Related papers: Formally Verifying Quantum Phase Estimation Circui…
Quantum computers are expected to perform the full-configuration interaction calculations with less computational resources compared to classical ones, thanks to the use of the quantum phase estimation (QPE) algorithms. However, only a…
Formal methods have been a successful approach for modelling and verifying the correctness of complex technologies like microprocessor chip design, biological systems and others. This is the main motivation of developing quantum formal…
We demonstrate experimental implementation of robust phase estimation (RPE) to learn the phases of X and Y rotations on a trapped $\textrm{Yb}^+$ ion qubit. We estimate these phases with uncertainties less than $4\cdot10^{-4}$ radians using…
Quantum computations are expressed in general as quantum circuits, which are specified by ordered lists of quantum gates. The resulting specifications are used during the optimisation and execution of the expressed computations. However,…
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…
We introduce a new variant of Quantum Amplitude Estimation (QAE), called Iterative QAE (IQAE), which does not rely on Quantum Phase Estimation (QPE) but is only based on Grover's Algorithm, which reduces the required number of qubits and…
Many researchers have been heavily investigated on quantum phase estimation (QPE) algorithms to find the unknown phase, since QPE is the core building block of the most quantum algorithms such as the Shor's factoring algorithm, quantum…
Gottesman, Kitaev and Preskill have formulated a way of encoding a qubit into an oscillator such that the qubit is protected against small shifts (translations) in phase space. The idea underlying this encoding is that error processes of…
Quantum computing is greatly advanced in recent years and is expected to transform the computation paradigm in the near future. Quantum circuit simulation plays a key role in the toolchain for the development of quantum hardware and…
Beyond ground state energy estimation, quantum phase estimation (QPE) applied to many-electron systems has the potential to output an approximation of the ground state, enabling in a second step an evaluation of observables other than the…
We propose an analysis of the Quantum Phase Estimation (QPE) algorithm applied to many-electron systems by investigating its free parameters such as the time step, number of phase qubits, initial state preparation, number of measurement…
Achieving quantum speedups in practical tasks remains challenging for current noisy intermediate-scale quantum (NISQ) devices. These devices always encounter significant obstacles such as inevitable physical errors and the limited…
Quantum Phase Estimation (QPE), the quantum algorithm for estimating eigenvalues of a given Hermitian matrix and preparing its eigenvectors, is considered the most promising approach to finding the ground states and their energies of…
Simulating quantum imaginary-time evolution (QITE) is a major promise of quantum computation. However, the known algorithms are either probabilistic (repeat until success) with impractically small success probabilities or coherent (quantum…
Recursive techniques have recently been introduced into quantum programming so that a variety of large quantum circuits and algorithms can be elegantly and economically programmed. In this paper, we present a proof system for formal…
We introduce a new paradigm for analysing and finding bugs in quantum circuits. In our approach, the problem is given by a triple $\{P\}\,C\,\{Q\}$ and the question is whether, given a set $P$ of quantum states on the input of a circuit…
Simulating electronic structure on a quantum computer requires encoding of fermionic systems onto qubits. Common encoding methods transform a fermionic system of $N$ spin-orbitals into an $N$-qubit system, but many of the fermionic…
Atomic (qubit) and optical or microwave (modal) phase-estimation protocols are placed on the same footing in terms of quantum-circuit diagrams. Circuit equivalences are used to demonstrate the equivalence of protocols that achieve the…
We propose a quantum tomography scheme for pure qudit systems which adopts random base measurements and generative learning methods, along with a built-in fidelity estimation approach to assess the reliability of the tomographic states. We…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…