# Kosuke Mitarai's research while affiliated with Osaka University and other places

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## Publications (54)

Pricing a multi-asset derivative is an important problem in financial engineering, both theoretically and practically. Although it is suitable to numerically solve partial differential equations to calculate the prices of certain types of derivatives, the computational complexity increases exponentially as the number of underlying assets increases...

The variational quantum eigensolver (VQE), which has attracted attention as a promising application of noisy intermediate-scale quantum devices, finds a ground state of a given Hamiltonian by variationally optimizing the parameters of quantum circuits called Ansätze. Since the difficulty of the optimization depends on the complexity of the problem...

The demonstration of quantum error correction (QEC) is one of the most important milestones in the realization of fully-fledged quantum computers. Toward this, QEC experiments using the surface codes have recently been actively conducted. However, it has not yet been realized to protect logical quantum information beyond the physical coherence time...

Implementing time evolution operators on quantum circuits is important for quantum simulation. However, the standard way, Trotterization, requires a huge numbers of gates to achieve desirable accuracy. Here, we propose a local variational quantum compilation (LVQC) algorithm, which allows to accurately and efficiently compile a time evolution opera...

Variational quantum eigensolver (VQE) is an appealing candidate for the application of near-term quantum computers. A technique introduced in [Higgot et al., Quantum 3, 156 (2019)10.22331/q-2019-07-01-156], which is named variational quantum deflation (VQD), has extended the ability of the VQE framework for finding excited states of a Hamiltonian....

Current quantum computers are limited in the number of qubits and coherence time, constraining the algorithms executable with sufficient fidelity. Variational quantum eigensolver (VQE) is an algorithm to find an approximate ground state of a quantum system and expected to work on even such a device. The deep VQE [K. Fujii, et al., arXiv:2007.10917]...

t-Stochastic Neighbor Embedding (t-SNE) is a non-parametric data visualization method in classical machine learning. It maps the data from the high-dimensional space into a low-dimensional space, especially a two-dimensional plane, while maintaining the relationship, or similarities, between the surrounding points. In t-SNE, the initial position of...

Variational quantum eigensolver (VQE) is regarded as a promising candidate of hybrid quantum-classical algorithm for the near-term quantum computers. Meanwhile, VQE is confronted with a challenge that statistical error associated with the measurement as well as systematic error could significantly hamper the optimization. To circumvent this issue,...

Quantum circuits that are classically simulatable tell us when quantum computation becomes less powerful than or equivalent to classical computation. Such classically simulatable circuits are of importance because they illustrate what makes universal quantum computation different from classical computers. In this work, we propose a novel family of...

Measuring expectation values of observables is an essential ingredient in variational quantum algorithms. A practical obstacle is the necessity of a large number of measurements for statistical convergence to meet requirements of precision, such as chemical accuracy in the application to quantum chemistry computations. Here we propose an algorithm...

The kernel trick allows us to employ high-dimensional feature space for a machine learning task without explicitly storing features. Recently, the idea of utilizing quantum systems for computing kernel functions using interference has been demonstrated experimentally. However, the dimension of feature spaces in those experiments have been smaller t...

Variational quantum algorithms (VQA) have been proposed as one of the most promising approaches to demonstrate quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, it has been unclear whether VQA algorithms can maintain quantum advantage under the intrinsic noise of the NISQ devices, which deteriorates the quantumness. Her...

We propose a sampling-based simulation for fault-tolerant quantum error correction under coherent noise. A mixture of incoherent and coherent noise, possibly due to over-rotation, is decomposed into Clifford channels with a quasiprobability distribution. Then, an unbiased estimator of the logical error probability is constructed by sampling Cliffor...

Quantum kernel method is one of the key approaches to quantum machine learning, which has the advantages that it does not require optimization and has theoretical simplicity. By virtue of these properties, several experimental demonstrations and discussions of the potential advantages have been developed so far. However, as is the case in classical...

To explore the possibilities of a near-term intermediate-scale quantum algorithm and long-term fault-tolerant quantum computing, a fast and versatile quantum circuit simulator is needed. Here, we introduce Qulacs, a fast simulator for quantum circuits intended for research purpose. We show the main concepts of Qulacs, explain how to use its feature...

Variational quantum eigensolver (VQE), which attracts attention as a promising application of noisy intermediate-scale quantum devices, finds a ground state of a given Hamiltonian by variationally optimizing the parameters of quantum circuits called ansatz. Since the difficulty of the optimization depends on the complexity of the problem Hamiltonia...

