We propose a quantum optical device to experimentally realize quantum processes, which perform the regularization of the---in general highly singular---Glauber-Sudarshan $P$~functions of arbitrary quantum states before their application and/or measurement. This allows us to produce a broad class of nonclassical states with regular $P$~functions, also called nonclassicality quasiprobabilities. For this purpose, the input states are combined on highly transmissive beam splitters with specific Gaussian or non-Gaussian classical states. We study both balanced and unbalanced homodyne detections for the direct sampling of the output states of the implemented processes, which requires no further regularization or state-reconstruction. By numerical simulations we demonstrate the feasibility of our approach and we outline the generalization to multimode light.
We consider the two-step method [A. R. Kuzmak and V. M. Tkachuk, Phys. Lett. A 378 (2014) 1469] for preparation of an arbitrary quantum gate on two spins with anisotropic Heisenberg interaction. At the first step, the system evolves during some period of time. At the second step, we apply pulsed magnetic field individually to each spin. We obtain the conditions for realization of SWAP, iSWAP, $\sqrt{SWAP}$ and entangled gates. Finally, we consider the implementation of this method on the physical system of ultracold atoms in optical lattice.
We propose a deterministic remote state preparation (RSP) scheme for preparing an arbitrary (including pure and mixed) qubit, where a partially entangled state and finite classical communication are used. To our knowledge, our scheme is the first RSP scheme that fits into this category. One other RSP scheme proposed by Berry shares close features, but can only be used to prepare an arbitrary pure qubit. Even so, our scheme saves classical communication by approximate 1 bit per prepared qubit under equal conditions. When using a maximally entangled state, the classical communication for our sch…
We introduce a protocol capable of generating a general measurement operator for a mechanical resonator. The technique requires a qubit-resonator interaction and uses a coherent pulse to drive qubit transitions. This is followed by projective measurement of the qubit's energy, constraining the resonator in a state that depends on the pulse shape. The freedom to choose a pulse shape for the coherent drive enables an arbitrary position-basis measurement operator. Using this measurement operator, we outline a two pulse protocol that probabilistically generates a pure mechanical state with a desir…
We address the issue of improving the quality of the joint remote preparation of an arbitrary two-qubit in case four qubits of the quantum channel which consists of a GHZ state and a GHZ-like one are subjected to noises. Two controlling parameters are added, one in the quantum channel and other in the measurement of the second sender, in order to optimize the averaged fidelities. The results from analyzing the behaviors of the optimal averaged fidelities show that there are essentially two different ways for the optimization of the efficiency of the protocol. The first is simply choosing suita…
We quantify and analyze the controller's power in controlled remote state preparation schemes. Our analysis provides a lower bound on the control power required for controlled remote preparation of arbitrary D-dimensional states. We evaluate several existing controlled remote state preparation protocols and show that some proposed non-maximally entangled channels are not suitable for perfect controlled remote preparation of arbitrary quantum states from the con- troller's point of view. We find that for remotely preparing D-dimensional states, the entropy of each controller should be no less t…
We present two schemes for joint remote preparation of an arbitrary four-qubit j\c{hi}i -type entangled state via three three- and (N+1)-qubit GHZ states as the quantum channel, respectively. In these schemes, two senders (or N senders) share the original state which they wish to help the receiver to remotely prepare. To complete the JRSP schemes, several novel sets of mutually orthogonal basis vectors are introduced. It is shown that, only if two senders (or N senders) collaborate with each other, and perform projective measurements under suitable measuring basis on their own qubits respectiv…
We propose a class of preparation schemes for orbital angular momentum and polarisation qubits carried by single photons or classical states of light based on coherent feedback control by an ancillary degree of freedom of light. The preparation methods use linear optics and include the transcription of an arbitrary polarisation state onto a two-level OAM system (swap) for arbitrary OAM values plus/minus "l" within a light beam, i.e. without spatial interferometer. The preparations can be carried out with unit efficiency independent from the potentially unknown initial state of the system. More…
