Imperial College London

Professor Myungshik Kim

Faculty of Natural SciencesDepartment of Physics

Chair in Theoretical Quantum Information Sciences
 
 
 
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Contact

 

+44 (0)20 7594 7754m.kim

 
 
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Location

 

1202Electrical EngineeringSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
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272 results found

Smith AWR, Paige AJ, Kim MS, 2023, Faster variational quantum algorithms with quantum kernel-based surrogate models, Quantum Science and Technology, Vol: 8, ISSN: 2058-9565

We present a new optimization strategy for small-to-intermediate scale variational quantum algorithms (VQAs) on noisy near-term quantum processors which uses a Gaussian process surrogate model equipped with a classically-evaluated quantum kernel. VQAs are typically optimized using gradient-based approaches however these are difficult to implement on current noisy devices, requiring large numbers of objective function evaluations. Our approach shifts this computational burden onto the classical optimizer component of these hybrid algorithms, greatly reducing the number of quantum circuit evaluations required from the quantum processor. We focus on the variational quantum eigensolver (VQE) algorithm and demonstrate numerically that these surrogate models are particularly well suited to the algorithm's objective function. Next, we apply these models to both noiseless and noisy VQE simulations and show that they exhibit better performance than widely-used classical kernels in terms of final accuracy and convergence speed. Compared to the typically-used stochastic gradient-descent approach to VQAs, our quantum kernel-based approach is found to consistently achieve significantly higher accuracy while requiring less than an order of magnitude fewer quantum circuit executions. We analyze the performance of the quantum kernel-based models in terms of the kernels' induced feature spaces and explicitly construct their feature maps. Finally, we describe a scheme for approximating the best-performing quantum kernel using a classically-efficient tensor network representation of its input state and so provide a pathway for scaling this strategy to larger systems.

Journal article

Chen W, Lu Y, Zhang S, Zhang K, Huang G, Qiao M, Su X, Zhang J, Zhang J-N, Banchi L, Kim MS, Kim Ket al., 2023, Scalable and programmable phononic network with trapped ions, Nature Physics, Vol: 19, Pages: 877-883, ISSN: 1745-2473

A network of bosons evolving among different modes while passing through beam splitters and phase shifters has been applied to demonstrate quantum computational advantage. While such networks have mostly been implemented in optical systems using photons, alternative realizations addressing major limitations in photonic systems such as photon loss have been explored recently. Quantized excitations of vibrational modes (phonons) of trapped ions are a promising candidate to realize such bosonic networks. Here, we demonstrate a minimal-loss programmable phononic network in which any phononic state can be deterministically prepared and detected. We realize networks with up to four collective vibrational modes, which can be extended to reveal quantum advantage. We benchmark the performance of the network for an exemplary tomography algorithm using arbitrary multi-mode states with fixed total phonon number. We obtain high reconstruction fidelities for both single- and two-phonon states. Our experiment demonstrates a clear pathway to scale up a phononic network for quantum information processing beyond the limitations of classical and photonic systems.

Journal article

Haug T, Self CN, Kim MS, 2023, Quantum machine learning of large datasets using randomized measurements, Machine Learning: Science and Technology, Vol: 4, Pages: 1-17, ISSN: 2632-2153

Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum kernels are impractical for large datasets as they scale with the square of the dataset size. Here, we measure quantum kernels using randomized measurements. The quantum computation time scales linearly with dataset size and quadratic for classical post-processing. While our method scales in general exponentially in qubit number, we gain a substantial speed-up when running on intermediate-sized quantum computers. Further, we efficiently encode high-dimensional data into quantum computers with the number of features scaling linearly with the circuit depth. The encoding is characterized by the quantum Fisher information metric and is related to the radial basis function kernel. Our approach is robust to noise via a cost-free error mitigation scheme. We demonstrate the advantages of our methods for noisy quantum computers by classifying images with the IBM quantum computer. To achieve further speedups we distribute the quantum computational tasks between different quantum computers. Our method enables benchmarking of quantum machine learning algorithms with large datasets on currently available quantum computers.

