable speedup center around the HHL algorithm. Due to restrictions on the hardware and its significant demand on qubits and gates in known implementations, its execution is…
We establish an isomorphism between quantum circuits and a subspace of polyatomic molecules, which suggests that molecules can be used as descriptors of quantum circuits for quantum machine learning. Our numerical results show that the…
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
Quantum computing shows promise for addressing computationally intensive problems but is constrained by the exponential resource requirements of general quantum state tomography (QST), which fully characterizes quantum states through…
The Poisson equation occurs in many areas of science and engineering. Here we focus on its numerical solution for an equation in d dimensions. In particular we present a quantum algorithm and a scalable quantum circuit design which…
In order to realize a Quantum CPU some schemes for executing fundamental mathematical tasks are needed. In this paper we present some quantum circuits which, using elementary arithmetic operations, allow an approximated calculation of…
Quantum signal processing (QSP) studies quantum circuits interleaving known unitaries (the phases) and unknown unitaries encoding a hidden scalar (the signal). For a wide class of functions one can quickly compute the phases applying a…
Quantum computers hold great promise to enhance machine learning, but their current qubit counts restrict the realisation of this promise. In an attempt to placate this limitation techniques can be applied for evaluating a quantum circuit…
We present a classically solvable model that leads to optimized low-depth quantum circuits leveraging separable pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
Quantum computers promise to revolutionise electronic simulations by overcoming the exponential scaling of many-electron problems. While electronic wave functions can be represented using a product of fermionic unitary operators, shallow…
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
Parametrized quantum circuits (PQC) are quantum circuits which consist of both fixed and parametrized gates. In recent approaches to quantum machine learning (QML), PQCs are essentially ubiquitous and play the role analogous to classical…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…