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The Density Matrix Renormalisation Group (DMRG) is the state of the art for accurate simulation of quantum systems on a 1D lattice. It works by efficiently truncating the Hilbert space based on the local entanglement, producing important physical insights which have spawned a growing field of tensor network techniques. However, several key experiments operate in the continuum, and attempts to generalise the DMRG to continuous systems have proved difficult and challenging. Here we introduce an intuitive and practical method for extending the tools of traditional DMRG to the continuum by using a flexible set of local basis functions that are subject to a continuity constraint. We benchmark our approach against the Bethe Ansatz for interacting bosons in a box trap, and demonstrate improved scaling over simple discretisation that can be controlled by the basis set. We then apply our technique to find ground states of bosons in a sinusoidal trap, recovering known limits and showing a superfluid to Mott transition in a shallow lattice.

Quantum 2020

Density Matrix Renormalisation Group for continuous systems

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dmrg

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The Institute of Physics and IOP Publishing, in partnership with the Chinese Physical Society (CPS) and the University of Science and Technology of China (USTC) are proud to have brought together the international quantum science community online for this inaugural conference.


Early career and leading researchers from universities, industry and government worldwide came together to share, learn and collaborate on the latest research and emerging areas of high interest across quantum science and technology. The broad themes covered by Quantum 2020 included:

Quantum communication;
Quantum computing and quantum simulation;
Quantum sensing, metrology and imaging;
Quantum information theory, software and algorithms;
Quantum foundations;
Quantum technology in industry.
The four-day event featured talks from world-renowned scientists, interactive poster sessions and two exciting panel discussions on the themes of Quantum Technology in Industry and Quantum Technology Programmes Around the World.


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The Institute of Physics and IOP Publishing, in partnership with the Chinese Physical Society (CPS) and the University of Science and Technology of China (USTC) are proud to have brought together the international quantum science community online for this inaugural conference.

Early career and leading researchers from universities, industry and government worldwide came together to share, learn and collaborate on the latest research and emerging areas of high interest across quantum science and technology. 

Quantum computers are expected to outperform conventional computers for a range of important problems, once they can be scaled up to large numbers of qubits, typically millions. For most solid-state qubit technologies, e.g. those using superconducting circuits or semiconductor spins, scaling poses a significant challenge as every additional qubit increases the heat generated, while the cooling power of dilution refrigerators is severely limited at their operating temperature below 100 mK. Here we demonstrate operation of a scalable silicon quantum processor unit cell, comprising two qubits confined to quantum dots (QDs) at ∼1.5 kelvin. We achieve this by isolating the QDs from the electron reservoir, initialising and reading the qubits solely via tunnelling of electrons between the two QDs. We coherently control the qubits using electrically-driven-spin-resonance in isotopically enriched silicon 28Si, attaining single-qubit gate fidelities of 98.6% and coherence time T2* = 2μs during `hot' operation, comparable to those of spin qubits in natural silicon at millikelvin temperatures. Our work indicates that a spin-based quantum computer could be operated at elevated temperatures in a simple pumped 4He system, offering orders of magnitude higher cooling power than dilution refrigerators, potentially enabling classical control electronics to be integrated with the qubit array.

Operation of a silicon quantum processor unit cell above one kelvin

A hybrid system consisting of a quantum dot (QD) based single-photon source and a rubidium-memory is a promising platform for implementing quantum networks. For this purpose, GaAs QDs in AlGaAs are interesting since they can emit single photons frequency-matched to rubidium atoms. However, GaAs QDs suffered so far from strong telegraph noise due to an unstable charge environment. Here, we present ultra-low noise and charge-tunable GaAs QDs. We place the QDs inside a p-i-n diode and show deterministic electrical tuning of the charge-state and the emission frequency of the QDs. For a typical QD, the resonance fluorescence has an ultra-narrow linewidth of 640 MHz, just slightly above the lifetime-limit (590 MHz). The QDs are extremely stable and do not show telegraph-noise (blinking). Under resonant excitation, we achieve a high single-photon purity in combination with high photon indistinguishability (HOM-visibility up to 98%). We additionally demonstrate high fidelity optical spin initialization on an electron- as well as a hole-spin. We find that the spin has a long lifetime of up to 50μs. Together with the excellent photonic properties, the new QDs form a promising platform for a spin-photon interface.

Low-Noise GaAs Quantum Dots for Quantum Photonics

We present an imaging system that uses a photon’s position and time-of-flight information to image an object. Since the position of the photons is correlated with their momentum, it is possible to identify the pairs by checking the photons’ timestamp information and localize one of the pair for Spatio-temporal ghost imaging thanks to the momentum conservation of down conversion event. While the timing information of signal (idler) is recorded as reference the idler (signal) is measured after being back-scattered from the object being imaged. With a real-time cross-correlation check of signal and idler photons, the pairs can be identified. The results exhibit multifold quantum enhancement over classical detection in an extremely noisy background. The two-dimensional imaging is performed by mapping the position of signal (idler) photons and register the corresponding coincidence events. The rate of coincidences for a certain position is used to create the image of the object. We also analyze the parameters affecting the image resolution in two dimensions. The method is implemented on imaging of microscopic objects and it was shown that the polarization entanglement is also well preserved during the scattering from the object being imaged.

