Quantum State Preparation Research Articles

A secure deterministic remote state preparation via a seven-qubit entangled channel of a two-qubit entangled state under the impact of quantum noise

In this study, a deterministic remote state preparation protocol is presented for the preparation of arbitrary two-qubit entangled states through a seven-qubit entangled channel prepared from the state proposed by Borras et al. (2007). The implementation of any protocol for quantum communication is inherently susceptible to quantum noise, presenting a challenge to the reliability and security of quantum communication systems. The introduction of noise results in a transition from a pure to a mixed quantum state. This paper examines six distinct noise models, including bit-flip noise, phase-flip noise, bit-phase-flip noise, amplitude damping, phase damping, and depolarizing noise, and analyzes their impact on the entangled channel. The alterations to the density matrices resulting from the introduction of noise are evaluated. The fidelity between the original and remotely prepared quantum states is also analyzed and visually represented. Additionally, a thorough security analysis is conducted to demonstrate the robustness of the protocol against both internal and external attacks.

Simulation of positive operator-valued measures and quantum instruments via quantum state-preparation algorithms

In Ref. [Phys. Rev. A 100, 062317 (2019)], the authors reported an algorithm to implement, in a circuit-based quantum computer, a general quantum measurement (GQM) of a two-level quantum system, a qubit. Even though their algorithm seems right, its application involves the solution of an intricate non-linear system of equations in order to obtain the angles determining the quantum circuit to be implemented for the simulation. In this article, we identify and discuss a simple way to circumvent this issue and implement GQMs on any $d$-level quantum system through quantum state preparation algorithms. Using some examples for one qubit, one qutrit and two qubits, we illustrate the easy of application of our protocol. Besides, we show how one can utilize our protocol for simulating quantum instruments, for which we also give an example. All our examples are demonstrated using IBM's quantum processors.

Performance analysis for OFDM-based multi-carrier continuous-variable quantum key distribution with an arbitrary modulation protocol.

Multi-carrier continuous-variable quantum key distribution (CV-QKD) is considered to be a promising way to boost the secret key rate (SKR) over the existing single-carrier CV-QKD scheme. However, the extra excess noise induced in the imperfect multi-carrier quantum state preparation process of N subcarriers will limit the performance of the system. Here, a systematic modulation noise model is proposed for the multi-carrier CV-QKD based on the orthogonal frequency division multiplexing (OFDM). Subsequently, the performance of multi-carrier CV-QKD with arbitrary modulation protocol (e.g. QPSK, 256QAM and Gaussian modulation protocol) can be quantitatively evaluated by combining the security analysis method of the single-carrier CV-QKD. Under practical system parameters, the simulation results show that the SKR of the multi-carrier CV-QKD can still be significantly improved by increasing the carrier number N even with imperfect practical modulations. Specifically, the total SKR of multi-carrier CV-QKD can be optimized by carefully choosing N. The proposed model provides a feasible theoretical framework for the future multi-carrier CV-QKD experimental implementation.

Dissipation-driven formation of entangled dark states in strongly coupled inhomogeneous many-qubit systems in solid-state nanocavities

We study quantum dynamics of many-qubit systems strongly coupled to a quantized electromagnetic cavity field in the presence of decoherence and dissipation for both quantum emitters and cavity photons, taking into account the varying coupling strength of different qubits to the cavity field and the spread of their transition frequencies. Compact analytic solutions for time-dependent quantum state amplitudes and observables are derived for a broad class of open quantum systems in Lindblad approximation with the use of the stochastic Schr\"odinger equation approach. We show that depending on the initial quantum state preparation, an ensemble of qubits can evolve into a rich variety of many-qubit entangled states with destructive or constructive interference between the qubits. In particular, when only a small fraction of qubits are initially excited, the dissipation in a cavity will inevitably drive the system into robust dark states that are completely decoupled from the cavity and live much longer than the decay time of the cavity field. We also determine the conditions under which coherent coupling to the quantized cavity field overcomes the dephasing caused by a spread of transition frequencies in multiqubit systems and leads to the formation of a decoupled dark state.

