Table of contents

Dimensionality reduction (DR) techniques play an extremely critical role in the data mining and pattern recognition field. However, most DR approaches involve large-scale matrix computations, which cause too high running complexity to implement in the big data scenario efficiently. The recent developments in quantum information processing provide a novel path to alleviate this problem, where a potential quantum acceleration can be obtained comparing with the classical counterpart. Nevertheless, existing proposals for quantum DR methods faced the common dilemma of the nonlinear generalization owing to the intrinsic linear limitation of quantum computation. In this paper, an architecture to simulate the arbitrary nonlinear kernels on a universal quantum computer is illustrated and further propose the quantum kernel principal component analysis (QKPCA) algorithm. The key idea is employing the truncated Taylor expansion to approximate the arbitrary nonlinear kernel within the fixed error and then constructing the corresponding Hamiltonian simulation for the quantum phase estimation algorithm. It is demonstrated theoretically that the QKPCA is qualified for the nonlinear DR task while the exponential speedup is also maintained. In addition, this research has the potential ability to develop other quantum DR approaches and existing linear quantum machine learning models.

In Penning traps electromagnetic forces are used to confine charged particles under well-controlled conditions for virtually unlimited time. Sensitive detection methods have been developed to allow observation of single stored ions. Various cooling methods can be employed to reduce the energy of the trapped particle to nearly at rest. In this review we summarize how highly charged ions (HCIs) offer unique possibilities for precision measurements in Penning traps. Precision atomic and nuclear masses as well as magnetic moments of bound electrons allow among others to determine fundamental constants like the mass of the electron or to perform stringent tests of fundamental interactions like bound-state quantum electrodynamics. Recent results and future perspectives in high-precision Penning-trap spectroscopy with HCIs will be discussed.

We present t|ket⟩, a quantum software development platform produced by Cambridge Quantum Computing Ltd. The heart of t|ket⟩ is a language-agnostic optimising compiler designed to generate code for a variety of NISQ devices, which has several features designed to minimise the influence of device error. The compiler has been extensively benchmarked and outperforms most competitors in terms of circuit optimisation and qubit routing.

For variational algorithms on the near term quantum computing hardware, it is highly desirable to use very accurate ansatze with low implementation cost. Recent studies have shown that the antisymmetrized geminal power (AGP) wavefunction can be an excellent starting point for ansatze describing systems with strong pairing correlations, as those occurring in superconductors. In this work, we show how AGP can be efficiently implemented on a quantum computer with circuit depth, number of CNOTs, and number of measurements being linear in system size. Using AGP as the initial reference, we propose and implement a unitary correlator on AGP and benchmark it on the ground state of the pairing Hamiltonian. The results show highly accurate ground state energies in all correlation regimes of this model Hamiltonian.

Some new physics models of quantum gravity or dark matter predict drifts or oscillations of the fundamental constants. A relatively simple model relates molecular vibrations to the proton-to-electron mass ratio μ. Many vibrational transitions are at optical frequencies with prospects for use as highly accurate optical clocks. We give a brief summary of new physics models that lead to changes in μ and the current limits on drifts and oscillation amplitudes. After an overview of laboratory procedures, we give examples of molecules with experiments currently in development or underway. These experiments' projected systematic and statistical uncertainties make them leading candidates in next-generation searches for time-variation of μ.

Measurements of the electron's electric dipole moment (eEDM) are demanding tests of physics beyond the standard model. We describe how ultracold YbF molecules could be used to improve the precision of eEDM measurements by two to three orders of magnitude. Using numerical simulations, we show how the combination of magnetic focussing, two-dimensional transverse laser cooling, and frequency-chirped laser slowing, can produce an intense, slow, highly-collimated molecular beam. We show how to make a magneto-optical trap of YbF molecules and how the molecules could be loaded into an optical lattice. eEDM measurements could be made using the slow molecular beam or using molecules trapped in the lattice. We estimate the statistical sensitivity that could be reached in each case and consider how sources of noise can be reduced so that the shot-noise limit of sensitivity can be reached. We also consider systematic effects due to magnetic fields and vector light shifts and how they could be controlled.

Simulation of the dynamics of quantum materials is emerging as a promising scientific application for noisy intermediate-scale quantum (NISQ) computers. Due to their high gate-error rates and short decoherence times, however, NISQ computers can only produce high-fidelity results for those quantum circuits smaller than some given circuit size. Dynamic simulations, therefore, pose a challenge as current algorithms produce circuits that grow in size with each subsequent time-step of the simulation. This underscores the crucial role of quantum circuit compilers to produce executable quantum circuits of minimal size, thereby maximizing the range of physical phenomena that can be studied within the NISQ fidelity budget. Here, we present two domain-specific (DS) quantum circuit compilers for the Rigetti and IBM quantum computers, specifically designed to compile circuits simulating dynamics under a special class of time-dependent Hamiltonians. The compilers outperform state-of-the-art general-purpose compilers in terms of circuit size reduction by around 25%–30% as well as wall-clock compilation time by around 40% (dependent on system size and simulation time-step). Drawing on heuristic techniques commonly used in artificial intelligence, both compilers scale well with simulation time-step and system size. Code for both compilers is open-source and packaged into a full-stack quantum simulation software with tutorials included for ease of use for future researchers wishing to perform dynamic simulations of quantum materials on quantum computers. As our DS compilers provide significant improvements in both compilation time and simulation fidelity, they provide a building block for accelerating progress toward physical quantum supremacy.