Reservoir computing is a framework used to exploit natural nonlinear dynamics with many degrees of freedom, which is called a reservoir, for a machine learning task. Here we introduce the NMR implementation of quantum reservoir computing and quantum extreme learning machine using the nuclear quantum reservoir. The implementation utilizes globally c...

Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers, owing to the extremely high computational cost. Quantum computers promise a solution, although fault-tolerant quantum computers will probably not be available in the near future. Current quantum de...

Due to the linearity of quantum operations, it is not straightforward to implement nonlinear transformations on a quantum computer, making some practical tasks like a neural network hard to be achieved. In this work, we define a task called nonlinear transformation of complex amplitudes and provide an algorithm to achieve this task. Specifically, w...

We propose a method for learning temporal data using a parametrized quantum circuit. We use the circuit that has a similar structure as the recurrent neural network, which is one of the standard approaches employed for this type of machine learning task. Some of the qubits in the circuit are utilized for memorizing past data, while others are measu...

We propose a sampling-based simulation for fault-tolerant quantum error correction under coherent noise. A mixture of incoherent and coherent noise, possibly due to over-rotation, is decomposed into Clifford channels with a quasi-probability distribution. Then, an unbiased estimator of the logical error probability is constructed by sampling Cliffo...

Quantum circuits that are classically simulatable tell us when quantum computation becomes less powerful than or equivalent to classical computation. Such classically simulatable circuits are of importance because they illustrate what makes universal quantum computation different from classical computers. In this work, we propose a novel family of...

We show a certain kind of non-local operations can be simulated by sampling a set of local operations with a quasi-probability distribution when the task of a quantum circuit is to evaluate an expectation value of observables. Utilizing the result, we describe a strategy to decompose a two-qubit gate to a sequence of single-qubit operations. Requir...

As the hardware technology for quantum computing advances, its possible applications are actively searched and developed. However, such applications still suffer from the noise on quantum devices, in particular when using two-qubit gates whose fidelity is relatively low. One way to overcome this difficulty is to substitute such non-local operations...

We propose a method for learning temporal data using a parametrized quantum circuit. We use the circuit that has a similar structure as the recurrent neural network which is one of the standard approaches employed for this type of machine learning task. Some of the qubits in the circuit are utilized for memorizing past data, while others are measur...

Applications such as simulating large quantum systems or solving large-scale linear algebra problems are immensely challenging for classical computers due their extremely high computational cost. Quantum computers promise to unlock these applications, although fault-tolerant quantum computers will likely not be available for several years. Currentl...

We propose a quantum-classical hybrid algorithm to simulate the nonequilibrium steady state of an open quantum many-body system, named the dissipative-system variational quantum eigensolver (dVQE). To employ the variational optimization technique for a unitary quantum circuit, we map a mixed state into a pure state with a doubled number of qubits a...

We introduce Qulacs, a fast simulator for quantum circuits intended for research purpose. To explore the possibilities of a near-term intermediate-scale quantum algorithm and long-term fault-tolerant quantum computing, a fast and versatile quantum circuit simulator is needed. Herein we show the main concepts of Qulacs, explain how to use its featur...

Variational quantum algorithms are appealing applications of near-term quantum computers. However, there are two major issues to be solved, that is, we need an efficient initialization strategy for parametrized quantum circuit and to know the limitation of the algorithms by benchmarking it on large scale problems. Here, we propose a perturbative ap...

We propose an orbital optimized method for unitary coupled cluster theory (OO-UCC) within the variational quantum eigensolver (VQE) framework for quantum computers. OO-UCC variationally determines the coupled cluster amplitudes and also molecular orbital coefficients. Owing to its fully variational nature, first-order properties are readily availab...

We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate variational quantum eigensolver (VQE) with reducing the dimensions of the system, where the interactions between divided subsystems are taken as an effective Hamiltonian expanded...

We developed an advanced 2ω method for thermal conductivity (κ) measurements that is also applicable to samples with a wide range of thicknesses, to which the flash method cannot be applied. The conventional 2ω method, which features a simple setup combined with thermoreflectance, is a κ measurement method for thin films on substrates. However, it...

As the hardware technology for quantum computing advances, its possible applications are actively searched and developed. However, such applications still suffer from the noise on quantum devices, in particular when using two-qubit gates whose fidelity is relatively low. One way to overcome this difficulty is to substitute such non-local operations...

Variational quantum eigensolver (VQE) is an appealing candidate for the application of near-term quantum computers. A technique introduced in [Higgot et al., Quantum 3, 156 (2019)], which is named variational quantum deflation (VQD), has extended the ability of the VQE framework for finding excited states of a Hamiltonian. However, no method to eva...

