Related papers: Property testing of unitary operators
Quantum programs exhibit inherent non-deterministic behavior, which poses more significant challenges for error discovery compared to classical programs. While several testing methods have been proposed for quantum programs, they often…
We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local…
Obtaining the expectation value of an observable on a quantum computer is a crucial step in the variational quantum algorithms. For complicated observables such as molecular electronic Hamiltonians, a common strategy is to present the…
Probabilities of the outcomes of consecutive quantum measurements can be obtained by construction probability amplitudes, thus implying unitary evolution of the measured system, broken each time a measurement is made. In practice, the…
We consider the problem of testing whether an unknown $n$-variable Boolean function is a $k$-junta in the distribution-free property testing model, where the distance between function is measured with respect to an arbitrary and unknown…
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
Randomized benchmarking is a powerful technique to efficiently estimate the performance and reliability of quantum gates, circuits and devices. Here we propose to perform randomized benchmarking in a coherent way, where superpositions of…
One of the main subjects of this paper is to study quantum property testing with local measurement. In particular, we establish a novel $\ell_2$ norm connection between quantum property testing problems and the corresponding distribution…
This papers considers the junta testing problem in a recently introduced ``relative error'' variant of the standard Boolean function property testing model. In relative-error testing we measure the distance from $f$ to $g$, where $f,g:…
Efficiently calculating the low-lying eigenvalues of Hamiltonians, written as sums of Pauli operators, is a fundamental challenge in quantum computing. While various methods have been proposed to reduce the complexity of quantum circuits…
If the system is known to be in one of two non-orthogonal quantum states, $|\psi_1\rangle$ or $|\psi_2\rangle$, it is not possible to discriminate them by a single measurement due to the unitarity constraint. In a regular Hermitian quantum…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
Symmetry adaptation, universality, and gate efficiency are central but often competing requirements in quantum algorithms for electronic structure and many-body physics. For example, fully symmetry-adapted universal operator pools typically…
We study equivalence determination of unitary operations, a task analogous to quantum state discrimination. The candidate states are replaced by unitary operations given as a quantum sample, i.e., a black-box device implementing a candidate…
The cost of measuring quantum expectation values of an operator can be reduced by grouping the Pauli string ($SU(2)$ tensor product) decomposition of the operator into maximally commuting sets. We detail an algorithm, presented in [1], to…
We study quantum process tomography given the prior information that the map is a unitary or close to a unitary process. We show that a unitary map on a $d$-level system is completely characterized by a minimal set of $d^2{+}d$ elements…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
Standard randomized benchmarking protocols entail sampling from a unitary 2 design, which is not always practical. In this article we examine randomized benchmarking protocols based on subgroups of the Clifford group that are not unitary 2…
We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…