Single Qubit Research Articles

Room Temperature Quantum Control of N‐Donor Electrons at Si/SiO2 Interface

AbstractThe manuscript theoretically discusses various important aspects for donor atom based single qubit operations in silicon (Si) quantum computer architecture at room temperature using a single nitrogen (N) deep‐donor close to the Si/SiO2 interface. Quantitative investigation of room temperature single electron shuttling between a single N‐donor atom and the interface is the focus of attention under the influence of externally applied electric and magnetic field. To apprehend the realistic experimental configurations, central cell correction along with effective mass approach is adopted throughout the study. Furthermore, a detailed discussion currently explores the significant time scales implicated in the process and their suitability for experimental purposes. Theoretical estimates are also provided for all the external fields required to successfully achieve coherent single electron shuttling and their stable maintenance at the interface as required. The results presented in this work offer practical guidance for quantum electron control using N‐donor atoms in Si at room temperature.

Cryptanalysis and improvement of efficient multiparty quantum secret sharing based on a novel structure and single qubits

In the paper (EPJ Quant. Technol. 10:29, 2023), Kuo et al. proposed a multiparty quantum secret sharing protocol based on a novel structure and single qubits. Owing to the absence of an entanglement state, the proposed protocol is more practical than other quantum secret sharing protocols which use entanglement properties. Therefore, we study the security of the proposed protocol and find there exists a security loophole in the n-party (n≥4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$n\\geq 4$\\end{document}) secret sharing case in it, that is, two dishonest agents can collude to obtain (part of) Alice’s secret without the help of the other agents. In order to overcome the security loophole, we give an improved protocol and make a security analysis for it. By calculating, the qubit efficiency of the three-party case in it is equal to 18\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\frac{1}{8}$\\end{document}, which is higher than that in Hillery et al.’s protocol (Phys. Rev. A 59:1829, 1999).

Improving the estimation of environment parameters via a two-qubit scheme

We demonstrate how using two qubits can drastically improve the estimation of environment parameters compared to using only a single qubit. The two qubits are coupled to a common harmonic oscillator environment, and the properties of the environment are imprinted upon the dynamics of the two qubits. The reduced density matrix of only one of these qubits contains a decoherence factor and an additional factor taking into account the indirect interaction induced between the qubits due to the interaction with their common environment. This additional factor can drastically improve the estimation of the environment parameters, as quantified by the quantum Fisher information. In particular, we investigate the estimation of the cutoff frequency, the coupling strength, and the temperature using our two-qubit scheme compared to simply using a single qubit. We find that the precision of the estimates can be improved by orders of magnitude.

The Gauge Picture of Quantum Dynamics

Although local Hamiltonians exhibit local time dynamics, this locality is not explicit in the Schrödinger picture in the sense that the wavefunction amplitudes do not obey a local equation of motion. We show that geometric locality can be achieved explicitly in the equations of motion by "gauging" the global unitary invariance of quantum mechanics into a local gauge invariance. That is, expectation values ⟨ψ|A|ψ⟩ are invariant under a global unitary transformation acting on the wavefunction |ψ⟩→U|ψ⟩ and operators A→UAU†, and we show that it is possible to gauge this global invariance into a local gauge invariance. To do this, we replace the wavefunction with a collection of local wavefunctions |ψJ⟩, one for each patch of space J. The collection of spatial patches is chosen to cover the space; e.g. we could choose the patches to be single qubits or nearest-neighbor sites on a lattice. Local wavefunctions associated with neighboring pairs of spatial patches I and J are related to each other by dynamical unitary transformations UIJ. The local wavefunctions are local in the sense that their dynamics are local. That is, the equations of motion for the local wavefunctions |ψJ⟩ and connections UIJ are explicitly local in space and only depend on nearby Hamiltonian terms. (The local wavefunctions are many-body wavefunctions and have the same Hilbert space dimension as the usual wavefunction.) We call this picture of quantum dynamics the gauge picture since it exhibits a local gauge invariance. The local dynamics of a single spatial patch is related to the interaction picture, where the interaction Hamiltonian consists of only nearby Hamiltonian terms. We can also generalize the explicit locality to include locality in local charge and energy densities.

