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Variational quantum algorithms are considered one of the most promising methods for obtaining near-term quantum advantages; however, most of these algorithms are only expressed in the conventional quantum circuit scheme. The roadblock to…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits as…
A projective measurement of energy (PME) on a quantum system is a quantum measurement, determined by the Hamiltonian of the system. PME protocols exist when the Hamiltonian is given in advance. Unknown Hamiltonians can be identified by…
The accumulation of noise in quantum computers is the dominant issue stymieing the push of quantum algorithms beyond their classical counterparts. We do not expect to be able to afford the overhead required for quantum error correction in…
Estimating the eigenstate properties of quantum systems is a long-standing, challenging problem for both classical and quantum computing. Existing universal quantum algorithms typically rely on ideal and efficient query models (e.g. time…
Estimating observable expectation values in eigenstates of quantum systems has a broad range of applications and is an area where early fault-tolerant quantum computers may provide practical quantum advantage. We develop a hybrid…
Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating…
Quantum amplitude estimation is a key subroutine in a number of powerful quantum algorithms, including quantum-enhanced Monte Carlo simulation and quantum machine learning. Maximum-likelihood quantum amplitude estimation (MLQAE) is one of a…
This paper introduces Witnessed Quantum Time Evolution (WQTE), a novel quantum algorithm for efficiently computing the eigen-energy spectra of arbitrary quantum systems without requiring eigenstate preparation-a key limitation of…
Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in…
The state-of-the-art quantum computing hardware has entered the noisy intermediate-scale quantum (NISQ) era. Having been constrained by the limited number of qubits and shallow circuit depth, NISQ devices have nevertheless demonstrated the…
When estimating the eigenvalues of a given observable, even fault-tolerant quantum computers will be subject to errors, namely algorithmic errors. These stem from approximations in the algorithms implementing the unitary passed to phase…
We propose a quantum algorithm for finding eigenvalues of non-unitary matrices. We show how to construct, through interactions in a quantum system and projective measurements, a non-Hermitian or non-unitary matrix and obtain its eigenvalues…
The Variational Quantum Eigensolver (VQE) is widely regarded as a promising algorithm for calculating ground states of quantum systems that are intractable for classical computers. This promise is typically motivated by the hope of…
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a quantum process. QPT is a major quantum information processing tool, since it especially allows one to experimentally characterize the actual behavior of…
Machine learning has emerged as a promising approach to study the properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods$-$such as Monte Carlo$-$which…
We present BAE, a problem-tailored and noise-aware Bayesian algorithm for quantum amplitude estimation. In a fault tolerant scenario, BAE is capable of saturating the Heisenberg limit; if device noise is present, BAE can dynamically…
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…
We present a hybrid quantum algorithm for estimating gaps in many-body energy spectra, supported by an analytic proof of its inherent resilience to state preparation and measurement errors, as well as mid-circuit multi-qubit depolarizing…