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Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…
Molecular quantum simulations with the variational quantum eigensolver (VQE) rely on ansatz states that approximate the molecular ground states. These ansatz states are generally defined by parametrized fermionic excitation operators and an…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi--controlled Toffoli gates. The first algorithm…
We propose a scheme to perform probabilistic quantum gates on remote trapped atom qubits through interference of optical frequency qubits. The method does not require localization of the atoms to the Lamb-Dicke limit, and is not sensitive…
In gate-defined semiconductor spin qubits, the highly tunable Heisenberg exchange interaction is leveraged to implement fermionic two-qubit gates such as CZ and SWAP. However, the broader family of fermionic simulation (fSim) gates remains…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
Variational Quantum Algorithms are a vital part of quantum computing. It is a blend of quantum and classical methods for tackling tough problems in machine learning, chemistry, and combinatorial optimization. Yet as these algorithms scale…
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
Recently, the development of quantum chips has made great progress-- the number of qubits is increasing and the fidelity is getting higher. However, qubits of these chips are not always fully connected, which sets additional barriers for…
Quasiprobabilistic cutting techniques allow us to partition large quantum circuits into smaller subcircuits by replacing non-local gates with probabilistic mixtures of local gates. The cost of this method is a sampling overhead that scales…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…
We present explicit expressions for the central piece of a variational method developed by Shi et al. which extends variational wave functions that are efficiently computable on classical computers beyond mean-field to generalized Gaussian…
Portfolio optimization is a cornerstone of financial decision-making, traditionally relying on classical algorithms to balance risk and return. Recent advances in quantum computing offer a promising alternative, leveraging quantum…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…
We present an efficient algorithm to reduce the number of non-Clifford gates in quantum circuits and the number of parametrized rotations in parametrized quantum circuits. The method consists in finding rotations that can be merged into a…
Exterior calculus with its three operations meet, join and hodge star complement, is used for the representation of fermion-hole systems and for fermionic analogues of logical gates. Two different schemes that implement fermionic quantum…
The model of open quantum systems is adopted to describe the non-local dynamical behaviour of qubits processed by entangling gates. The analysis gets to the conclusion that a distinction between evaluation steps and task-oriented computing…
Quantum computation based on geometric phase is generally believed to be more robust against certain errors or noises than the conventional dynamical strategy. However, the gate error caused by the decoherence effect is inevitable, and thus…