Deep Reinforcement Learning for Preparation of Thermal and Prethermal Quantum States

We propose a method based on deep reinforcement learning that efficiently prepares a quantum many-body pure state in thermal or prethermal equilibrium. The main physical intuition underlying the method is that the information on the equilibrium states can be efficiently encoded/extracted by focusing on only a few local observables, relying on the typicality of equilibrium states. Instead of resorting to the expensive preparation protocol that adopts global features such as the quantum state fidelity, we show that the equilibrium states can be efficiently prepared only by learning the expectation values of local observables. We demonstrate our method by preparing two illustrative examples: Gibbs ensembles in non-integrable systems and generalized Gibbs ensembles in integrable systems. Pure states prepared solely from local observables are numerically shown to successfully encode the macroscopic properties of the equilibrium states. Furthermore, we find that the preparation errors, with respect to the system size, decay exponentially for Gibbs ensembles and polynomially for generalized Gibbs ensembles, which are in agreement with the finite-size fluctuation within thermodynamic ensembles. Our method paves a path toward studying the thermodynamic and statistical properties of quantum many-body systems in quantum hardware.

Search for optimal driving in finite quantum systems with precursors of criticality

Using the adiabatic perturbation theory of driven dynamics [Phys. Rev. A 78, 052508 (2008)] we design a hierarchy of quantum state preparation protocols that systematically increase the fidelity at very long driving times. We test these and other protocols, including those based on the geometric analysis of the parameter space, in a single-qubit system and in a fully connected multiqubit system showing in its infinite-size limit several quantum phase transitions. Our protocols excel in the asymptotic driving regime, above a crossover time from the Landau-Zener regime which increases with a decreasing minimal energy gap along the driving path (with the size of the system). In the medium-time domain, the performance of all tested protocols is indecisive.

Dissipative quantum computation and quantum state preparation based on BEC qubits

Among environmental effects, dissipation allows the stabilization of quantum resources, a fact that may accomplish key advantages over unitary quantum state manipulation. In this paper, we study an open quantum system composed ofNtwo-mode Bose–Einstein condensates (BECs), namely, BEC qubits, interacting with their environments. Usually, the coupling of a system with its environment results in a dissipation process that washes out the quantum effects, but the environment may also play exactly the opposite role. Here, we show that the coupling of a BEC qubit with its local environments can be exploited to establish dissipative state engineering and dissipative quantum computation. Also, we discuss how to generate entanglement and transfer it using such macroscopic BEC qubits. Generally, the couplings can be manipulated such that the system is driven to a desired steady state. We demonstrate that the steady state of a BEC qubit just depends on the tunneling strength between its two modes and the features of the local environments. By preparing the proper physical conditions and adjusting the parameters involved in the model, it can be shown that the steady state of the system may coincide with its initial state. Also, the interaction between the BEC qubits and local environments can be engineered to provide physically controlled single- and two-qubit operations, which are necessary for performing dissipative universal quantum computation. With the prosperous development of quantum computing, such a system can be employed to implement quantum computers based on non-unitary operations.

Scalable Measures of Magic Resource for Quantum Computers

Nonstabilizerness or magic resource characterizes the amount of non-Clifford operations needed to prepare quantum states. It is a crucial resource for quantum computing and a necessary condition for quantum advantage. However, quantifying magic resource beyond a few qubits has been a major challenge. Here, we introduce efficient measures of magic resource for pure quantum states with a sampling cost that is independent of the number of qubits. Our method uses Bell measurements over two copies of a state, which we implement in experiment together with a cost-free error-mitigation scheme. We show the transition of classically simulable stabilizer states into intractable quantum states on the IonQ quantum computer. For applications, we efficiently distinguish stabilizer and nonstabilizer states with low measurement cost even in the presence of experimental noise. Further, we propose a variational quantum algorithm to maximize our measure via the shift rule. Our algorithm can be free of barren plateaus even for highly expressible variational circuits. Finally, we experimentally demonstrate a Bell-measurement protocol for the stabilizer Rényi entropy as well as the Wallach-Meyer entanglement measure. Our results pave the way to understanding the nonclassical power of quantum computers, quantum simulators, and quantum many-body systems.6 MoreReceived 27 April 2022Accepted 6 December 2022DOI:https://doi.org/10.1103/PRXQuantum.4.010301Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum algorithmsQuantum benchmarkingQuantum computationQuantum correlations in quantum informationQuantum information theoryQuantum Information