Journal article

Lee J, Park J, Kim J, Kim MS, Nha Het al., 2023, Non-Gaussian entanglement criteria for atomic homodyne detection, Physical Review A, Vol: 107, ISSN: 2469-9926

Homodyne measurement is a crucial tool widely used to address continuous variables for bosonic quantum systems. While an ideal homodyne detection provides a powerful analysis, e.g., to effectively measure quadrature amplitudes of light in quantum optics, it relies on the use of a strong reference field, the so-called local oscillator, typically in a coherent state. Such a strong coherent local oscillator may not be readily available, particularly for a massive quantum system like a Bose-Einstein condensate, posing a substantial challenge in dealing with continuous variables appropriately. It is necessary to establish a practical framework that includes the effects of nonideal local oscillators for a rigorous assessment of various quantum tests and applications. We here develop entanglement criteria beyond a Gaussian regime applicable for this realistic homodyne measurement that do not require assumptions on the state of local oscillators. We discuss the working conditions of homodyne detection to effectively detect non-Gaussian quantum entanglement under various states of local oscillators.

Journal article

Haug T, Kim M, 2023, Scalable measures of magic for quantum computers, PRX Quantum, Vol: 4, ISSN: 2691-3399

Nonstabilizerness or magic resource characterizes the amount of non-Clifford operations needed to prepare quantum states. It is a crucial resource for quantum computing and a necessary condition for quantum advantage. However, quantifying magic resource beyond a few qubits has been a major challenge. Here, we introduce efficient measures of magic resource for pure quantum states with a sampling cost that is independent of the number of qubits. Our method uses Bell measurements over two copies of a state, which we implement in experiment together with a cost-free error-mitigation scheme. We show the transition of classically simulable stabilizer states into intractable quantum states on the IonQ quantum computer. For applications, we efficiently distinguish stabilizer and nonstabilizer states with low measurement cost even in the presence of experimental noise. Further, we propose a variational quantum algorithm to maximize our measure via the shift rule. Our algorithm can be free of barren plateaus even for highly expressible variational circuits. Finally, we experimentally demonstrate a Bell-measurement protocol for the stabilizer Rényi entropy as well as the Wallach-Meyer entanglement measure. Our results pave the way to understanding the nonclassical power of quantum computers, quantum simulators, and quantum many-body systems.

Journal article

Hanks M, Kim MS, 2022, Fault tolerance in qudit circuit design, PHYSICAL REVIEW A, Vol: 106, ISSN: 2469-9926

Journal article

Haug T, Kim MS, 2022, Natural parametrized quantum circuit, PHYSICAL REVIEW A, Vol: 106, ISSN: 2469-9926

Journal article

Bellini M, Kwon H, Biagi N, Francesconi S, Zavatta A, Kim MSet al., 2022, Demonstrating quantum microscopic reversibility using coherent states of light, Physical Review Letters, Vol: 129, Pages: 1-6, ISSN: 0031-9007

The principle of microscopic reversibility lies at the core of fluctuation theorems, which have extended our understanding of the second law of thermodynamics to the statistical level. In the quantum regime, however, this elementary principle should be amended as the system energy cannot be sharply determined at a given quantum phase space point. In this Letter, we propose and experimentally test a quantum generalization of the microscopic reversibility when a quantum system interacts with a heat bath through energy-preserving unitary dynamics. Quantum effects can be identified by noting that the backward process is less likely to happen in the existence of quantum coherence between the system’s energy eigenstates. The experimental demonstration has been realized by mixing coherent and thermal states in a beam splitter, followed by heterodyne detection in an optical setup. We verify that the quantum modification for the principle of microscopic reversibility is critical in the low-temperature limit, while the quantum-to-classical transition is observed as the temperature of the thermal field gets higher.

Journal article

Koukoulekidis N, Jee H, Jennings D, Kim M, Kwon Het al., 2022, Faster Born probability estimation via gate merging and frame optimisation, Quantum, Vol: 6, Pages: 838-838, ISSN: 2521-327X

Outcome probability estimation via classical methods is an important task for validating quantum computing devices. Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling, where the amount of negativity present in the circuit frame representation quantifies the overhead on the number of samples required to achieve a certain precision. In this paper, we propose two classical sub-routines: circuit gate merging and frame optimisation, which optimise the circuit representation to reduce the sampling overhead. We show that the runtimes of both sub-routines scale polynomially in circuit size and gate depth. Our methods are applicable to general circuits, regardless of generating gate sets, qudit dimensions and the chosen frame representations for the circuit components. We numerically demonstrate that our methods provide improved scaling in the negativity overhead for all tested cases of random circuits with Clifford+T and Haar-random gates, and that the performance of our methods compares favourably with prior quasi-probability simulators as the number of non-Clifford gates increases.