Noise Tolerant Spatio-temporal Ghost Imaging with an Entangled Source

The design of quantum experiments can be challenging for humans. Computational and artificial intelligence methods have therefore been introduced to discover tailored quantum experiments with particular desired functionalities. However, these algorithms are slow, require large amounts of data or work for specific platforms that are difficult to generalize. 

Here we present Theseus, an efficient algorithm for the design of quantum experiments. The algorithm' core is a physics-inspired, graph-theoretical representation of quantum states, which makes it significantly faster than previous comparable approaches. Topological optimization then uncovers the solution's conceptual cores which human scientists can understand and generalize without performing any further calculations. We use Theseus to solve several open questions in experimental quantum optics. The solutions are not only within reach of modern laboratories but also provide new generalizable ideas, for example, a method to exploit destructive interference of vacuum.

We anticipate that Theseus will become an essential tool in quantum optics for studies of fundamental questions and developments of practical applications. Furthermore, the unique ability to systematically inspire new understanding goes beyond standard optimization and enters realm of providing scientific understanding, an essential aim of science.

Conceptual understanding through efficient inverse-design of quantum optical experiments

In this work, we answer the question: how sudden or adiabatic is a change in the frequency of a quantum harmonic oscillator (HO)? 
With this purpose, we study and characterise the squeezing parameter (SP) and the variance of the so-called instantaneous quadrature operator when performing a frequency transition in the HO for different transition speeds interpolating the sudden and adiabatic limits. Then we characterise adiabaticity concerning to squeezing. Finally, we obtain analytic expressions enabling us to fit the SP and the variance of the instantaneous quadrature operator as a function of the parameters of the system and the transition speed. 


Time-dependent quantum harmonic oscillator: a continuous route from adiabatic to sudden changes

Semiconductor nanocrystals (NCs), thanks to tunability and control afforded by quantum confinement effects with unique properties, have been broadly applied in light emitting diodes displays, chiral sensing and asymmetric catalysis, etc. However, a systematic control of these NCs was extremely difficult not to say impossible. Thus, it is still mandatory and relevant to find out an effective synthetic approach to achieve semiconductor NCs with tunable properties. In this work, we studied the precise control of quantum rods synthesis, and used them for chirality and laser-induced deposition purposes.
The anisotropic factor of circularly polarized luminescence (CPL, glum) can reach 8.5×10-4, and the the raito of single-tipped HNPs could be improved significantly from 42% to 81% in Au-CdSe/CdS HNPs .

Improved semiconductor nanocrystal: a platform for CPL and controlled laser photodeposition of single metal nanodot

In this study, we showed that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulate. We examined a Stern—Gerlach experiment to explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. The EPR—Bohm experiment was considered to conclude that the correlation of the EPR pair is not a consequence of instantaneous propagation of the collapse of the wave function. We also referred to its relation to the counterfactual non-definiteness of quantum mechanics. Finally, we showed that our theory can be applied to experiments with continuous eigenvalues, such as the double-slit experiment with electrons. This also illuminates how pure quantum mechanics describes the fact that electrons behave as interfering particles, I.e., particles whose detection rate is consistent with interference.

Decoherence as an inherent characteristic of quantum mechanics

We delve into the problem of the choice of the interaction Hamiltonian in quantum transitions by using the gauge invariant formalism. We demonstrate that the gauge invariant transition amplitudes for the bare-bare transitions, which is the case in the majority of experiments, are identical to the conventional results with the velocity form interaction Hamiltonian. Under the electric dipole approximation, the gauge invariant formalism derives the modified length form interaction Hamiltonian in any gauge. We propose a simple experiment that one can perform to verify our prediction. On the other hand, the gauge invariant transition amplitudes for the dressed-dressed transitions, which is the case in the Lamb shift experiment, are identical to the conventional results with the length form interaction Hamiltonian. There is no preferred gauge in the calculations of transition amplitudes. The present investigation resolves the long-standing versus controversy and clarifies the prevailing misconception in the literature.

Reference
(1) Hsiang-Shun Chou, J. Phys. Commn. 3, 115014 (2019)


Gauge invariant resolution of the A.p versus r.E controversy

The awareness of the relevance of the projectile’s beam coherence effects in ion-atom and ion-molecule collisions has motivated an extensive study on this subject in recent years. The traditional way to compute the fully differential cross section (FDCS) of a reaction describes the incoming beam of projectiles as a purely coherent quantum system, i.e. a plane-wave. Nevertheless, this assumption seems not justified enough when we look at this postulate under the light of the density matrix theory. We describe how the time propagation of an incoherent mixture of an ensemble of massive particles, described by identical wave packets located at different positions upon a much larger region, can eventually develop coherence at a given distance L, and its implications for scattering theory. Furthermore, we show the results of these concepts applied to specific experimental results.

The role of classical uncertainties on the coherence properties of collisions processes

We present optimal schemes, based on photon number measurements, for Gaussian state tomography and for Gaussian process tomography. An n-mode Gaussian state is completely specified by 2n^2 +3n parameters. Our scheme requires exactly 2n^2 +3n distinct photon number measurements to tomograph the state and is therefore optimal. Further, we describe an optimal scheme to characterize Gaussian processes by using coherent state probes and photon number measurements.

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