Improving the performance of quantum approximate optimization for preparing non-trivial quantum states without translational symmetry

The variational preparation of complex quantum states using the quantum approximate optimization algorithm (QAOA) is of fundamental interest, and becomes a promising application of quantum computers. Here, we systematically study the performance of QAOA for preparing ground states of target Hamiltonians near the critical points of their quantum phase transitions, and generating Greenberger–Horne–Zeilinger (GHZ) states. We reveal that the performance of QAOA is related to the translational invariance of the target Hamiltonian: without the translational symmetry, for instance due to the open boundary condition (OBC) or randomness in the system, the QAOA becomes less efficient. We then propose a generalized QAOA assisted by the parameterized resource Hamiltonian (PRH-QAOA), to achieve a better performance. In addition, based on the PRH-QAOA, we design a low-depth quantum circuit beyond one-dimensional geometry, to generate GHZ states with perfect fidelity. The experimental realization of the proposed scheme for generating GHZ states on Rydberg-dressed atoms is discussed. Our work paves the way for performing QAOA on programmable quantum processors without translational symmetry, especially for recently developed two-dimensional quantum processors with OBC.

DeepQPrep: Neural Network Augmented Search for Quantum State Preparation

DeepQPrep: Neural Network Augmented Search for Quantum State Preparation

Simulation of hyperfine-rotational spectrum of electromagnetic dipole transition rotation of BrF molecules

The transition dipole of the hyperfine-rotation spectrum of <i>J</i> = 1←0 within the vibronic ground (X<sup>1</sup>Σ, <i>v</i> = 0) state of BrF molecule is derived, and thus, the transition selection rules are summarized as follows: Δ<i>J =</i> ±1; Δ<i>F</i><sub>1</sub> = 0, ±1 and Δ<i>F </i>= 0, ±1, and those of Δ<i>F</i><sub>1</sub> = Δ<i>F</i> are intense while those of Δ<i>F</i><sub>1</sub> ≠ Δ<i>F</i> are weak. Some spectral lines result from both the electric dipole transition and nuclear magnetic dipole transition due to perturbations, however, the magnetic dipole transition only contributes about one-billionth in the spectral intensity. The spectral linewidth is determined to be about 18 kHz by calculating the spectral transition probability. The obtained spectral linewidth and relative intensities are consistent with the experimental results. Additionally, the hyperfine-rotation spectral positions are determined by diagonalizing the Hamiltonian matrix in the basis of |<i>JI</i><sub>1</sub><i>F</i><sub>1</sub><i>I</i><sub>2</sub><i>F</i><inline-formula><tex-math id="Z-20230210104836">\begin{document}$\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221957_Z-20230210104836.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221957_Z-20230210104836.png"/></alternatives></inline-formula>, which is also in good agreement with the experiments within 10<sup>–8</sup> (one-fiftieth of the spectral line width). Hence, the microwave hyperfine-rotation spectrum is simulated. In addition, we find that the nuclear spin-spin interaction not only slightly shifts the hyperfine-rotation spectral positions but also changes the sequence of the spectra. As to those unavailable constants of molecules, the fairly precise molecular constants can be achieved by quantum chemical calculation, say, by employing MOLPRO program, and then the simulated spectra can guide the spectral assignment. Besides the guidance of spectral assignment, our results are also helpful for other relevant applications such as in absolute single quantum state preparation.