Journal article

Koukoulekidis N, Kwon H, Jee HH, Jennings D, Kim MSet al., 2022, Faster Born probability estimation via gate merging and frame optimisation, Quantum, Vol: 6, Pages: 838-838, ISSN: 2521-327X

Outcome probability estimation via classical methods is an important task for validating quantum computing devices. Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling, where the amount of negativity present in the circuit frame representation quantifies the overhead on the number of samples required to achieve a certain precision. In this paper, we propose two classical sub-routines: circuit gate merging and frame optimisation, which optimise the circuit representation to reduce the sampling overhead. We show that the runtimes of both sub-routines scale polynomially in circuit size and gate depth. Our methods are applicable to general circuits, regardless of generating gate sets, qudit dimensions and the chosen frame representations for the circuit components. We numerically demonstrate that our methods provide improved scaling in the negativity overhead for all tested cases of random circuits with Clifford+T and Haar-random gates, and that the performance of our methods compares favourably with prior quasi-probability simulators as the number of non-Clifford gates increases.

Journal article

Bressanini G, Kwon H, Kim MS, 2022, Noise thresholds for classical simulability of nonlinear boson sampling, Physical Review A: Atomic, Molecular and Optical Physics, Vol: 106, Pages: 1-9, ISSN: 1050-2947

Boson sampling, a computational problem conjectured to be hard to simulate on a classical machine, is a promising candidate for an experimental demonstration of quantum advantage using bosons. However, inevitable experimental noise and imperfections, such as loss in the interferometer and random counts at the detectors, could challenge the sampling task from entering the regime where quantum advantage is achievable. In this work we introduce higher-order nonlinearities as a means to enhance the computational complexity of the problem and the protocol's robustness against noise, i.e., to increase the noise threshold that allows us to perform an efficient classical simulation of the problem. Using a phase-space method based on the negativity volume of the relevant quasiprobability distributions, we establish a necessary nonclassicality condition that any experimental proof of quantum advantage must satisfy. Our results indicate that the addition of single-mode Kerr nonlinearity at the input-state preparation level, while retaining a linear-optical evolution, makes the boson-sampling protocol more robust against noise and consequently relaxes the constraints on the noise parameters required to show quantum advantage.

Journal article

Zhang H, Wan L, Haug T, Mok W-K, Paesani S, Shi Y, Cai H, Chin LK, Karim MF, Xiao L, Luo X, Gao F, Dong B, Assad S, Kim MS, Laing A, Kwek LC, Liu AQet al., 2022, Resource-efficient high-dimensional subspace teleportation with a quantum autoencoder., Science Advances, Vol: 8, Pages: 1-11, ISSN: 2375-2548

Quantum autoencoders serve as efficient means for quantum data compression. Here, we propose and demonstrate their use to reduce resource costs for quantum teleportation of subspaces in high-dimensional systems. We use a quantum autoencoder in a compress-teleport-decompress manner and report the first demonstration with qutrits using an integrated photonic platform for future scalability. The key strategy is to compress the dimensionality of input states by erasing redundant information and recover the initial states after chip-to-chip teleportation. Unsupervised machine learning is applied to train the on-chip autoencoder, enabling the compression and teleportation of any state from a high-dimensional subspace. Unknown states are decompressed at a high fidelity (~0.971), obtaining a total teleportation fidelity of ~0.894. Subspace encodings hold great potential as they support enhanced noise robustness and increased coherence. Laying the groundwork for machine learning techniques in quantum systems, our scheme opens previously unidentified paths toward high-dimensional quantum computing and networking.