Implementation of the Projective Quantum Eigensolver on a Quantum Computer.

We study the performance of our previously proposed projective quantum eigensolver (PQE) on IBM's quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H2, we find that we are able to obtain energies within 4 millihartree (2.5 kcal/mol) of the exact energy along the entire potential energy curve, with the accuracy limited by both the stochastic error and the inconsistent performance of the IBM devices. We find that an optimization algorithm using direct inversion of the iterative subspace can converge swiftly, even to excited states, but stochastic noise can prompt large parameter updates. For the 4-site transverse-field Ising model at its critical point, PQE with an appropriate application of qubit tapering can recover 99% of the correlation energy, even after discarding several parameters. The large number of CNOT gates needed for the additional parameters introduces a concomitant error that, on the IBM devices, results in a loss of accuracy despite the increased expressivity of the trial state. Error extrapolation techniques and tapering or postselection are recommended to mitigate errors in PQE hardware experiments.

Testing the accuracy of qubit rotations on a public quantum computer

We analyze the results of the test of π/2 qubit rotations on a public quantum computer provided by IBM. We measure a single qubit rotated by π/2 about a random axis, and we accumulate vast statistics of the results. The test performed on different devices shows systematic deviations from the theoretical predictions, which appear at level 10–3. Some of the differences, beyond 5 standard deviations, cannot be explained by simple corrections due to nonlinearities of pulse generations. The magnitude of the deviation is comparable with the randomized benchmarking of the gate, but we additionally observe a pronounced parametric dependence. We discuss other possible reasons for the deviations, including states beyond the single-qubit space. The deviations have a similar structure for various devices used at different times, so they can also serve as a diagnostic tool to eliminate imperfect gate implementations and a faithful description of the involved physical systems.

Exceptionally strong coupling of defect emission in hexagonal boron nitride to stacking sequences

Van der Waals structures present a unique opportunity for tailoring material interfaces and integrating photonic functionalities. By precisely manipulating the twist angle and stacking sequences, it is possible to elegantly tune and functionalize the electronic and optical properties of layered van der Waals structures. Among these materials, two-dimensional hexagonal boron nitride (hBN) stands out for its remarkable optical properties and wide band gap, making it a promising host for solid state single photon emitters at room temperature. Previous investigations have demonstrated the observation of bright single photon emission in hBN across a wide range of wavelengths. In this study, we unveil an application of van der Waals technology in modulating their spectral shapes and brightness by carefully controlling the stacking sequences and polytypes. Our theoretical analysis reveals remarkably large variations in the Huang-Rhys factors–an indicator of the interaction between a defect and its surrounding lattice–reaching up to a factor of 3.3 for the same defect in different stacking sequences. We provide insights into the underlying mechanism behind these variations, shedding light on the design principles necessary to achieve rational and precise control of defect emission. This work paves the way for enhancing defect identification and facilitating the engineering of highly efficient single photon sources and qubits using van der Waals materials.

Quantum physics cannot be captured by classical linear hidden variable theories even in the absence of entanglement

Recent experimental tests of Bell inequalities confirm that entangled quantum systems cannot be described by local classical theories but still do not answer the question whether or not quantum systems could, in principle, be modeled by linear hidden variable theories. In this paper, we study the quantum trajectories of a single qubit that experiences a sequence of repeated generalized measurements. It is shown that this system, which constitutes a hidden quantum Markov model, is more likely to produce complex time correlations than any classical hidden Markov model with two output symbols. From this, we conclude that quantum physics cannot be replaced by linear hidden variable theories. Indeed, it has already been recognized that not only entanglement but also non-classical time correlations of quantum systems with quantum feedback are a valuable resource for quantum technology applications.

