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Variational Quantum Eigensolver (VQE) circuits are an application of the variational method of quantum mechanics used to solve problems of finding the eigenvalues of Hermitian operators in systems, where the dimension of the problem space grows exponentially. The circuit model is based on the VQE algorithm which uses an ansatze based state preparation technique through the use of parameterized circuits. The important property of such variational form is to be able to span the set of attainable states which is solely dependent on the ansatz and the classical optimizer utilized. We present a study on the various gradient based and gradient free optimizers that can be fitting to this regime and report on the efficiency and accuracy of the overall VQE operation for a standardized problem of calculating the smallest eigenvalues of a given Hamiltonian. We further explore how the effectiveness of such routine is affected by varying circuit depths. We aim to present our results in this conference and discuss how this knowledge can be leveraged to design fault tolerant NISQ era VQE algorithms.

Quantum 2020

Analysis of Classical Optimization Routines used in the Preparation of Quantum States in Variational Quantum Eigensolver

hybrid-quantum

optimization

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. 

poster

Detectors of propagating microwave photons have recently been realized using superconducting circuits. However a number-resolved photocounter is still missing. In this poster, we demonstrate a single-shot counter for propagating microwave photons that can resolve up to 3 photons. It is based on a pumped Josephson Ring Modulator that can catch an arbitrary propagating mode by frequency conversion and store its quantum state in a stationary memory mode. A transmon qubit then counts the number of photons in the memory mode using a series of binary questions. Using measurement based feedback, the number of questions is minimal and scales logarithmically with the maximal number of photons. The detector features a detection efficiency of 0.96 ± 0.04, and a dark count probability of 0.030 ± 0.002 for an average dead time of 4.5µs. To maximize its performance, the device is first used as an in situ waveform detector from which an optimal pump is computed and applied. Depending on the number of incoming photons, the detector succeeds with a probability that ranges from 56 % to 99 %.

Number-resolved photocounter for propagating microwave mode

Squeezed states, whose fluctuations on one quadrature is below the zero point fluctuations (ZPF) at the expense the other, have become a central resource for quantum sensing and information processing. Squeezing is usually generated by parametrically pumping a resonator. While any amount of squeezing can theoretically be obtained for the outgoing field, the intraresonator squeezing is limited to 3 dB below the ZPF. Indeed, input-output relations impose that the intraresonator fluctuations result from the average of the ingoing ZPF and outgoing squeezed fluctuations. Using reservoir engineering techniques, the 3 dB limit has recently been overcome in a mechanical resonator [Lei PRL 117 (2016)]. However, a proof of principle is still missing for electromagnetic modes. 
In this work, we use two parametric pumps and a dump mode to engineer an effective coupling to an artificial squeezed reservoir. We perform in-situ Wigner tomography of the squeezed microwave mode using an ancillary superconducting qubit. The intraresonator squeezing reaches as much as 5.55 +-0.03 dB, going well beyond the 3 dB limit. Interestingly, the non-classicality of the squeezed state is demonstrated using photon number statistics and we also observe the dynamics of the squeezing process thanks to the state tomography.


Direct Wigner tomography of steady-state squeezing beyond 3 dB in a microwave resonator.


Quantum and classical physics are related through the phase space probability distribution of quantum states. Though these probabilities are not always well 
positive but their negative values are indicative of non-classical behavior of quantum state. Besides three quasi- probability distribution, Wigner function is 
discussed widely because of its behavior and its physical realization. Quantum entanglement finds many applications in quantum information processing and 
more entanglement will make the processes more secure, fast and faithful. Quantum entanglement and coherence represent correlation in two systems: the 
former is a tensor product of states of two systems correlated such that the measurement on one system would reveal the state of another system as well while 
the latter represent the correlated phases of system. It is shown that the coherence in the system gets entangled with the incoherent part of the system giving the 
same quantity of entanglement as of coherence. This suggests that both the states carry same amount of information despite of their different physical meaning. 
Degree of coherence can be measured in terms of the well-known quantifiers of entanglement which is measured by Wigner function. Entangled states and 
quantum coherence are detected by the non-positive values of corresponding Wigner function