Journal article

Song W, Lim Y, Jeong K, Lee J, Park JJ, Kim MS, Bang Jet al., 2022, Polynomial T-depth quantum solvability of noisy binary linear problem: from quantum-sample preparation to main computation, New Journal of Physics, Vol: 24, Pages: 1-11, ISSN: 1367-2630

The noisy binary linear problem (NBLP) is known as a computationally hard problem, and therefore, it offers primitives for post-quantum cryptography. An efficient quantum NBLP algorithm that exhibits a polynomial quantum sample and time complexities has recently been proposed. However, the algorithm requires a large number of samples to be loaded in a highly entangled state and it is unclear whether such a precondition on the quantum speedup can be obtained efficiently. Here, we present a complete analysis of the quantum solvability of the NBLP by considering the entire algorithm process, namely from the preparation of the quantum sample to the main computation. By assuming that the algorithm runs on 'fault-tolerant' quantum circuitry, we introduce a reasonable measure of the computational time cost. The measure is defined in terms of the overall number of T gate layers, referred to as T-depth complexity. We show that the cost of solving the NBLP can be polynomial in the problem size, at the expense of an exponentially increasing logical qubits.

Journal article

Ma Y, Pace MCC, Kim MS, 2022, Unifying the sorensen-molmer gate and the milburn gate with an optomechanical example, Physical Review A: Atomic, Molecular and Optical Physics, Vol: 106, ISSN: 1050-2947

The Sørensen-Mølmer gate and Milburn gate are two geometric phase gates, generating nonlinear self-interaction of a target mode via its interaction with an auxiliary mechanical mode, in the continuous- and pulsed-interaction regimes, respectively. In this paper we aim at unifying the two gates by demonstrating that the Sørensen-Mølmer gate is the continuous limit of the Milburn gate, emphasizing the geometrical interpretation in the mechanical phase space. We explicitly consider imperfect gate parameters, focusing on relative errors in time for the Sørensen-Mølmer gate and in phase angle increment for the Milburn gate. We find that, although the purities of the final states increase for the two gates upon reducing the interaction strength together with traversing the mechanical phase space multiple times, the fidelities behave differently. We point out that the difference exists because the interaction strength depends on the relative error when taking the continuous limit from the pulsed regime, thereby unifying the mathematical framework of the two gates. We demonstrate this unification in the example of an optomechanical system, where mechanical dissipation is also considered. We highlight that the unified framework facilitates our method of deriving the dynamics of the continuous-interaction regime without solving differential equations.

Journal article

Chevalier H, Kwon H, Khosla KE, Pikovski I, Kim MSet al., 2022, Many-body probes for quantum features of spacetime, AVS Quantum Science, Vol: 4, Pages: 1-10, ISSN: 2639-0213

Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work, we inspect the capacity for correlated many-body systems to probe non-classicalities of spacetime through modifications of the commutation relations. We find an analytic derivation of the dynamics for a single mode light field interacting with a single mechanical oscillator and with coupled oscillators to first order corrections to the commutation relations. Our solution is valid for any coupling function as we work out the full Magnus expansion. We numerically show that it is possible to have superquadratic scaling of a nonstandard phase term, arising from the modification to the commutation relations, with coupled mechanical oscillators.

Journal article

Thekkadath G, Sempere-Llagostera S, Bell B, Patel R, Kim M, Walmsley Iet al., 2022, Experimental demonstration of Gaussian boson sampling with displacement, PRX Quantum, Vol: 3, ISSN: 2691-3399

Gaussian boson sampling (GBS) is a quantum sampling task in which one has to draw samples from the photon-number distribution of a large-dimensional nonclassical squeezed state of light. In an effort to make this task intractable for a classical computer, experiments building GBS machines have mainly focused on increasing the dimensionality and squeezing strength of the nonclassical light. However, no experiment has yet demonstrated the ability to displace the squeezed state in phase space, which is generally required for practical applications of GBS. In this work, we build a GBS machine that achieves the displacement by injecting a laser beam alongside a two-mode squeezed vacuum state into a 15-mode interferometer. We focus on two new capabilities. Firstly, we use the displacement to reconstruct the multimode Gaussian state at the output of the interferometer. Our reconstruction technique is in situ and requires only three measurement settings regardless of the state dimension. Secondly, we study how the addition of classical laser light in our GBS machine affects the complexity of sampling its output photon statistics. We introduce and validate approximate semiclassical models that reduce the computational cost when a significant fraction of the detected light is classical.