Digital simulation of convex mixtures of Markovian and non-Markovian single qubit Pauli channels on NISQ devices

Quantum algorithms for simulating quantum systems provide a clear and provable advantage over classical algorithms in fault-tolerant settings. There is also interest in quantum algorithms and their implementation in Noisy Intermediate Scale Quantum (NISQ) settings. In these settings, various noise sources and errors must be accounted for when executing any experiments. Recently, NISQ devices have been verified as versatile testbeds for simulating open quantum systems and have been used to simulate simple quantum channels. Our goal is to solve the more complicated problem of simulating convex mixtures of single qubit Pauli channels on NISQ devices. We consider two specific cases: mixtures of Markovian channels that result in a non-Markovian channel (M + M = nM) and mixtures of non-Markovian channels that result in a Markovian channel (nM + nM = M). For the first case, we consider mixtures of Markovian single qubit Pauli channels; for the second case, we consider mixtures of Non-Markovian single qubit depolarising channels, which is a special case of the single qubit Pauli channel. We show that efficient circuits, which account for the topology of currently available devices and current levels of decoherence, can be constructed by heuristic approaches that reduce the number of CNOT gates used in our circuit. We also present a strategy for regularising the process matrix so that the process tomography yields a completely positive and trace-preserving (CPTP) channel.Key pointsThis work simulates the convex mixtures of single qubit Markovian and non-Markovian quantum channels on NISQ devices provided by the IMBQE.The circuits used to implement the channels take into account the topolgy of the quantum device used as well as the number of CNOT gates used.We present a strategy for regularising the process matrix to ensure the quantum process tomography yields a CPTP channel. Something that is not correctly implemented in Qiskit.A method is outlined for finding mixtures of non-Markovian depolarising channels that yield a Markovian depolarising channel. It is also shown that, one cannot convexly mix two Markovian depolarising channels that leads to a non-Markovian depolarising channel.

Efficient bosonic nonlinear phase gates

Continuous-variable (CV) quantum information processing harnesses versatile experimental tools that leverage the power of infinite-dimensional oscillators controlled by a single qubit. Increasingly available elementary Rabi gates have been proposed as a resource for implementing universal CV gates, but the requirement of many weak, non-commuting gates is a bottleneck in scaling up such an approach. In this study, we propose a resource-efficient technique using Fourier expansion to implement arbitrary non-linear phase gates in a single oscillator. This method reduces the number of sequentially required gates exponentially. These gates represented by cubic, quartic, and other arbitrary nonlinear potentials have applications in CV quantum information processing with infinite-dimensional oscillators controlled by a single qubit. Our method outperforms previous approaches and enables the experimental realization of a wide range of applications, including the development of bosonic quantum sensors, simulations, and computation using trapped ions and superconducting circuits.

Analogue Quantum Simulation with Fixed-Frequency Transmon Qubits

We experimentally assess the suitability of transmon qubits with fixed frequencies and fixed interactions for the realization of analogue quantum simulations of spin systems. We test a set of necessary criteria for this goal on a commercial quantum processor using full quantum process tomography and more efficient Hamiltonian tomography. Significant single qubit errors at low amplitudes are identified as a limiting factor preventing the realization of analogue simulations on currently available devices. We additionally find spurious dynamics in the absence of drive pulses, which we identify with coherent coupling between the qubit and a low dimensional environment. With moderate improvements, analogue simulation of a rich family of time-dependent many-body spin Hamiltonians may be possible.

Quantum homogenization in non-Markovian collisional model

Collisional models are a category of microscopic framework designed to study open quantum systems. The framework involves a system sequentially interacting with a bath comprised of identically prepared units. In this regard, quantum homogenization is a process where the system state approaches the identically prepared state of bath unit in the asymptotic limit. Here, we study the homogenization process for a single qubit in the non-Markovian collisional model framework generated via additional bath-bath interaction. With partial swap operation as both system-bath and bath-bath unitary, we numerically demonstrate that homogenization is achieved irrespective of the initial states of the system or bath units. This is reminiscent of the Markovian scenario, where partial swap is the unique operation for a universal quantum homogenizer. On the other hand, we observe that the rate of homogenization is slower than its Markovian counter part. Interestingly, a different choice of bath-bath unitary speeds up the homogenization process but loses the universality, being dependent on the initial states of the bath units.