Scanning wigner Quasi probability distribution for the presence of quantum coherence and entanglement

Optomechanical systems are promising platforms for controlled light-matter interactions. They are capable of providing several fundamental and practical novel features when the mechanical oscillator is cooled down to nearly reach its ground state. In this framework, measuring the effective temperature of the oscillator is perhaps the most relevant step in the characterization of those systems. In conventional schemes, the cavity is driven strongly, and the overall system is well-described by a linear (Gaussian preserving) Hamiltonian. Here, we depart from this regime by considering an undriven optomechanical system via non-Gaussian radiation-pressure interaction. To measure the temperature of the mechanical oscillator, initially in a thermal state, we use light as a probe to coherently interact with it and create an entangled state. We show that the optical probe gets a nonlinear phase, resulting from the non-Gaussian interaction, and undergoes an incoherent phase diffusion process. To efficiently infer the temperature from the entangled light-matter state, we propose using a nonlinear Kerr medium before a homodyne detector. Remarkably, placing the Kerr medium enhances the precision to nearly saturate the ultimate quantum bound given by the quantum Fisher information. Furthermore, it also simplifies the thermometry procedure as it makes the choice of the homodyne local phase independent of the temperature, which avoids the need for adaptive sensing protocols.

Mechanical oscillator thermometry in the nonlinear optomechanical regime

The evolution of quantum systems under measurement is a central aspect of quantum mechanics. Decades of experimental progress have enabled the observation of the inner dynamics of a quantum measurement and the determination of the number of bits of information it reveals [1,2]. 
When a two level system -- a qubit -- is used as a probe of a larger system, it naturally leads to answering a single yes-no question about the system state followed by its corresponding quantum collapse. Each measurement thus reveals at most one bit of information. Is it possible to lift this constraint by not using the qubit as an ancilla?
Here we report an experiment where more than 3 bits of information about the photon number in a microwave resonator are simultaneously recorded by a superconducting qubit into 9 propagating modes of a transmission line. This recording occurs by exciting these 9 modes using multiplexed spectroscopy owing to the dependence of the qubit frequency on photon number [3,4]. We demonstrate the simultaneous acquisition of microwave signals emitted by the qubit into the nine propagating modes that each reveals information about a photon number from 0 to 8, enabled by the large bandwidth of present near quantum limited amplifiers
[5]. Further observing the multiplexed measurement back-action on the resonator allowed us to evidence an optimal qubit drive amplitude for information extraction. Our experiment unleashes the full potential of quantum meters by bringing the measurement process in the frequency domain. It extends the reach of simultaneous probing of a single qubit by multiple observers [6,7] to arbitrary systems such as our resonator. This concept can be applied to improve or renew quantum control based on measurement [8] with possible applications in quantum error correction and sensing.

1. Guerlin, C.et al. Progressive field-state collapse and quantum non-demolition photoncounting. Nature448, 889–93 (2007).
2. Murch, K. W., Weber, S. J., Macklin, C. & Siddiqi, I. Observing single quantum trajectories of a superconducting quantum bit. Nature502, 211–214 (2013).
3. Minev, Z. K.et al. To catch and reverse a quantum jump mid-flight. Nature(2019).
4. Schuster, D. I.et al. Resolving photon number states in a superconducting circuit. Nature445,515–518 (2007).
5. Gely, M. F.et al. Observation and stabilization of photonic Fock states in a hot radio-frequency resonator. Science363, 1072–1075 (2019).
6. Hacohen-Gourgy, S.et al. Dynamics of simultaneously measured non-commuting observables. Nature538, 491 (2016).
7. Ficheux, Q., Jezouin, S., Leghtas, Z. & Huard, B. Dynamics of a qubit while simultaneously monitoring its relaxation and dephasing. Nature Communications9, 1926 (2018).
8. Wiseman, H. M. & Milburn, G. J. Quantum Measurement and Control (Cambridge UniversityPress, 2009).