Markov chain Monte Carlo enhanced variational quantum algorithms

Variational quantum algorithms have the potential for significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these algorithms is generally nonconvex, leading the algorithms to converge to local, rather than global, minima and the production of suboptimal solutions. In this work, we introduce a variational quantum algorithm that couples classical Markov chain Monte Carlo techniques with variational quantum algorithms, allowing the former to provably converge to global minima and thus assure solution quality. Due to the generality of our approach, it is suitable for a myriad of quantum minimization problems, including optimization and quantum state preparation. Specifically, we devise a Metropolis–Hastings method that is suitable for variational quantum devices and use it, in conjunction with quantum optimization, to construct quantum ensembles that converge to Gibbs states. These performance guarantees are derived from the ergodicity of our algorithm’s state space and enable us to place analytic bounds on its time-complexity. We demonstrate both the effectiveness of our technique and the validity of our analysis through quantum circuit simulations for MaxCut instances, solving these problems deterministically and with perfect accuracy, as well as large-scale quantum Ising and transverse field spin models of up to 50 qubits. Our technique stands to broadly enrich the field of variational quantum algorithms, improving and guaranteeing the performance of these promising, yet often heuristic, methods.

Security of Bennett–Brassard 1984 Quantum-Key Distribution under a Collective-Rotation Noise Channel

The security analysis of the Ekert 1991 (E91), Bennett 1992 (B92), six-state protocol, Scarani–Acín–Ribordy–Gisin 2004 (SARG04) quantum key distribution (QKD) protocols, and their variants have been studied in the presence of collective-rotation noise channels. However, besides the Bennett–Brassard 1984 (BB84) being the first proposed, extensively studied, and essential protocol, its security proof under collective-rotation noise is still missing. Thus, we aim to close this gap in the literature. Consequently, we investigate how collective-rotation noise channels affect the security of the BB84 protocol. Mainly, we study scenarios where the eavesdropper, Eve, conducts an intercept-resend attack on the transmitted photons sent via a quantum communication channel shared by Alice and Bob. Notably, we distinguish the impact of collective-rotation noise and that of the eavesdropper. To achieve this, we provide rigorous, yet straightforward numerical calculations. First, we derive a model for the collective-rotation noise for the BB84 protocol and parametrize the mutual information shared between Alice and Eve. This is followed by deriving the quantum bit error rate (QBER) for two intercept-resend attack scenarios. In particular, we demonstrate that, for small rotation angles, one can extract a secure secret key under a collective-rotation noise channel when there is no eavesdropping. We observe that noise induced by rotation of 0.35 radians of the prepared quantum state results in a QBER of 11%, which corresponds to the lower bound on the tolerable error rate for the BB84 QKD protocol against general attacks. Moreover, a rotational angle of 0.53 radians yields a 25% QBER, which corresponds to the error rate bound due to the intercept-resend attack. Finally, we conclude that the BB84 protocol is robust against intercept-resend attacks on collective-rotation noise channels when the rotation angle is varied arbitrarily within particular bounds.

Ultra-high-Q nanomechanical resonators for force sensing

Nanomechanical resonators with ultra-high quality factors have become a central element in fundamental research, enabling measurements below the standard quantum limit and the preparation of long-lived quantum states. Here, I propose that such resonators will allow the detection of electron and nuclear spins with high spatial resolution, paving the way to future nanoscale magnetic resonance imaging instruments. The article lists the challenges that must be overcome before this vision can become reality, and indicates potential solutions.

Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications.

Quantum state preparation is an important subroutine for quantum computing. We show that any n-qubit quantum state can be prepared with a Θ(n)-depth circuit using only single- and two-qubit gates, although with a cost of an exponential amount of ancillary qubits. On the other hand, for sparse quantum states with d⩾2 nonzero entries, we can reduce the circuit depth to Θ(log(nd)) with O(ndlogd) ancillary qubits. The algorithm for sparse states is exponentially faster than best-known results and the number of ancillary qubits is nearly optimal and only increases polynomially with the system size. We discuss applications of the results in different quantum computing tasks, such as Hamiltonian simulation, solving linear systems of equations, and realizing quantum random access memories, and find cases with exponential reductions of the circuit depth for all these three tasks. In particular, using our algorithm, we find a family of linear system solving problems enjoying exponential speedups, even compared to the best-known quantum and classical dequantization algorithms.