Journal article

Song W, Lim Y, Jeong K, Ji Y-S, Lee J, Kim J, Kim MS, Bang Jet al., 2022, Quantum solvability of noisy linear problems by divide-and-conquer strategy, Quantum Science and Technology, Vol: 7, ISSN: 2058-9565

Noisy linear problems have been studied in various science and engineering disciplines. A class of 'hard' noisy linear problems can be formulated as follows: Given a matrix $\hat{A}$ and a vector b constructed using a finite set of samples, a hidden vector or structure involved in b is obtained by solving a noise-corrupted linear equation $\hat{A}\mathbf{x}\approx \mathbf{b}+\boldsymbol{\eta }$, where η is a noise vector that cannot be identified. For solving such a noisy linear problem, we consider a quantum algorithm based on a divide-and-conquer strategy, wherein a large core process is divided into smaller subprocesses. The algorithm appropriately reduces both the computational complexities and size of a quantum sample. More specifically, if a quantum computer can access a particular reduced form of the quantum samples, polynomial quantum-sample and time complexities are achieved in the main computation. The size of a quantum sample and its executing system can be reduced, e.g., from exponential to sub-exponential with respect to the problem length, which is better than other results we are aware. We analyse the noise model conditions for such a quantum advantage, and show when the divide-and-conquer strategy can be beneficial for quantum noisy linear problems.

Journal article

Tang H, Banchi L, Wang T-Y, Shang X-W, Tan X, Zhou W-H, Feng Z, Pal A, Li H, Hu C-Q, Kim MS, Jin X-Met al., 2022, Generating Haar-uniform randomness using stochastic quantum walks on a photonic chip, Physical Review Letters, Vol: 128, ISSN: 0031-9007

As random operations for quantum systems are intensively used in various quantum information tasks, a trustworthy measure of the randomness in quantum operations is highly demanded. The Haar measure of randomness is a useful tool with wide applications, such as boson sampling. Recently, a theoretical protocol was proposed to combine quantum control theory and driven stochastic quantum walks to generate Haar-uniform random operations. This opens up a promising route to converting classical randomness to quantum randomness. Here, we implement a two-dimensional stochastic quantum walk on the integrated photonic chip and demonstrate that the average of all distribution profiles converges to the even distribution when the evolution length increases, suggesting the 1-pad Haar-uniform randomness. We further show that our two-dimensional array outperforms the one-dimensional array of the same number of waveguide for the speed of convergence. Our Letter demonstrates a scalable and robust way to generate Haar-uniform randomness that can provide useful building blocks to boost future quantum information techniques.

Journal article

Kwon H, Mukherjee R, Kim MS, 2022, Reversing Lindblad dynamics via continuous Petz recovery map, Physical Review Letters, Vol: 128, Pages: 1-7, ISSN: 0031-9007

An important issue in developing quantum technology is that quantum states are so sensitive to noise. We propose a protocol that introduces reverse dynamics, in order to precisely control quantum systems against noise described by the Lindblad master equation. The reverse dynamics can be obtained by constructing the Petz recovery map in continuous time. By providing the exact form of the Hamiltonian and jump operators for the reverse dynamics, we explore the potential of utilizing the near-optimal recovery of the Petz map in controlling noisy quantum dynamics. While time-dependent dissipation engineering enables us to fully recover a single quantum trajectory, we also design a time-independent recovery protocol to protect encoded quantum information against decoherence. Our protocol can efficiently suppress only the noise part of dynamics thereby providing an effective unitary evolution of the quantum system.

Journal article

Thekkadath GS, Bell BA, Patel RB, Kim MS, Walmsley IAet al., 2022, Measuring the joint spectral mode of photon pairs using intensity interferometry, Physical Review Letters, Vol: 128, Pages: 1-6, ISSN: 0031-9007

The ability to manipulate and measure the time-frequency structure of quantum light is useful for information processing and metrology. Measuring this structure is also important when developing quantum light sources with high modal purity that can interfere with other independent sources. Here, we present and experimentally demonstrate a scheme based on intensity interferometry to measure the joint spectral mode of photon pairs produced by spontaneous parametric down-conversion. We observe correlations in the spectral phase of the photons due to chirp in the pump. We show that our scheme can be combined with stimulated emission tomography to quickly measure their mode using bright classical light. Our scheme does not require phase stability, nonlinearities, or spectral shaping and thus is an experimentally simple way of measuring the modal structure of quantum light.