Multiplexing photon number measurement of a resonator using a dispersively coupled qubit

Quantum key distribution is the first application of quantum physics which has entered the commercial market. The security of QKD protocols relies on the quantum nature of the physical system used. In this work, we present a QKD protocol, security of which depends upon the contextuality of mono-party system. It has been shown[1] that Bell CHSH non-locality inequality[2] probes contextuality in single four-level system. We use this contextuality inequality in the proposed protocol as a security check. The advantage of the proposed protocols as compared to Ekert is that it does not involve entangled states, but provides the same level of security. Thus, the cost of generation of entangled states is saved. The experimental key generation rate of proposed protocol will also be higher than the one with entangled states because one can use weak coherent pulses instead of limited brightness of entangled photon pair sources[3].With advancement in generation and manipulation of higher dimensional OAM states, our protocols can be experimentally realized. Thus, we also propose the setup for experimental implementation of the protocol using orbital angular momentum states. Our work is generalizable to conference QKD as w

Contextuality based Quantum key distribution(QKD)

The frequency stabilisation or 'locking' of narrow linewidth lasers to atomic transitions is a common requirement in atomic and molecular physics experiments. There are many well-established techniques for locking a laser on, or close to resonance including saturated absorption spectroscopy (SAS), polarisation spectroscopy, dichroic atomic vapour level lock (DAVLL), etc. However, it can be desirable to lock away from resonance which is more difficult. Here we demonstrate a simple, tunable frequency reference based upon SAS and frequency modulation spectroscopy using the Rb-85 D1 line in a strong magnetic field as a reference for a Cs Rydberg transition.

Zeeman Shifted Atomic Reference for efficient laser stabilisation and Rydberg excitation

We discuss here three use case studies of domain wall encoding presented in [1]. One is the flight gate scheduling problem, another is the network routing problem and the third is the 3-coloring problem. The data for the flight gate problem is retrieved from database of a medium size German airport where the scale of complexity has been reduced to fit into current capacity of quantum processor. The network graph structure is emulated using a realistic topology generator for WMN (NPART) and the encodings were conducted in NS3. And the 3-coloring problem instances are generated using the random graph tool in Python. We can show the algorithms that employ domain wall encoding can successfully return solutions that conform to the formatting and domain wall encoding demonstrates higher embedding efficiency over the traditional one hot encoding method. We used X-Hot ratio to investigate into the disconformity issue of one hot scheme and notice that all the bad solution variables are in 0-Hot format. In all cases examined here, we find that the domain wall encoding almost always yields superior performance to one hot.
[1] Chancellor N 2019 Quantum Sci. Technol. 4 045004 https://doi.org/10.1088/2058-9565/ab33c2


Domain Wall Encoding Use Case Studies

A nanomechanical oscillator can be used as a sensitive probe of a small linearized mechanical force. We propose a basic short-pulsed quantum optomechanical scheme using a coherent light mode in the cavity and weak light-matter interactions. By applying homodyne detection to only the interacting light mode, we obtained a method which combines high-precision multiparameter estimation with robustness. We demonstrate the feasibility of our scheme using the parameters of state-of-the-art experimental setups, and thereby open the way to new nanomechanical sensors.

High-precision multiparameter estimation of mechanical force by quantum optomechanics

Topological quantum computing promises a hardware-level solution for the problem of decoherence. In particular, quantum gates based on the braiding of Majorana zero modes in superconductors are expected to be robust against control imperfections. Here, we combine earlier ideas for initialisation, control and readout to propose a setup where the robustness of the braiding-based gate could be demonstrated. By numerical experiments, we demonstrate how quasistatic disorder degrades the quality of braiding-based gates, and how that effect is reduced by increasing the system size. Our numerical experiments shed light on various practical aspects of future experiments aiming at demonstrating topologically protected quantum dynamics.

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Analysis of Classical Optimization Routines used in the Preparation of Quantum States in Variational Quantum Eigensolver

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Number-resolved photocounter for propagating microwave mode

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