Hybrid classical-quantum machine learning based on dissipative two-qubit channels

Although the environmental effects, i.e., dissipation and decoherence seem to be the strongest adversaries in the quantum information realm, here, we address how dissipation can be harnessed for quantum state preparation and universal quantum computation. In this line, we propose a realistic scheme for hybrid classical-quantum neural networks based on dissipative two-qubit channels. In particular, we design a variational quantum circuit consisting of a set of universal quantum gates. We encode classical information in the initial states of a two-qubit system interacting with a global environment. This composite system plays the role of a dissipative quantum channel (DQC). A pooling layer concatenates the output states of the DQCs resulting in the outcome of the circuit. Both the DCQs and the pooling layer provide superposition and entanglement which are the key ingredients of any universal quantum computation protocol. Finally, we investigate the capability and adaptability of this model by doing some machine learning tasks. It is reasonable to postulate that a quantum computer based on DQCs may outperform a classical computer because, in contrast to the latter, the former is capable of producing atypical patterns through non-classical phenomena.

A Quantum Algorithm for Pricing Asian Options on Valuation Trees

We develop a novel quantum algorithm for approximating the price of a discrete floating-strike Asian option based on an underlying valuation tree. The paths of the tree are encoded in bit-representation into a qubit register, where quantum state preparation is used to load the corresponding distribution onto the states. We implement the expectation value of the option pricing formula as a composition of the price probabilities, the payout and an indicator function, mapping their respective values to amplitudes of additional qubits. Thus, the underlying no longer has to be discretized into the same bit values for different times, resulting in smaller quantum circuits. The algorithm may be used with quantum amplitude estimation, enabling a quadratic speed-up over classical Monte Carlo methods.

Coherent state representation of squeezing operator and its applications

In a previous paper Zhan et al. (2022) proposed the coherent state representation for linear operator, which shows a beautiful theoretical value. Inspired by the work, we further extend it to the nonlinear case, including single- and two-mode squeezing process. Based on squeezing operators’ transformation relation, we introduce their coherent state representations and derive their normal ordering forms by using the technique of integration within product of operator. As applications, we examine some operators’s normal ordering forms and show the entanglement property of prepared quantum states via the Schmidt decomposition. In particular, we further consider two cascaded two-mode squeezing operators, in which a generalized SU(1,1) interferometer is involved. In addition, the application of two-mode squeezing operator followed by photon-subtraction to generate non-Gaussian entangled states in quantum teleportation is discussed. Our results will be useful in preparation of quantum states and quantum metrology.

Optimization of variational-quantum-eigensolver measurement by partitioning Pauli operators using multiqubit Clifford gates on noisy intermediate-scale quantum hardware

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 Pauli operators allows for fewer measurements and an overall speedup of the measurement process. Using results from coloring random graphs, we give evidence for an upper bound on the expected minimum number of simultaneously measurable parts necessary to partition a set of Pauli operators. By expanding our gate set to allow multiqubit Clifford gates before measurement, we were able to cut down the number of measurements considerably compared to previous approaches. We conjecture that this improvement is, in general, linear with respect to the lengths of the Pauli operators. We conclude by demonstrating the feasibility of this approach by implementing the variational quantum eigensolver on the Aspen-4-4Q-A quantum processor unit. In doing so, we calculate the ground-state energies of ${\mathrm{H}}_{2}$ using fewer measurements than is possible with single-qubit gates with no statistically significant difference in accuracy.

Improved Iterative Quantum Algorithm for Ground‐State Preparation

AbstractFinding the ground state of a Hamiltonian system is of great significance in many‐body quantum physics and quantum chemistry. An improved iterative quantum algorithm to prepare the ground state of a Hamiltonian is proposed. The crucial point is to optimize a cost function on the state space via the quantum gradient descent (QGD) implemented on quantum devices. Practical guideline on the selection of the learning rate in QGD are provided by finding a fundamental upper bound and establishing a relationship between the algorithm and the first‐order approximation of the imaginary time evolution. Furthermore, a variational quantum state preparation method is adapted as a subroutine to generate an ancillary state by utilizing only polylogarithmic quantum resources. The performance of the algorithm is demonstrated by numerical calculations of the deuteron molecule and Heisenberg model without and with noises. Compared with the existing algorithms, the approach has advantages including the higher success probability at each iteration, the measurement precision‐independent sampling complexity, the lower gate complexity, and only quantum resources are required when the ancillary state is well prepared.