Journal article

Ma Y, Guff T, Morley GW, Pikovski I, Kim MSet al., 2022, Limits on inference of gravitational entanglement, Physical Review Research, Vol: 4, Pages: 1-7, ISSN: 2643-1564

Combining gravity with quantum mechanics remains one of the biggest challenges of physics. In the past years, experiments with opto-mechanical systems have been proposed that may give indirect clues about the quantum nature of gravity. In a recent variation of such tests [D. Carney et al., Phys.Rev.X Quantum 2, 030330 (2021)], the authors ropose to gravitationally entangle an atom interferometer with a mesoscopic oscillator. The interaction results in periodic drops and revivals of the interferometeric visibility, which under specific assumptions indicate the gravitational generation of entanglement. Here we study semi-classical models of the atom interferometer that can reproduce the same effect. We show that the core signature – periodic collapses and revivals of the visibility – can appear if the atom is subject to a random unitary channel, including the casewhere the oscillator is fully classical and situations even without explicit modelling of the oscillator. We also show that the non-classicality of the oscillator vanishes unless the system is very close to its ground state, and even when the system is in the ground state, the non-classicality is limitedby the coupling strength. Our results thus indicate that deducing ntanglement from the proposed experiment is very challenging, since fulfilling and verifying the non-classicality assumptions is a significant challenge on its own right.

Journal article

Thekkadath GS, Sempere-Llagostera S, Bell BA, Patel RB, Kim MS, Walmsley IAet al., 2022, Experimental demonstration of Gaussian boson sampling with displacement

We inject squeezed vacuum and weak coherent light into a multiport interferometer and measure the output photon statistics. Our work explores the capabilities of a displacement field in Gaussian boson sampling.

Conference paper

Smith AWR, Khosla KE, Self CN, Kim MSet al., 2021, Qubit readout error mitigation with bit-flip averaging, Science Advances, Vol: 7, Pages: 1-10, ISSN: 2375-2548

Quantum computers are becoming increasingly accessible, and may soonoutperform classical computers for useful tasks. However, qubit readout errorsremain a significant hurdle to running quantum algorithms on current devices.We present a scheme to more efficiently mitigate these errors on quantumhardware and numerically show that our method consistently gives advantage overprevious mitigation schemes. Our scheme removes biases in the readout errorsallowing a general error model to be built with far fewer calibrationmeasurements. Specifically, for reading out $n$-qubits we show a factor of$2^n$ reduction in the number of calibration measurements without sacrificingthe ability to compensate for correlated errors. Our approach can be combinedwith, and simplify, other mitigation methods allowing tractable mitigation evenfor large numbers of qubits.

Journal article

Ma Y, Kim MS, Stickler BA, 2021, Torque-free manipulation of nanoparticle rotations via embedded spins, Physical Review B: Condensed Matter and Materials Physics, Vol: 104, ISSN: 1098-0121

Spin angular momentum and mechanical rotation both contribute to the total angular momentum of rigid bodies, leading to spin-rotational coupling via the Einstein–de Haas and Barnett effects. Here, we show that the revolutions of symmetric nanorotors can be strongly affected by a small number of intrinsic spins. The resulting dynamics are observable with freely rotating nanodiamonds with embedded nitrogen-vacancy centers and persist for realistically shaped near-symmetric particles, opening the door to torque-free schemes to control their rotations at the quantum level.

Journal article

Haug T, Bharti K, Kim MS, 2021, Capacity and quantum geometry of parametrized quantum circuits, PRX Quantum, Vol: 2, Pages: 1-14, ISSN: 2691-3399

To harness the potential of noisy intermediate-scale quantum devices, it is paramount to find the best type of circuits to run hybrid quantum-classical algorithms. Key candidates are parametrized quantum circuits that can be effectively implemented on current devices. Here, we evaluate the capacity and trainability of these circuits using the geometric structure of the parameter space via the effective quantum dimension, which reveals the expressive power of circuits in general as well as of particular initialization strategies. We assess the expressive power of various popular circuit types and find striking differences depending on the type of entangling gates used. Particular circuits are characterized by scaling laws in their expressiveness. We identify a transition in the quantum geometry of the parameter space, which leads to a decay of the quantum natural gradient for deep circuits. For shallow circuits, the quantum natural gradient can be orders of magnitude larger in value compared to the regular gradient; however, both of them can suffer from vanishing gradients. By tuning a fixed set of circuit parameters to randomized ones, we find a region where the circuit is expressive but does not suffer from barren plateaus, hinting at a good way to initialize circuits. We show an algorithm that prunes redundant parameters of a circuit without affecting its effective dimension. Our results enhance the understanding of parametrized quantum circuits and can be immediately applied to improve variational quantum algorithms.

