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The Green&#39;s function plays a crucial role when studying the nature of quantum many-body systems, especially strongly correlated systems. Although the development of quantum computers in the near future may enable us to compute energy spectra of classically intractable systems, methods to simulate the Green&#39;s function with near-term quantum algorithms have not been proposed yet. Here, we propose two methods to calculate the Green&#39;s function of a given Hamiltonian on near-term quantum computers. The first one makes use of a variational dynamics simulation of quantum systems and computes the dynamics of the Green&#39;s function in real time directly. The second one utilizes the Lehmann representation of the Green&#39;s function and a method which calculates excited states of the Hamiltonian. Both methods require shallow quantum circuits and are compatible with near-term quantum computers. We numerically simulated the Green&#39;s function of the Fermi-Hubbard model and demonstrated the validity of our proposals.

Quantum 2020

Calculation of the Green&#39;s function on near-term quantum computers

quantum many-body systems

nisq devices

quantum computing

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. 

The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly correlated systems. Although the development of quantum computers in the near future may enable us to compute energy spectra of classically intractable systems, methods to simulate the Green's function with near-term quantum algorithms have not been proposed yet. Here, we propose two methods to calculate the Green's function of a given Hamiltonian on near-term quantum computers. The first one makes use of a variational dynamics simulation of quantum systems and computes the dynamics of the Green's function in real time directly. The second one utilizes the Lehmann representation of the Green's function and a method which calculates excited states of the Hamiltonian. Both methods require shallow quantum circuits and are compatible with near-term quantum computers. We numerically simulated the Green's function of the Fermi-Hubbard model and demonstrated the validity of our proposals.

Calculation of the Green's function on near-term quantum computers

technical paper

Quantum computers can be used for supervised learning by treating parameterised quantum circuits as models that map data inputs to predictions. While a lot of work has been done to investigate practical implications of this approach, many important theoretical properties of these models remain unknown. Here we investigate how the strategy with which data is encoded into the model influences the expressive power of parametrised quantum circuits as function approximators. We show that one can naturally write a quantum model as a partial Fourier series in the data, where the accessible frequencies are determined by the nature of the data encoding gates in the circuit. By repeating simple data encoding gates multiple times, quantum models can access increasingly rich frequency spectra. We show that there exist quantum models which can realise all possible sets of Fourier coefficients, and therefore, if the accessible frequency spectrum is asymptotically rich enough, such models are universal function approximators.

What Functions can Quantum Models Learn?

Designing feasible and qualitative methods for estimation of topological invariants, such as the Chern number, is of great significance for experimental realization of topological quantum matter.We present two key results in this direction. We first show that for two-band systems supported on Bravais lattices with 2n-fold rotation symmetry, the Chern number (mod 2n) of one of the energy bands can be inferred from the spin polarization of the band wavefunction at the high-symmetry crystal momenta in the Brillouin zone. We leverage this result to design an experimental scheme for ultracold bosonic gases that uses Bloch oscillations and Zeeman spectroscopy for validation of the topological phases with Chern number ±2 on a triangular lattice. As part of the latter result, we present the first experimental scheme to our knowledge for simulating spin-orbit coupling on a triangular optical lattice. Our results highlight Bloch oscillations as a robust tool for detection of topological order, and also open doors to new experiments based on spin-orbit coupled systems beyond square lattices.

