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Like their classical counterparts, today’s quantum computers are also easily affected by errors. It is crucial to develop error correction procedures to reduce the effects of the noise in the system. However, the current mainstream error correction codes, like the surface code and toric code, often require a large number of physical qubits, which is not feasible on the NISQ (noisy intermediate-scale quantum) devices where the number of available qubits is limited (&lt; 100 qubits). This work proposed a variational quantum circuit based scheme to discover device-specific error correction codes for the NISQ computing systems in which the encode and recovery (syndrome) layers of our error correction circuit are trained together. Various choices of local optimizers are explored, and performances were compared with each other. We adopted shallow and simple-structured circuits in both encode and recovery layers to alleviate the barren plateau problem in the training of parameterized quantum circuits. The error correction circuit was trained against different kinds of error models, including depolarizing, phase and amplitude damping errors. We adopted a stronger loss constraint. We adopted a stronger loss constraint which, unlike previous attempts, enabled the error correction circuit to achieve higher fidelity on the encoding qubits.

Quantum 2020

Quantum Error Correction with Shallow Variational Quantum Circuits

variational quantum circuits

quantum error correction

quantum machine learning

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. 

Like their classical counterparts, today’s quantum computers are also easily affected by errors. It is crucial to develop error correction procedures to reduce the effects of the noise in the system. However, the current mainstream error correction codes, like the surface code and toric code, often require a large number of physical qubits, which is not feasible on the NISQ (noisy intermediate-scale quantum) devices where the number of available qubits is limited (< 100 qubits). This work proposed a variational quantum circuit based scheme to discover device-specific error correction codes for the NISQ computing systems in which the encode and recovery (syndrome) layers of our error correction circuit are trained together. Various choices of local optimizers are explored, and performances were compared with each other. We adopted shallow and simple-structured circuits in both encode and recovery layers to alleviate the barren plateau problem in the training of parameterized quantum circuits. The error correction circuit was trained against different kinds of error models, including depolarizing, phase and amplitude damping errors. We adopted a stronger loss constraint. We adopted a stronger loss constraint which, unlike previous attempts, enabled the error correction circuit to achieve higher fidelity on the encoding qubits.

poster

We studied the morphology of quantum vortex surfaces in positron-atom ionization collisions. By conducting a detailed calculation of the position of vortices in the final momentum space with no kinematic restrictions, we could analyze the characteristics of the full four-dimensional vortex structure. This is the first time that these structures are fully calculated for positron-atom collisions. Quantum vortices have been scrutinized both theoretically and experimentally over the last decade for the ionization of atomic and molecular targets by the impact of proton, electron, and positron projectiles. Because they are submanifolds of co-dimension 2 on the phase space of the T-matrix element of the collision, they appear as points in two dimensions, lines in three dimensions, and surfaces in four dimensions. A previous exhaustive study of the ionization of atoms for different positron impact energies allowed us to show how these structures emerge in a collinear geometry as pairs of isolated points. In a subsequent work, we proved that many structures that appeared isolated when studied in two dimensions were part of a single vortex ring. In the current study, we were able to trace the full vortex structure surface.

Vortex surfaces in the ionization of atoms by positron impact

Quantum defects in solids have become a leading candidate for potential qubits. This is due to their long coherence times, the ability to read the spin state through monitoring of luminescence, and spin manipulation through microwave irradiation. These defects can be thought of as artificial molecules, as they share similar properties to fluorescent molecules containing transition metal ions. We are investigating single molecule magnets to see if we can manipulate and detect their spin by monitoring their luminescence. This is similar to the nitrogen vacancy center (NV) defect in diamond; however, we would like to find a single molecule which exhibits this behavior. The other avenue of work we are taking is use the NV center as a means of detecting molecules which do not exhibit this spin dependent luminescence. This would be done by measuring the relaxation rate of the NV center in the presence of these molecules while under an externally applied magnetic field. This relaxation would increase when the energy transitions in the molecule and NV center are on resonance from the Zeeman splitting.

Single Molecule Magnets for Spintronics and Quantum Information Processing

We analyse single hole spin interactions of disorder based quantum dots in p-type silicon MOSFET devices at a temperature of T = 2 K. Through the formation of a double-quantum dot system exhibiting Pauli spin-blockade, we characterize the magnetic field dependence of the leakage current to estimate a spin-orbit length of l_so = 300 nm. This provides support for fast electrical control of single hole spin via a strong spin orbit interaction using a readily scalable platform such as industry silicon MOSFET technology for future quantum information processing applications.


Single spin sensing in silicon p-type Metal-Oxide-Semiconductor Field-Effect Transistors


I introduce an energy constrained approximate twirling operation that can be used to diagonalize effective logical channels in GKP quantum error correction, project states into the GKP code space and construct a dynamical decoupling sequence with displacements pulses to distil the GKP stabilizer Hamiltonians from a suitable substrate-Hamiltonian. The latter is given by an LC-oscillator comprising a superinductance in parallel to a Josephson Junction. I find that moderate resources are sufficient to engineer a GKP Hamiltonian without explicit dissipation or qubit-reset. The ideas and techniques developed in this paper are transferable to general quantum systems and provide a novel perspective on (Floquet-) Hamiltonian engineering.

GKP Error Correction: Finite energy twirling and Hamiltonian engineering via dynamical decoupling

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.

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

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).

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Quantum Error Correction with Shallow Variational Quantum Circuits

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