Fidelity Of State Research Articles

Benchmarking Adaptive Variational Quantum Eigensolvers.

By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H2, NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.

Verification of a resetting protocol for an uncontrolled superconducting qubit

Quantum resetting protocols allow a quantum system to be sent to a state in the past by making it interact with quantum probes when neither the free evolution of the system nor the interaction is controlled. We experimentally verify the simplest non-trivial case of a quantum resetting protocol, known as the {{mathcal{W}}}_{4} protocol, with five superconducting qubits, testing it with different types of free evolutions and target–probe interactions. After projection, we obtained a reset state fidelity as high as 0.951, and the process fidelity was found to be 0.792. We also implemented 100 randomly chosen interactions and demonstrated an average success probability of 0.323 for left|1rightrangle and 0.292 for left|-rightrangle, and experimentally confirmed the nonzero probability of success for unknown interactions; the numerical simulated values are about 0.3. Our experiment shows that the simplest quantum resetting protocol can be implemented with current technologies, making such protocols a valuable tool in the eternal fight against unwanted evolution in quantum systems.

Rapid biexciton-state preparation in a quantum dot using on-off pulse sequences

We consider the problem of pulsed biexciton preparation in a quantum dot and show that a pulse-sequence with a simple on-off-on modulation can achieve complete preparation of the target state faster than the commonly used constant and hyperbolic secant pulses. The durations of the pulses composing the sequence are obtained from the solution of a transcendental equation. Furthermore, using numerical optimal control, we demonstrate that for a wide range of values of the maximum pulse amplitude, the proposed pulse-sequence prepares the biexciton state in the numerically obtained minimum time, for the specific system under consideration. We finally show with numerical simulations that, even in the presence of dissipation and dephasing, high levels of biexciton state fidelity can be generated in short times.

Cloning of Quantum Entanglement.

Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement-a highly nonclassical correlation-remained unexplored. Based on a multiphoton linear optics platform, we demonstrate quantum cloning of two-photon entangled states for the first time. Remarkably our results show that one maximally entangled photon pair can be broadcast into two entangled pairs, both with state fidelities above 50%. Our results are a key step towards cloning of complex quantum systems, and are likely to provide new insights into quantum entanglement.

Completely positive quantum trajectories with applications to quantum state smoothing

Here, we are concerned with comparing estimation schemes for the quantum state under continuous measurement (quantum trajectories), namely quantum state filtering and, as introduced by us [Phys. Rev. Lett. 115, 180407 (2015)], quantum state smoothing. Unfortunately, the cumulative errors in the most typical simulations of quantum trajectories with a total time of simulation $T$ can reach orders of $T \Delta t$. Moreover, these errors may correspond to deviations from valid quantum evolution as described by a completely positive map. Here we introduce a higher-order method that reduces the cumulative errors in the complete positivity of the evolution to of order $T\Delta t^2$, whether for linear (unnormalised) or nonlinear (normalised) quantum trajectories. Our method also guarantees that the discrepancy in the average evolution between different detection methods (different `unravellings', such as quantum jumps or quantum diffusion) is similarly small. This equivalence is essential for comparing quantum state filtering to quantum state smoothing, as the latter assumes that all irreversible evolution is unravelled, although the estimator only has direct knowledge of some records. In particular, here we compare, for the first time, the average difference between filtering and smoothing conditioned on an event of which the estimator lacks direct knowledge: a photon detection within a certain time window. We find that the smoothed state is actually {\em less pure}, both before and after the time of the jump. Similarly, the fidelity of the smoothed state with the `true' (maximal knowledge) state is also lower than that of the filtered state before the jump. However, after the jump, the fidelity of the smoothed state is higher.

Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase damping and amplitude damping noise channels

In this work, we studied the relaxation dynamics of coherences of different order present in a system of two coupled nuclear spins. We used a previously designed model for intrinsic noise present in such systems which considers the Lindblad master equation for Markovian relaxation. We experimentally created zero-, single- and double- quantum coherences in several two-spin systems and performed a complete state tomography and computed state fidelity. We experimentally measured the decay of zero- and double- quantum coherences in these systems. The experimental data fitted well to a model that considers the main noise channels to be a correlated phase damping channel acting simultaneously on both spins in conjunction with a generalized amplitude damping channel acting independently on both spins. The differential relaxation of multiple-quantum coherences can be ascribed to the action of a correlated phase damping channel acting simultaneously on both the spins.

Effects of finite momentum width on the reversal dynamics in a BEC based atom optics δ-kicked rotor

This experimental work demonstrates the importance of finite-width effects in the evolution of a quantum system, where the results deviate considerably from the plane wave approximation even for an initial state with a very narrow momentum width i.e a Bose–Einstein condensate. The system under consideration is an atom optics δ-kicked rotor for which a fidelity based measurement has been proposed to possess a rapid scaling of sensitivity (N −3) with pulse number N. Although attractive, we demonstrate that this scaling does not hold in the regime where the momentum selectivity of the pulse sequence becomes significantly smaller than the momentum width of the initial state. Additionally, the momentum distribution post kicking shows a lattice-phase dependent intra-order and inter-order asymmetry in the diffracted orders. The intra-order asymmetry, in which no net momentum current is present, is a previously unreported type of effect. For a two pulse case, the inter-order asymmetry signal is found to be about five times more sensitive to the resonance than the initial state fidelity. Both of these asymmetries provide a zero-crossing signal which can be used to diagnose any undesirable lattice phase offset at resonant and off-resonant pulse periods.