Detection of Topological Order in Ultracold Atoms

We present multi-layer, mechanically-compliant photonic crystal slabs for use in cavity optomechanical experiments. The slabs have mechanical frequencies in the range of several hundred kilohertz and demonstrate reflectance of close to unity at telecom wavelengths [1]. An optomechanical system consisting of a mechanical resonator array in an optical cavity has been proposed as a method to reach the elusive single-photon strong coupling regime in optomechanics [2]. A critical requirement of such a system is to have highly reflective and uniform mechanical resonators of well-defined spacing. In this work we present our progress in this direction. We demonstrate devices fabricated in an AlGaAs heterostructure consisting of sub-μm spaced, near-identical mechanical resonators on top of a distributed Bragg reflector. We pattern these resonators with photonic crystal structures for engineering their out-of-plane reflectivity. We characterize the mechanical and optical properties of the slabs. The presented devices can be combined with micro-mirrors on an external chip forming a fully integrated chip-based realization of a multi-element optomechanical system. Additonally, two photonic crystal slabs with sub-μm gap can exhibit so-called photonic bound states in the continuum (BICs). Such photonic BICs can be exploited for surpassing the performance of conventional Fabry-Perot-based optomechanical microcavities [3].
References:
[1] S. K. Manjeshwar et al., Appl. Phys. Lett. 116, 264001 (2020)
[2] A. Xuereb et al., Phys. Rev. Lett. 109, 223601 (2012)
[3] J. M. Fitzgerald et al., arXiv:2007.07883 [quant-ph]

Multi-layer suspended photonic crystal membranes in AlGaAs heterostructures for integrated cavity optomechanics

Einstein’s Equivalence Principle (EEP) is a cornerstone in the development
of General Relativity. Its validity implies that gravity is a geometrical
phenomena. Several experiments have proven that EEP is valid in the
classical regime. Nevertheless, its validity for quantum systems is still
undergoing experimental tests. In this work we study, following two
different approaches, the quantum free fall of quantum particles. Our
results suggest that EEP is violated in the quantum regime, but naturally
emerges as the energy/mass approaches macroscopic values. We first show
that the transient current density of a suddenly released beam of quantum
particles depends explicitly on the particle’s mass (thus contradicting
the universality of free fall), but such dependence disappear as the mass
increases (indicating the emerge of the EEP). We also consider the problem
of a quantum particle bouncing above a mirror in the presence of the
Earth’s gravitational field. By means of a simple method based on Fourier
analysis, we show that the classical probability distribution (which is
mass independent) emerges from its quantum-mechanical analogue in the
limit of large quantum numbers (high energy regime), thus also supporting
the emergence of the EEP from quantum mechanics.

On the validity of Einstein's Equivalence Principle in Quantum Mechanics

Tensor network theory and quantum simulation are respectively the key classical and quantum methods in understanding many-body quantum physics. Here we show hybridization of these two seemingly independent methods, inheriting both their distinct advantageous features of efficient representations of many-body wave functions. We introduce the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors. As an example, we demonstrate efficient quantum simulation with hybrid tree tensor networks that use quantum hardware whose size is significantly smaller than the one of the target system. We numerically test our method for finding the ground state of 1D and 2D spin systems of up to 8×8 and 4×3 qubits with operations only acting on 8+1 and 4+1 qubits, respectively. Our approach paves the way to the near-term quantum simulation of large practical problems with intermediate size quantum hardware, with potential applications in quantum chemistry, quantum many-body physics, quantum field theory, and quantum gravity thought experiments.

Quantum Simulation with Hybrid Tensor Networks

We consider the estimation of a Hamiltonian parameter of a set of highly photosensitive samples, which are damaged after a few photons Nabs are absorbed. The samples are modelled as a two mode photonic system, where photons simultaneously acquire information on the unknown parameter and are absorbed at a fixed rate. We show that arbitrarily intense coherent states can obtain information at a rate that scales at most linearly with Nabs, whereas quantum states with finite intensity can overcome this bound. The quantum advantage scales like N/Nabs (where N is the number of photons in the quantum state), so that few-photon entangled states can already surpass the classical bound when Nabs is small. We discuss an implementation in cavity QED, where Fock states are both prepared and measured by coupling atomic ensembles to the cavities.