The variational quantum eigensolver (VQE) and its variants, which is a method for finding eigenstates and eigenenergies of a given Hamiltonian, are appealing applications of near-term quantum computers. Although the eigenenergies are certainly important quantities which determine properties of a given system, their derivatives with respect to param...

We employ so-called quantum kernel estimation to exploit complex quantum dynamics of solid-state nuclear magnetic resonance for machine learning. We propose to map an input to a feature space by input-dependent Hamiltonian evolution, and the kernel is estimated by the interference of the evolution. Simple machine learning tasks, namely one-dimensio...

The variational quantum eigensolver (VQE), a variational algorithm to obtain an approximated ground state of a given Hamiltonian, is an appealing application of near-term quantum computers. To extend the framework to excited states, we here propose an algorithm, the subspace-search variational quantum eigensolver (SSVQE). This algorithm searches a...

We propose an orbital optimized method for unitary coupled cluster theory (OO-UCC) within the variational quantum eigensolver (VQE) framework for quantum computers. OO-UCC variationally determines the coupled cluster amplitudes and also molecular orbital coefficients. Owing to its fully variational nature, first-order properties are readily availab...

We show a certain kind of non-local operations can be decomposed into a sequence of local operations. Utilizing the result, we describe a strategy to decompose a general two-qubit gate to a sequence of single-qubit operations. Required operations are projective measurement of a qubit in Pauli basis, and $\pi/2$ rotation around x, y, and z axes. The...

We propose a quantum-classical hybrid algorithm to simulate the non-equilibrium steady state of an open quantum many-body system, named the dissipative-system Variational Quantum Eigensolver (dVQE). To employ the variational optimization technique for a unitary quantum circuit, we map a mixed state into a pure state with a doubled number of qubits...

In quantum computing, the indirect measurement of unitary operators such as the Hadamard test plays a significant role in many algorithms. However, in certain cases, the indirect measurement can be reduced to the direct measurement, where a quantum state is destructively measured. Here, we investigate under what conditions such a replacement is pos...

The variational quantum eigensolver (VQE) and its variants, which is a method for finding eigenstates and eigenenergies of a given Hamiltonian, are appealing applications of near-term quantum computers. Although the eigenenergies are certainly important quantities which determines properties of a given system, their derivatives with respect to para...

The variational quantum eigensolver (VQE) is an attractive possible application of near-term quantum computers. Originally, the aim of the VQE is to find a ground state for a given specific Hamiltonian. It is achieved by minimizing the expectation value of the Hamiltonian with respect to an ansatz state by tuning parameters θ on a quantum circuit,...

Quantum simulation is one of the key applications of quantum computing, which can accelerate research and development in chemistry, material science, etc. Here, we propose an efficient method to simulate the time evolution driven by a static Hamiltonian, named subspace variational quantum simulator (SVQS). SVQS employs the subspace-search variation...

Many quantum algorithms, such as the Harrow-Hassidim-Lloyd (HHL) algorithm, depend on oracles that efficiently encode classical data into a quantum state. The encoding of the data can be categorized into two types: analog encoding, where the data are stored as amplitudes of a state, and digital encoding, where they are stored as qubit strings. The...

In quantum computing, the indirect measurement of unitary operators such as the Hadamard test plays a significant role in many algorithms. However, in certain cases, the indirect measurement can be reduced to the direct measurement, where a quantum state is destructively measured. Here we investigate in what cases such a replacement is possible and...

The variational quantum eigensolver (VQE), a variational algorithm to obtain an approximated ground state of a given Hamiltonian, is an appealing application of near-term quantum computers. The original work [Peruzzo et al.; \textit{Nat. Commun.}; \textbf{5}, 4213 (2014)] focused only on finding a ground state, whereas the excited states can also i...

The variational quantum eigensolver (VQE) is an attracting possible application of near-term quantum computers. Originally, the aim of the VQE is to find a ground state for a given specific Hamiltonian. It is achieved by minimizing the expectation value of the Hamiltonian with respect to an ansatz state by tuning parameters \(\bm{\theta}\) on a qua...

We experimentally demonstrate quantum machine learning using NMR based on a framework of quantum reservoir computing. Reservoir computing is for exploiting natural nonlinear dynamics with large degrees of freedom, which is called a reservoir, for a machine learning purpose. Here we propose a concrete physical implementation of a quantum reservoir u...

Many quantum algorithms, such as Harrow-Hassidim-Lloyd (HHL) algorithm, depend on oracles that efficiently encode classical data into a quantum state. The encoding of the data can be categorized into two types; analog-encoding where the data are stored as amplitudes of a state, and digital-encoding where they are stored as qubit-strings. The former...