We describe a variety of searches for new physics beyond the standard model of particle physics which may be enabled in the coming years by the use of optically levitated masses in high vacuum. Such systems are expected to reach force and acceleration sensitivities approaching (and possibly eventually exceeding) the standard quantum limit over the next decade. For new forces or phenomena that couple to mass, high precision sensing using objects with masses in the fg–ng range have significant discovery potential for new physics. Such applications include tests of fundamental force laws, searches for non-neutrality of matter, high-frequency gravitational wave detectors, dark matter searches, and tests of quantum foundations using massive objects.

Variational quantum eigensolver (VQE) for electronic structure calculations is believed to be one major potential application of near term quantum computing. Among all proposed VQE algorithms, the unitary coupled cluster singles and doubles excitations (UCCSD) VQE ansatz has achieved high accuracy and received a lot of research interest. However, the UCCSD VQE based on fermionic excitations needs extra terms for the parity when using Jordan–Wigner transformation. Here we introduce a new VQE ansatz based on the particle preserving exchange gate to achieve qubit excitations. The proposed VQE ansatz has gate complexity up-bounded to O(n⁴) for all-to-all connectivity where n is the number of qubits of the Hamiltonian. Numerical results of simple molecular systems such as BeH₂, H₂O, N₂, H₄ and H₆ using the proposed VQE ansatz gives very accurate results within errors about 10⁻³ Hartree.

The amplified spontaneous emission (ASE) noise has been extensively studied and employed to build quantum random number generators (QRNGs). While the previous relative works mainly focus on the realization and verification of the QRNG system, the comprehensive physical model and randomness quantification for the general detection of the ASE noise are still incomplete, which is essential for the quantitative security analysis. In this paper, a systematical physical model for the detection and acquisition of the ASE noise with added electronic noise is developed and verified, based on which the numerical simulations are performed under various setups and the simulation results all significantly fit well with the corresponding experimental data. Then, a randomness quantification method and the corresponding experimentally verifiable approach are proposed and validated, which quantifies the randomness purely resulted from the quantum process and improves the security analysis for the QRNG based on the detection of the ASE noise. The physical model and the randomness quantification method proposed in this paper are of significant feasibility and applicable for the QRNG system with randomness originating from the detection of the photon number with arbitrary distributions.

We show that a quantum Otto cycle in which the medium, an interacting ultracold gas, is driven between a superfluid and an insulating phase can outperform similar single particle cycles. The presence of an energy gap between the two phases can be used to improve performance, while the interplay between lattice forces and the particle distribution can lead to a many-body cooperative effect. Since finite time driving of this cycle can create unwanted non-equilibrium dynamics which can significantly impair the performance of the engine cycle, we also design an approximate shortcut to adiabaticity for the many-body state that can be used to achieve an efficient Otto cycle around a critical point.

There is widespread interest in calculating the energy spectrum of a Hamiltonian, for example to analyze optical spectra and energy deposition by ions in materials. In this study, we propose a quantum algorithm that samples the set of energies within a target energy-interval without requiring good approximations of the target energy-eigenstates. We discuss the implementation of direct and iterative amplification protocols and give resource and runtime estimates. We illustrate initial applications by amplifying excited states on molecular hydrogen.

The Lindblad form of the master equation has proven to be one of the most convenient ways to describe the impact of an environment interacting with a quantum system of interest. For single systems the jump operators characterizing these interactions usually take simple forms with a clear interpretation. However, for coupled systems these operators take significantly different forms and the full dynamics cannot be described by jump operators acting on the individual subsystems only. In this work, we investigate the differences between a common phenomenological model for the master equation and the more rigorous dressed-state master equation for optomechanical systems. We provide an analytical method to obtain the absorption spectrum of the system for both models and show the breakdown of the phenomenological model in both the bad cavity and the ultra-strong coupling limit. We present a careful discussion of the indirect dephasing of the optical cavity in both models and its role in the differences of their predicted absorption spectra. Our work provides a simple experimental test to determine whether the simpler phenomenological model can be used to describe the system and is a step forward toward a better understanding of the role of the coupling between subsystems for open-quantum-system dynamics.

Coherence times for superconducting qubits have greatly improved over time. Moreover, small logical qubit architectures using engineered dissipation have shown great promise for further improvements in the coherence of a logical qubit manifold comprised of few physical qubits. Nevertheless, optimal working parameters for small logical qubits are generally not well understood. This work presents several approaches to finding preferential parameter configurations by looking at three different cases of increasing complexity. We begin by looking at state stabilization of a single qubit using dissipation via coupling to a lossy object. We look at the limiting factors in this approach to error correction, and how we address those by numerically optimizing the parametric coupling strength with the lossy object having an effective time-varying dissipation rate—we call this a pulse-reset cycle. We then translate this approach to more efficient state stabilization to an abstracted three-qubit flip code, and end by looking at the very small logical qubit (VSLQ). By using these techniques, we can further increase logical state lifetimes for different architectures. We show significant advantages in using a pulse-reset cycle over numerically optimized, fixed parameter spaces.

Steane's seven-qubit quantum code is a natural choice for fault-tolerance experiments because it is small and just two extra qubits are enough to correct errors. However, the two-qubit error-correction technique, known as 'flagged' syndrome extraction, works slowly, measuring only one syndrome at a time. This is a disadvantage in experiments with high qubit rest error rates. We extend the technique to extract multiple syndromes at once, without needing more qubits. Qubits for different syndromes can flag errors in each other. This gives equally fast and more qubit-efficient alternatives to Steane's error-correction method, and also conforms to planar geometry constraints. We further show that Steane's code and some others can be error-corrected with no extra qubits, provided there are at least two code blocks. The rough idea is that two seven-qubit codewords can be temporarily joined into a twelve-qubit code, freeing two qubits for flagged syndrome measurement.