Generation of Schrödinger-cat states through photon-assisted Landau-Zener-Stückelberg interferometry

Schr\"odinger cat states are useful for many applications, ranging from quantum information processing to high-precision measurements. In this paper we propose a conceptually new method for creating such cat states, based on photon-assisted Landau-Zener-St\"uckelberg interferometry in a hybrid system consisting of a qubit coupled to a photon cavity. We show that by initializing the qubit in one of its basis states, performing three consecutive sweeps of the qubit energy splitting across the 1-photon resonance, and finally projecting the qubit to the same basis state, the parity of the photon field can be purified to very high degree; when the initial photon state is a coherent state, the final state will then be very close to a Schr\"odinger cat state. We present numerical simulations that confirm that our protocol could work with high fidelity ($\sim 0.99$) for coherent states of reasonable size ($|\alpha|^2 \sim 10$). Furthermore, we suggest that our protocol can also be used to transfer quantum information between the qubit and a superposition of orthogonal cat states in the cavity.

Controlling the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environments* *Project supported by the National Natural Science Foundation of China (Grant Nos. 12064012 and 11374096).

The uncertainty principle is a crucial aspect of quantum mechanics. It has been shown that the uncertainty principle can be tightened by quantum discord and classical correlation in the presence of quantum memory. We investigate the control of the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environment. Our results show that the entropic uncertainty of an observed system can be reduced and the quantum discord between the observed system and the quantum memory system can be enhanced in the steady state of the system by adding an dissipative ancilla. Particularly, via preparing the state of the system to the highest excited state with hight fidelity, the entropic uncertainty can be reduced markedly and the quantum discord can be enhanced obviously. We explain these results using the definition of state fidelity. Furthermore, we present an effective strategy to further reduce the the entropic uncertainty and to enhance the the quantum discord via quantum-jump-based feedback control. Therefore, our results may be of importance in the context of quantum information technologies.

The influence of imprecise quantum measurement on remote state preparation protocol

In this paper, the influence of imprecise quantum measurement on remote state preparation scheme is investigated. By analyzing the measurement parameters and corresponding errors, we obtain the evolution of output state in the process of remote state preparation. In terms of the fidelity of initial state and output state, the influence of imprecise quantum measurement is discussed. The results of this paper have the reference value for the selection of measurement basis when the quantum measurement on remote state preparation is imprecise.

Qubit-environment negativity versus fidelity of conditional environmental states for a nitrogen-vacancy-center spin qubit interacting with a nuclear environment

We study the evolution of qubit-environment entanglement, quantified using Negativity, for NV-center spin qubits interacting with an environment of $^{13}$C isotope partially polarized nuclear spins in the diamond lattice. We compare it with the evolution of the Fidelity of environmental states conditional on the pointer states of the qubit, which can serve as a tool to distinguish between entangling and non-entangling decoherence in pure-dephasing scenarios. The two quantities show remarkable agreement during the evolution in a wide range of system parameters, leading to the conclusion that the amount of entanglement generated between the qubit and the environment is proportional to the trace that the joint evolution leaves in the environment.

High-Fidelity Two-Qubit Gates Using a Microelectromechanical-System-Based Beam Steering System for Individual Qubit Addressing.

In a large scale trapped atomic ion quantum computer, high-fidelity two-qubit gates need to be extended over all qubits with individual control. We realize and characterize high-fidelity two-qubit gates in a system with up to four ions using radial modes. The ions are individually addressed by two tightly focused beams steered using microelectromechanical system mirrors. We deduce a gate fidelity of 99.49(7)% in a two-ion chain and 99.30(6)% in a four-ion chain by applying a sequence of up to 21 two-qubit gates and measuring the final state fidelity. We characterize the residual errors and discuss methods to further improve the gate fidelity towards values that are compatible with fault-tolerant quantum computation.

Three measures of fidelity for photon states

We show that the standard method of introducing the quantum description of the electromagnetic field -- by canonical field quantization -- is not the only one. We have chosen here the relativistic quantum mechanics of the photon as the starting point. The treatment of photons as elementary particles merges smoothly with the description in terms of the quantized electromagnetic field but it also reveals some essential differences. The most striking result is the appearance of various measures of fidelity for quantum states of photons. These measures are used to characterize the localization of photons.