As one of the most prominent subfields of quantum communication research, remote state preparation (RSP) plays a crucial role in quantum networks. Here we present a deterministic remote state preparation scheme to prepare an arbitrary two-qubit state via a seven-qubit entangled channel created from Borras \emph{et al.} state. Quantum noises are inherent to each and every protocol for quantum communication that is currently in use, putting the integrity of quantum communication systems and their dependability at risk. The initial state of the system was a pure quantum state, but as soon as ther…
Quantum error correction is an essential component for practical quantum computing on noisy quantum hardware. However, logical operations on error-corrected qubits require a significant resource overhead, especially for high-precision and high-fidelity non-Clifford rotation gates. To address this issue, we propose a postselection-based algorithm to efficiently prepare resource states for gate teleportation. Our algorithm achieves fault tolerance, demonstrating the exponential suppression of logical errors with code distance, and it applies to any stabilizer codes. We provide analytical derivat…
Werner states are defined as bipartite qudit states that remain unchanged under application of arbitrary unitary operators acting on both subsystems simultaneously. Their preparation is a crucial ingredient in entanglement distillation protocols. This thesis deals with an iterative approach to prepare Werner states asymptotically, using random unitary operations. The asymptotic dynamics of random unitary operations are linked to algebraic properties of the involved unitary operators applying results about general quantum operations. Then a family of random unitary operations is constructed, wh…
Preparation of quantum state lies at the heart of quantum information processing. The greedy algorithm provides a potential method to effectively prepare quantum states. However, the standard greedy algorithm, in general, cannot take the global maxima and instead becomes stuck on a local maxima. Based on the standard greedy algorithm, in this paper we propose a revised version to design dynamic pulses to realize universal quantum state preparation, i.e., preparing any arbitrary state from another arbitrary one. As applications, we implement this scheme to the universal preparation of single- a…
Quantum private comparison (QPC) aims to accomplish the equality comparison of the secrets from different users without disclosing their genuine contents by using the principles of quantum mechanics. In this paper, we summarize eight modes of quantum state preparation and transmission existing in current QPC protocols first. Then, by using the mode of scattered preparation and one-way convergent transmission, we construct a new multi-user quantum private comparison (MQPC) protocol with two-particle maximally entangled states, which can accomplish arbitrary pair's comparison of equality among K…
In this short review I aim to explain how we can construct a circuit implementation of the bucketbrigade qRAM first proposed in [1]. Used with classical data, this qRAM model can be used incombination with the quantum accessible data structure [2] to prepare arbitrary quantum statesquickly and repeatedly, once the data to be prepared is in memory
Quantum state preparation is an important class of quantum algorithms that is employed as a black-box subroutine in many algorithms, or used by itself to generate arbitrary probability distributions. We present a novel state preparation method that utilizes less quantum computing resource than the existing methods. Two variants of the algorithm with different emphases are introduced. One variant uses fewer qubits and no controlled gates, while the other variant potentially requires fewer gates overall. A general analysis is given to estimate the number of qubits necessary to achieve a desired …
Google Quantum AI（谷歌量子人工智能）；Department of Combinatorics and Optimization and Institute for Quantum Computing, University of Waterloo（滑铁卢大学组合优化与量子计算研究所）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Computing and Mathematical Sciences Department, Caltech（加州理工学院计算与数学科学系）
Quantum Amplitude Estimation (QAE) can achieve a quadratic speed-up for applications classically solved by Monte Carlo simulation. A key requirement to realize this advantage is efficient state preparation. If state preparation is too expensive, it can diminish the quantum advantage. Preparing arbitrary quantum states has exponential complexity with respect to the number of qubits, thus, is not applicable. Currently known efficient techniques require problems based on log-concave probability distributions, involve learning an unknown distribution from empirical data, or fully rely on quantum a…