Weakly invasive metrology: quantum advantage and physical implementations

A single quantum measurement cannot perfectly determine the state of a quantum system; however it is possible to perfectly rule out certain states. Quantum state elimination is of foundational interest, relating to the so-called reality of the wave function, as well as having applications in quantum information and quantum communication. We consider unambiguous quantum state elimination for two qubits, where each qubit can be in one of two possible states resulting in four possible two-qubit states. We provide an optimal measurement for eliminating two states out of four two-qubit states. We also explore different possible optical realisations of this state elimination measurement using linear optics and generate a realization that uses a minimum number of optical elements. This state elimination measurement could be used for an XOR oblivious transfer protocol, where a receiver obtains either the first, second, or XOR of two bits a sender sends and the sender not knowing which bit was received. Moreover, one could also envisage a novel quantum key distribution schemes employing state elimination, where the final bit value cannot be thought of as created at the sender and transmitted to the receiver, but is only realised once the receiver's measurement is complete.

Unambiguous quantum state elimination of pairs of quantum states for quantum communication

Quantum coherence of electron motion dramatically affects low temperature phenomena in confined conductors leading to such effects as Aharonov-Bohm oscillations in mesoscopic rings. In Ref. 1, a novel type of the oscillations manifesting itself in finite singly-connected conductors and associating with special diffusive trajectories grazing their boundaries was predicted. We apply this idea to implement SQUID-like oscillations in the critical current dependence on the magnetic field in Josephson junctions with superconducting electrodes and a weak link formed by periodically alternating normal and superparamagnetic ultrathin films, the sample details and the supporting information can be found the supporting information can be found in our paper [2]. We have identified the presence of a universal transfer matrix that maps the incident electron waves to the transmitted waves and is similar to that found before in numerous studies with coherent electromagnetic and acoustic waves passing through a multiply scattering medium. In our case, the presence of almost open conductance eigenchannels reveals itself in a pronounced background of the critical current-vs-field dependence. Possible improvement of quantum magnetic field sensors using the new type of Josephson junctions is discussed. 
1. I.L. Aleiner, A.V. Andreev, V. Vinokur, Phys. Rev. Lett. 114, 076802 (2015).
2. I.P. Nevirkovets, M.A. Belogolovskii, J.B. Ketterson, Phys. Rev. Appl. 14, 014092 (2020). 


Quantum transport in Josephson junctions with a periodic normal metal/superparamagnet weak link

We consider the transport properties of a single-electron transistor consisting of a diffusive normal-metal island and superconducting electrodes. We show that the interplay of a dissipative impedance of the gate electrode, a weak magnetic field, and a charging energy of the island causes a suppression of the critical supercurrent of the transistor. When the device is voltage biased, pumping of single electrons can be achieved by a periodic modulation of the gate voltage [1-3]. We derive the analytic expressions for the error rates and show that they are suppressed by the applied magnetic field [4].

[1] J. P. Pekola et al, Nat. Phys. 4 (2008) 120.
[2] D. V. Averin and J. P. Pekola, Phys. Rev. Lett. 101 (2008) 066801.
[3] S. Nakamura et al, Phys. Rev. Appl. 7 (2017) 054021.
[4] V. Bubanja, Phys. Rev. B 97 (2018) 224516.

Effect of quantum fluctuations on the critical supercurrent through a mesoscopic normal-metal island

The recent miniaturization of heat engines to the nanoscale introduces the possibility of engines that harness quantum resources. The analysis of quantum engines provides important insight into how their efficiency compares to classical analogues and deepens our understanding of thermodynamic mechanisms at the quantum scale. We examine a quantum Otto engine with a harmonic working medium consisting of two particles to explore the use of wave function symmetry as an accessible resource. It is shown that a bosonic working medium displays enhanced performance when compared to distinguishable particles, while a fermionic working medium displays reduced performance. To this end, we explore the trade-off between efficiency and power output and the parameter regimes under which the system functions as engine, refrigerator, or heater. Remarkably, the bosonic system operates under a wider parameter space both when operating as an engine and as a refrigerator.

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