Quantum backflow for dissipative two-identical-particle systems

In this work, dissipative quantum backflow is studied for a superposition of two stretched Gaussian wave packets and two identical spinless particles within the Caldirola-Kanai framework. Backflow is mainly an interference process and dissipation is not able to suppress it in the first case. For two identical spinless particles, apart from interference terms, the symmetry of the wave function seems to be crucial in this dynamics. The combined properties make bosons display this effect, even for the dissipative regime but, for fermions, backflow is not exhibited in any regime, dissipative and nodissipative. The anti-symmetric character of the corresponding wave function seems to be strong enough to prevent it. For bosons, backflow is also analyzed in terms of fidelity of one-particle states which is a well-known property of two quantum states. At very small values of fidelity, this effect is not seen even for bosons.

Fully Arbitrary Control of Frequency-Bin Qubits.

Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. In this Letter, we demonstrate fully arbitrary control of frequency-bin qubits in a quantum frequency processor for the first time. We numerically establish optimal settings for multiple configurations of electro-optic phase modulators and pulse shapers, experimentally confirming near-unity mode-transformation fidelity for all fundamental rotations. Performance at the single-photon level is validated through the rotation of a single frequency-bin qubit to 41 points spread over the entire Bloch sphere, as well as tracking of the state path followed by the output of a tunable frequency beam splitter, with Bayesian tomography confirming state fidelities F_{ρ}>0.98 for all cases. Such high-fidelity transformations expand the practical potential of frequency encoding in quantum communications, offering exceptional precision and low noise in general qubit manipulation.

Adiabatic preparation of entangled, magnetically ordered states with cold bosons in optical lattices

We analyze a scheme for preparation of magnetically ordered states of two-component bosonic atoms in optical lattices. We compute the dynamics during adiabatic and optimized time-dependent ramps to produce ground states of effective spin Hamiltonians, and determine the robustness to decoherence for realistic experimental system sizes and timescales. Ramping parameters near a phase transition point in both effective spin-1/2 and spin-1 models produces entangled spin-symmetric states that have potential future applications in quantum enhanced measurement. The preparation of these states and their robustness to decoherence is quantified by computing the quantum Fisher information (QFI) of final states. We identify that the generation of useful entanglement should in general be more robust to heating than it would be implied by the state fidelity, with corresponding implications for practical applications.

Analyzing photon-count heralded entanglement generation between solid-state spin qubits by decomposing the master-equation dynamics

We analyze and compare three different schemes that can be used to generate entanglement between spin qubits in optically-active single solid-state quantum systems. Each scheme is based on first generating entanglement between the spin degree of freedom and either the photon number, the time bin, or the polarization degree of freedom of photons emitted by the systems. We compute the time evolution of the entanglement generation process by decomposing the dynamics of a Markovian master equation into a set of propagation superoperators conditioned on the cumulative detector photon count. We then use the conditional density operator solutions to compute the efficiency and fidelity of the final spin-spin entangled state while accounting for spin decoherence, optical pure dephasing, spectral diffusion, photon loss, phase errors, detector dark counts, and detector photon number resolution limitations. We find that the limit to fidelity for each scheme is restricted by the mean wavepacket overlap of photons from each source, but that these bounds are different for each scheme. We also compare the performance of each scheme as a function of the distance between spin qubits.

Generation of distributed steady entangled state between two solid-state spins

The generation of distributed entangled states among solid-state spins is key to the development of large-scale quantum networks and quantum computation. We propose a dissipative scheme for generating stable entanglement between the electron-spin states of two separated nitrogen-vacancy centers, each coupled to a microtoroidal resonator and separated in space. An optical fiber-taper waveguide links the two microtoroidal resonators. Numerical simulations show that spontaneous emission from the NV centers and the collective decay of delocalized field modes can act as effective resources to generate stationary singlet-like states without the need for initialization and precise control of the evolution of the system over time. Results indicate that the proposed scheme can reach high-fidelity and purity of states, and is resilient against small parameter fluctuations. We also discuss how the pure spin dephasing that arises from longitudinal magnetic-near-field noise affects the fidelity of the target state.

Bounding the fidelity of quantum many-body states from partial information

We formulate an algorithm to lower bound the fidelity between quantum many-body states only from partial information, such as the one accessible by few-body observables. Our method is especially tailored to permutationally invariant states, but it gives nontrivial results in all situations where this symmetry is even partial. This property makes it particularly useful for experiments with atomic ensembles, where relevant many-body states can be certified from collective measurements. As an example, we show that a $\xi^2\approx-6\;\text{dB}$ spin squeezed state of $N=100$ particles can be certified with a fidelity up to $F=0.999$, only from the measurement of its polarization and of its squeezed quadrature. Moreover, we show how to quantitatively account for both measurement noise and partial symmetry in the states, which makes our method useful in realistic experimental situations.

Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement.

An adaptive method for quantum state fidelity estimation in bipartite higher dimensional systems is established. This method employs state verifier operators which are constructed by local POVM operators and adapted to the measurement statistics in the computational basis. Employing this method, the state verifier operators that stabilize Bell-type entangled states are constructed explicitly. Together with an error operator in the computational basis, one can estimate the lower and upper bounds on the state fidelity for Bell-type entangled states in few measurement configurations. These bounds can be tighter than the fidelity bounds derived in [Bavaresco et al., Nature Physics (2018), 14, 1032–1037], if one constructs more than one local POVM measurements additional to the measurement in the computational basis.