Journal article

Vovrosh J, Khosla KE, Greenaway S, Self C, Kim MS, Knolle Jet al., 2021, Simple mitigation of global depolarizing errors in quantum simulations., Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, Vol: 104, Pages: 1-8, ISSN: 1539-3755

To get the best possible results from current quantum devices error mitigation is essential. In this work we present a simple but effective error mitigation technique based on the assumption that noise in a deep quantum circuit is well described by global depolarizing error channels. By measuring the errors directly on the device, we use an error model ansatz to infer error-free results from noisy data. We highlight the effectiveness of our mitigation via two examples of recent interest in quantum many-body physics: entanglement measurements and real-time dynamics of confinement in quantum spin chains. Our technique enables us to get quantitative results from the IBM quantum computers showing signatures of confinement, i.e., we are able to extract the meson masses of the confined excitations which were previously out of reach. Additionally, we show the applicability of this mitigation protocol in a wider setting with numerical simulations of more general tasks using a realistic error model. Our protocol is device-independent, simply implementable, and leads to large improvements in results if the global errors are well described by depolarization.

Journal article

Lee S-W, Im D-G, Kim Y-H, Nha H, Kim MSet al., 2021, Quantum teleportation is a reversal of quantum measurement, Physical Review Research, Vol: 3, Pages: 1-16, ISSN: 2643-1564

We introduce a generalized concept of quantum teleportation in the framework of quantum measurement and reversing operation. Our framework makes it possible to find an optimal protocol for quantum teleportation enabling a faithful transfer of unknown quantum states with maximum success probability up to the fundamental limit of the no-cloning theorem. Moreover, an optimized protocol in this generalized approach allows us to overcome noise in quantum channel beyond the reach of existing teleportation protocols without requiring extra qubit resources. Our proposed framework is applicable to multipartite quantum communications and primitive functionalities in scalable quantum architectures.

Journal article

Stickler BA, Hornberger K, Kim MS, 2021, Quantum rotations of nanoparticles, NATURE REVIEWS PHYSICS, Vol: 3, Pages: 589-597

Journal article

Self CN, Khosla KE, Smith AWR, Sauvage F, Haynes PD, Knolle J, Mintert F, Kim MSet al., 2021, Variational quantum algorithm with information sharing, npj Quantum Information, Vol: 7, ISSN: 2056-6387

We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining multi-dimensional energy surfaces for small molecules and a spin model. Our method solves related variational problems in parallel by exploiting the global nature of Bayesian optimisation and sharing information between different optimisers. Parallelisation makes our method ideally suited to the next generation of variational problems with many physical degrees of freedom. This addresses a key challenge in scaling-up quantum algorithms towards demonstrating quantum advantage for problems of real-world interest.

Journal article

Smith AWR, Gray J, Kim MS, 2021, Efficient quantum state sample tomography with basis-dependent neural networks, PRX Quantum, Vol: 2, Pages: 1-15, ISSN: 2691-3399

We use a metalearning neural-network approach to analyze data from a measured quantum state. Once our neural network has been trained, it can be used to efficiently sample measurements of the state in measurement bases not contained in the training data. These samples can be used to calculate expectation values and other useful quantities. We refer to this process as “state sample tomography.” We encode the state’s measurement outcome distributions using an efficiently parameterized generative neural network. This allows each stage in the tomography process to be performed efficiently even for large systems. Our scheme is demonstrated on recent IBM Quantum devices, producing a model for a six-qubit state’s measurement outcomes with a predictive accuracy (classical fidelity) greater than 95% for all test cases using only 100 random measurement settings as opposed to the 729 settings required for standard full tomography using local measurements. This reduction in the required number of measurements scales favorably, with training data in 200 measurement settings, yielding a predictive accuracy greater than 92% for a ten-qubit state where 59 049 settings are typically required for full local measurement-based quantum state tomography. A reduction in the number of measurements by a factor, in this case, of almost 600 could allow for estimations of expectation values and state fidelities in practicable times on current quantum devices.

Journal article

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