Continuously monitored quantum systems beyond Lindblad dynamics

The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterizes expectation values, the entire ensemble of stochastic trajectories goes beyond simple linear observables, keeping a more attentive description of the entire dynamics. Here we go beyond the Lindblad dynamics and study the probability distribution of the expectation value of a given observable over the possible quantum trajectories. The measurements are applied to the entire system, having the effect of projecting the system into a product state. We develop an analytical tool to evaluate this probability distribution at any time t. We illustrate our approach by analyzing two paradigmatic examples: a single qubit subjected to magnetization measurements, and a free hopping particle subjected to position measurements.

Giant optical polarisation rotations induced by a single quantum dot spin

In the framework of optical quantum computing and communications, a major objective consists in building receiving nodes implementing conditional operations on incoming photons, using a single stationary qubit. In particular, the quest for scalable nodes motivated the development of cavity-enhanced spin-photon interfaces with solid-state emitters. An important challenge remains, however, to produce a stable, controllable, spin-dependent photon state, in a deterministic way. Here we use an electrically-contacted pillar-based cavity, embedding a single InGaAs quantum dot, to demonstrate giant polarisation rotations induced on reflected photons by a single electron spin. A complete tomography approach is introduced to extrapolate the output polarisation Stokes vector, conditioned by a specific spin state, in presence of spin and charge fluctuations. We experimentally approach polarisation states conditionally rotated by π2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{\\pi }{2}$$\\end{document}, π, and −π2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\\frac{\\pi }{2}$$\\end{document} in the Poincaré sphere with extrapolated fidelities of (97 ± 1) %, (84 ± 7) %, and (90 ± 8) %, respectively. We find that an enhanced light-matter coupling, together with limited cavity birefringence and reduced spectral fluctuations, allow targeting most conditional rotations in the Poincaré sphere, with a control both in longitude and latitude. Such polarisation control may prove crucial to adapt spin-photon interfaces to various configurations and protocols for quantum information.

Superconducting microwave cavities and qubits for quantum information systems

Superconducting microwave cavities featuring ultrahigh Q-factors, which measure the efficiency of energy storage in relation to energy loss in a system, are revolutionizing quantum computing by providing long coherence times exceeding 1 ms, crucial for the development of scalable multi-qubit quantum systems with low error rates. In this work, we provide an in-depth analysis of recent advances in ultrahigh Q-factor cavities, integration of Josephson junction-based qubits, and bosonic-encoded qubits in 3D cavities. We examine the sources of quantum state dephasing caused by damping and noise mechanisms in cavities and qubits, highlighting the critical challenges that need to be addressed to achieve even higher coherence times. We critically survey the latest progress made in implementing single 3D qubits using superconducting materials, normal metals, and multi-qubit and multi-state quantum systems. Our work sheds light on the promising future of this research area, including novel materials for cavities and qubits, modes with nontrivial topological properties, error correction techniques for bosonic qubits, and new light–matter interaction effects.

Time–Energy Uncertainty Relation in Nonrelativistic Quantum Mechanics

The time–energy uncertainty relation in nonrelativistic quantum mechanics has been intensely debated with regard to its formal derivation, validity, and physical meaning. Here, we analyze two formal relations proposed by Mandelstam and Tamm and by Margolus and Levitin and evaluate their validity using a minimal quantum toy model composed of a single qubit inside an external magnetic field. We show that the ℓ1 norm of energy coherence C is invariant with respect to the unitary evolution of the quantum state. Thus, the ℓ1 norm of energy coherence C of an initial quantum state is useful for the classification of the ability of quantum observables to change in time or the ability of the quantum state to evolve into an orthogonal state. In the single-qubit toy model, for quantum states with the submaximal ℓ1 norm of energy coherence, C<1, the Mandelstam–Tamm and Margolus–Levitin relations generate instances of infinite “time uncertainty” that is devoid of physical meaning. Only for quantum states with the maximal ℓ1 norm of energy coherence, C=1, the Mandelstam–Tamm and Margolus–Levitin relations avoid infinite “time uncertainty”, but they both reduce to a strict equality that expresses the Einstein–Planck relation between energy and frequency. The presented results elucidate the fact that the time in the Schrödinger equation is a scalar variable that commutes with the quantum Hamiltonian and is not subject to statistical variance.

