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The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…

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…

Current implementations of the Variational Quantum Eigensolver (VQE) technique for solving the electronic structure problem involve splitting the system qubit Hamiltonian into parts whose elements commute within their single qubit…

A central roadblock in the realization of variational quantum eigensolvers on quantum hardware is the high overhead associated with measurement repetitions, which hampers the computation of complex problems, such as the simulation of mid-…

Estimation of the expectation value of observables is a key subroutine in quantum computing and is also the bottleneck of the performance of many near-term quantum algorithms. Many works have been proposed to reduce the number of…

We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the…

Reducing the number of measurements required to estimate the expectation value of an observable is crucial for the variational quantum eigensolver to become competitive with state-of-the-art classical algorithms. To measure complicated…

Measuring the expectation value of the molecular electronic Hamiltonian is one of the challenging parts of the variational quantum eigensolver. A widely used strategy is to express the Hamiltonian as a sum of measurable fragments using…

To obtain estimates of electronic energies, the Variational Quantum Eigensolver (VQE) technique performs separate measurements for multiple parts of the system Hamiltonian. Current quantum hardware is restricted to projective single-qubit…

Any observable with finite eigenvalue spectrum can be measured using a multiport apparatus realizing an appropriate unitary transformation and an array of detector instruments, where each detector operates as an indicator of one possible…

Given the state of a quantum system, one can calculate the expectation value of any observable of the system. However, the inverse problem of determining the state by performing different measurements is not a trivial task. In various…

One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the…

Quantum chemistry is among the most promising applications of quantum computing, offering the potential to solve complex electronic structure problems more efficiently than classical approaches. A critical component of any quantum algorithm…

Estimating the expectation value of an operator corresponding to an observable is a fundamental task in quantum computation. It is often impossible to obtain such estimates directly, as the computer is restricted to measuring in a fixed…

The accurate estimation of quantum observables is a critical task in science. With progress on the hardware, measuring a quantum system will become increasingly demanding, particularly for variational protocols that require extensive…

Given a quantum state in the finite-dimensional Hilbert space $ \C^n $, the range of possible values of a quantum observable is usually identified with the discrete spectrum of eigenvalues of a corresponding Hermitian matrix. Here any such…

Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in a multitude of quantum algorithms. Simultaneously measuring sets of operators allows for fewer measurements and an overall speedup of the…

Solving the electronic structure problem using the Variational Quantum Eigensolver (VQE) technique involves measurement of the Hamiltonian expectation value. Current hardware can perform only projective single-qubit measurements, and thus,…

We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…

Experimental characterizations of a quantum system involve the measurement of expectation values of observables for a preparable state |psi> of the quantum system. Such expectation values can be measured by repeatedly preparing |psi> and…