Quantum reservoir computing provides a framework for exploiting the natural dynamics of quantum systems as a computational resource. It can implement real-time signal processing and solve temporal machine learning problems in general, which requires memory and nonlinear mapping of the recent input stream using the quantum dynamics in computational...

We propose a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, which we call quantum circuit learning. A quantum circuit driven by our framework learns a given task by tuning parameters implemented on it. The iterative optimization of the parameters allows us to circumvent the high-depth circuit. Theoretical i...

## Citations

... ð0Þcould be chosen as the better guess77,78 . Similarly to the SGD, the SGLBO computes an unbiased estimatorĝ ðtÞ of the gradient of the cost function at the pointθ ðtÞ , using 2s ðtÞ grad measurement shots due to Eq.(13). ...

... On the other hand, extensions of this work may include the implementation of error mitigation strategies based on symmetry [79], the description of low-energy excitations over the ground-state, for which HMFT has a well-stablished framework [35,36], or the benchmark of optimization routines and quantum hardware on exactly solvable models possessing VBS as exact ground-states [39,80]. From the experimental standpoint, we expect these results to motivate further development and refinement of the general tunable XY gates as key elements for variational quantum algorithms. ...

... In practice, because we truncateÂ after the single and double substitutions in Eq. (2), the representability of the unitary is considerably limited, and therefore the performance of the state-averaged MSQITE may not be promising. This is quite similar to an issue recently reported by Ibe et al. [51], that the multistate contracted VQE, which minimizes the averaged energy of orthogonal states generated by the same unitary [20], experiences large errors for excited state calculations. Indeed, below, we will show that with the state-specific MSQITE a model space converges to almost the exact one using only single and double excitations inÂ, whereas the accuracy of the state-averaged MSQITE is generally quite unsatisfactory and its errors in energy can be substantial especially when the number of states increases. ...

... Specifically, here we consider a particular class of local quantum circuits known as "dual unitary circuits" [57], which are defined by the property that their bulk dynamics remain unitary also when exchanging the roles of space and time. The most remarkable feature of these systems is that, despite being quantum chaotic, they allow for exact calculations of many relevant many-body quantities [27,50,[58][59][60][61][62][63][64][65][66][67][68][69]. Surprisingly, even the very quantum chaotic nature of dual-unitary circuits can be rigorously proven [45,49]. ...

... In this thesis, we have focused on developing the resource-theoretic foundations upon which simulators can be built, leav-ing implementation for future work. During the final stages of the preparation of this thesis, several papers have emerged demonstrating how stabiliser-based simulation methods can be employed in practical settings [187,188], and pointing the way to new directions of enquiry for improving performance. This research direction opens up the possibility of simulating error-correction protocols implemented on real-world quantum computing hardware where noise may look very different to the depolarising or dephasing noise model often assumed in earlier work. ...

... As such, we choose k = 6 for all runs, where |S| = 12 6 = 924. The circuits are trained via a gradient-free Covariance Matrix Adaptation Evolution Strategy (CMA-ES) optimizer [38] with a NLL loss function on the Qulacs quantum simulator [39]. While we optimize with NLL, we display the cost values in the form of the KL Divergence, as it is easier to visualize the success of the training process. ...

Reference: Do Quantum Circuit Born Machines Generalize?

... Another related approach appears in the area of variational quantum algorithms [125], believed to be advantageous for noisy NISQ quantum computers [474], that is rather similar to closed-loop optimal control. In these approaches, a quantum algorithm that contains parameterized gates (i.e., gates that contain, e.g., a rotation angle as a free parameter) is considered with the goal of moving a fiducial initial state into a desired final state. ...

... The distinctive feature of the OLP is the online operation, without storing any input, either classical or quantum. This is particularly advantageous in platforms where system ensembles can be measured at the output layer, at each input injection, as for atomic/molecular ensembles [79] or in multimode (pulsed) photonics [80], where fully online time series processing with weak measurements could be realized. ...

... Despite progress in various aspects of near-term quantum machine learning algorithms [26] including experimental realizations [16,[27][28][29][30], proposals for various platforms [28,31] and studies of statistical properties of quantum machine learning models [32][33][34], the encoding of input data is still a significant bottleneck for (quantum) photonic machine learning hardware. For example, the expressive power of quantum circuits based on parameterized single qubit rotations is limited by the number of encoding gates used [23,24]. ...

... Recent papers show benefits of using this approach for satellite image classification [6] or modeling joint probability distributions [8]. QML was also used to analyse time series [1,7,2]. In this paper we propose new approach to the task of time series prediction using Quantum Recurrent Neural Networks in continuous variable paradigm. ...