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We introduce an efficient algorithm for the systematic design of shallow-depth quantum circuits capable of preparing many-body quantum states represented as Matrix Product States (MPS). The proposed method leverages Schmidt spectrum…
We propose a unifying framework for the state preparation using quantum power method algorithms based on generalized quantum signal processing (GQSP). We apply GQSP to realize quantum analogs of classical power iteration, power Lanczos,…
Quantum state tomography is the standard tool in current experiments for verifying that a state prepared in the lab is close to an ideal target state, but up to now there were no rigorous methods for evaluating the precision of the state…
Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized…
The preparation of quantum states serves as a pivotal subroutine across various domains, including quantum communication protocols, quantum computing, and the exploration of quantum correlations and other resources within physical systems.…
We introduce an approximate description of an $N$-qubit state, which contains sufficient information to estimate the expectation value of any observable with precision independent of $N$. We show, in fact, that the error in the estimation…
Quantum computing offers potential solutions for finding ground states in condensed-matter physics and chemistry. However, achieving effective ground state preparation is also computationally hard for arbitrary Hamiltonians. It is necessary…
We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable positive operator valued measurement (POVM) on a finite number of…
Quantum state tomography (QST) is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become…
State preparation is a fundamental routine in quantum computation, for which many algorithms have been proposed. Among them, perhaps the simplest one is the Grover-Rudolph algorithm. In this paper, we analyse the performance of this…
Quantum phase estimation is an important routine in many quantum algorithms, particularly for estimating the ground state energy in quantum chemistry simulations. This estimation involves applying powers of a unitary to the ground state,…
Many quantum algorithms rely on a quality initial state for optimal performance. Preparing an initial state for specific applications can considerably reduce the cost of probabilistic algorithms such as the well studied quantum phase…
A single photon in a superposition of $d$ modes naturally encode a $d$-dimensional quantum system, a so-called qudit. We show that such superpositions can be leveraged to achieve a quantum speed-up of remote remote state preparation (RSP):…
Quantum signal processing (QSP) and quantum singular value transformation (QSVT), have emerged as unifying frameworks in the context of quantum algorithm design. These techniques allow to carry out efficient polynomial transformations of…
Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods…
We propose a variational approach for preparing entangled quantum states on quantum computers. The methodology involves training a unitary operation to match with a target unitary using the Fubini-Study distance as a cost function. We…
Intrinsic symmetry of the existing protocols of quantum dialogue are explored. It is shown that if we have a set of mutually orthogonal $n$-qubit states {\normalsize $\{|\phi_{0}>,|\phi_{1}>,....,|\phi_{i}<,...,|\phi_{2^{n}-1}>\}$ and a set…
Hybrid oscillator-qubit processors have recently demonstrated high-fidelity control of both continuous- and discrete-variable information processing. However, most of the quantum algorithms remain limited to homogeneous quantum…
We present a framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…