Accelerated Adiabatic Passage of a Single Electron Spin Qubit in Quantum Dots.

Adiabatic processes can keep the quantum system in its instantaneous eigenstate, which is robust to noises and dissipation. However, it is limited by sufficiently slow evolution. Here, we experimentally demonstrate the transitionless quantum driving (TLQD) of the shortcuts to adiabaticity in gate-defined semiconductor quantum dots (QDs) to greatly accelerate the conventional adiabatic passage for the first time. For a given efficiency of quantum state transfer, the acceleration can be more than twofold. The dynamic properties also prove that the TLQD can guarantee fast and high-fidelity quantum state transfer. In order to compensate for the diabatic errors caused by dephasing noises, the modified TLQD is proposed and demonstrated in experiment by enlarging the width of the counterdiabatic drivings. The benchmarking shows that the state transfer fidelity of 97.8% can be achieved. This work will greatly promote researches and applications about quantum simulations and adiabatic quantum computation based on the gate-defined QDs.

Highly optimized quantum circuits synthesized via data-flow engines

The formulation of quantum programs in terms of the fewest number of gate operations is crucial to retrieve meaningful results from the noisy quantum processors accessible these days. In this work, we demonstrate a use-case for Field Programmable Gate Array (FPGA) based data-flow engines (DFEs) to scale up variational quantum compilers to synthesize circuits up to 9-qubit programs. This gate decomposer utilizes a newly developed DFE quantum computer simulator that is designed to simulate arbitrary quantum circuit consisting of single qubit rotations and controlled two-qubit gates on FPGA chips. In our benchmark with the QISKIT package, the depth of the circuits produced by the SQUANDER package (with the DFE accelerator support) were less by 97% on average, while the fidelity of the circuits was still close to unity up to an error of ∼10−4.

Quantum speed limit time, non-Markovianity and quantum phase transition in extended [formula omitted] spin chain with Dzyaloshinsky–Moriya interaction

The effects of Dzyaloshinsky–Moriya (DM) interaction on quantum speed limit time (QSLT) of a single qubit and non-Markovianity of a coupled driven extended XY spin chain are investigated. The known quantum critical points of the model are left unaffected when DM interaction points in the direction of applied field. Anti-parallel DM interaction to the magnetic field leads to a new critical point of the model whose position is a function of the strength of the three-site interaction. Overall, the dynamics of the two quantities varies differently in a given phase of the model from point to point in the parameter space. Our findings also show that the anti-parallel DM interaction results in fast quantum evolution which might be beneficial for certain quantum computation purposes.

Structure design and logical CNOT implementation of multi-logical-qubits surface code

As its parallel processing ability, quantum computing has an exponential acceleration over classical computing. However, quantum systems are fragile and susceptible to noise. Quantum error correction code is an effective means to overcome quantum noise. Quantum surface codes are topologically stable subcodes that have great potential for large-scale fault-tolerant quantum computing because of their structural nearest neighbor characteristics and high fault-tolerance thresholds. The existing boundary-based surface codes can encode one logical qubit. This paper mainly studies how to implement multi-logical-qubits encoding based on the boundary, including designing the structure of the surface code, finding out the corresponding stabilizers and logical operations according to the structure, and further designing the coding circuit based on the stabilizers. After research on the single qubit CNOT implementation principle based on measurement and correcting and the logic CNOT implementation based on fusion and segmentation, we further optimized implementation scheme of the logic CNOT implementation based on fusion and segmentation. The scheme is extended to the designed multi-logical-qubits surface code to realize the CNOT operation between the multi-logical-qubits surface codes, and the correctness of the quantum circuit is verified by simulation. The multi-logical-qubits surface code designed in this paper overcomes the disadvantage that the single-logical-qubit surface code can not be densely embedded in the quantum chip, improves the length of some logical operations, and increases the fault tolerance ability. The idea of joint measurement reduces the requirement for ancilla qubits and reduces the demand for quantum resources in the implementation process.