Keisuke Fujii

• PhD
• Professor (Assistant) at Kyoto University

Optimal elemental configuration search in crystal is a crucial task to discovering industrially important materials such as lithium-ion battery cathodes. In this paper we present application of quantum approximate optimization algorithm, the representative near-term quantum algorithm for combinatorial optimization, to finding the most stable elemen...

Combinatorial optimization problems are one of the areas where near-term noisy quantum computers may have practical advantage against classical computers. Recently, a feedback-based quantum optimization algorithm has been proposed by Magann , . The method explicitly determines quantum circuit parameters by feeding back measurement results thus avoi...

Data visualization is important in understanding the characteristics of data that are difficult to see directly. It is used to visualize loss landscapes and optimization trajectories to analyze optimization performance. Popular optimization analysis is performed by visualizing a loss landscape around the reached local or global minimum using princi...

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 achieve. In this paper, we define a task called and provide an algorithm to achieve this task. Specifically, we construct a block encoding of complex amplitudes...

We propose a method for constructing circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry by using variational optimization of quantum circuits solely on classical computers. The circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as probability amplitudes and plays a cru...

Multivariable Quantum Signal Processing (M-QSP) \cite{Rossi2022multivariable} is expected to provide an efficient means to handle polynomial transformations of multiple variables simultaneously. However, we identified several inconsistencies in the main theorem, where necessary and sufficient conditions for achievable polynomials are provided, and...

Product formula (PF), which approximates the time evolution under a many-body Hamiltonian by the product of local time evolution operators, is one of the central approaches for simulating quantum dynamics by quantum computers. It has been of great interest whether PFs have a bound of the error from the exact time evolution, which is expressed by co...

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) have provided a unified framework for understanding many quantum algorithms, including factorization, matrix inversion, and Hamiltonian simulation. As a multivariable version of QSP, multivariable quantum signal processing (M-QSP) is proposed. M-QSP interleaves signal...

The Schwinger model is one of the simplest gauge theories. It is known that a topological term of the model leads to the infamous sign problem in the classical Monte Carlo method. In contrast to this, recently, quantum computing in Hamiltonian formalism has gained attention. In this work, we estimate the resources needed for quantum computers to co...

The quantum kernel method is one of the key approaches to quantum machine learning, which has the advantage of not requiring optimization and its 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 mach...

Quantum machine learning (QML) leverages quantum states for data encoding, with key approaches being explicit models that use parameterized quantum circuits and implicit models that use quantum kernels. Implicit models often have lower training errors but face issues such as overfitting and high prediction costs, while explicit models can struggle...

Combinatorial optimization problems are one of the areas where near-term noisy quantum computers may have practical advantage against classical computers. Recently a novel feedback-based quantum optimization algorithm has been proposed by Magann \textit{et al}. The method explicitly determines quantum circuit parameters by feeding back measurement...

Quantum computation is expected to accelerate certain computational tasks over classical counterparts. Its most primitive advantage is its ability to sample from classically intractable probability distributions. A promising approach to make use of this fact is the so-called quantum-enhanced Markov-chain Monte Carlo (qe-MCMC) method [D. Layden , ],...

Magic state distillation, which is a probabilistic process used to generate magic states, plays an important role in universal fault-tolerant quantum computers. On the other hand, to solve interesting problems, we need to run complex programs on fault-tolerant quantum computers, and hence, the system needs to use hardware resources efficiently. Tak...

We introduce the quantum adaptive distribution search (QuADS), a quantum continuous optimization algorithm that integrates Grover adaptive search (GAS) with the covariance matrix adaptation evolution strategy (CMA-ES), a classical technique for continuous optimization. QuADS utilizes the quantum-based search capabilities of GAS and enhances them wi...

We experimentally demonstrate a virtual two-qubit gate and characterize it using quantum process tomography (QPT). The virtual two-qubit gate decomposes an actual two-qubit gate into single-qubit unitary gates and projection gates in quantum circuits for expectation-value estimation. We implement projection gates via midcircuit measurements. The de...

Quantum eigenvalue transformation (QET) and its generalization, quantum singular value transformation (QSVT), are versatile quantum algorithms that allow us to apply broad matrix functions to quantum states, which cover many significant quantum algorithms such as Hamiltonian simulation. However, finding a parameter set which realizes preferable mat...

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...

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

We propose a method for constructing $\texttt{PREPARE}$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry by using variational optimization of quantum circuits solely on classical computers. The $\texttt{PREPARE}$ circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as...

When estimating the eigenvalues of a given observable, even fault-tolerant quantum computers will be subject to errors, namely algorithmic errors. These stem from approximations in the algorithms implementing the unitary passed to phase estimation to extract the eigenvalues, e.g. Trotterisation or qubitisation. These errors can be tamed by increasi...

Quantum computers (QCs), which work based on the law of quantum mechanics, are expected to be faster than classical computers in several computational tasks such as prime factoring and simulation of quantum many-body systems. In the last decade, research and development of QCs have rapidly advanced. Now hundreds of physical qubits are at our dispos...

We experimentally demonstrate a virtual two-qubit gate and characterize it using quantum process tomography (QPT). The virtual two-qubit gate decomposes an actual two-qubit gate into single-qubit operations and projective measurements in quantum circuits for expectation-value estimation. We implement projective measurements via mid-circuit dispersi...

We introduce the first large-scale dataset, MNISQ, for both the Quantum and the Classical Machine Learning community during the Noisy Intermediate-Scale Quantum era. MNISQ consists of 4,950,000 data points organized in 9 subdatasets. Building our dataset from the quantum encoding of classical information (e.g., MNIST dataset), we deliver a dataset...

Quantum computation is expected to accelerate certain computational task over classical counterpart. Its most primitive advantage is its ability to sample from classically intractable probability distributions. A promising approach to make use of this fact is the so-called quantum-enhanced Markov chain Monte Carlo (MCMC) [D. Layden, et al., arXiv:2...

Quantum simulation is one of the key applications of quantum computing, which accelerates research and development in the fields such as chemistry and material science. The recent development of noisy intermediate-scale quantum (NISQ) devices urges the exploration of applications without the necessity of quantum error correction. In this paper, we...

Quantum eigenvalue transformation (QET) and its generalization, quantum singular value transformation (QSVT), are versatile quantum algorithms that allow us to apply broad matrix functions to quantum states, which cover many of significant quantum algorithms such as Hamiltonian simulation. However, finding a parameter set which realizes preferable...

Variational quantum algorithms (VQAs) are expected to become a practical application of near-term noisy quantum computers. Although the effect of the noise crucially determines whether a VQA works, the heuristic nature of VQAs makes it difficult to establish analytic theories. Analytic estimations of the impact of the noise are urgent for searching...

The implementation of time-evolution operators U ( t ) , called Hamiltonian simulation, is one of the most promising usage of quantum computers. For time-independent Hamiltonians, qubitization has recently established efficient realization of time-evolution U ( t ) = e − i H t , with achieving the optimal computational resource both in time t and a...

Quantum machine learning has the potential to computationally outperform classical machine learning, but it is not yet clear whether it will actually be valuable for practical problems. While some artificial scenarios have shown that certain quantum machine learning techniques may be advantageous compared to their classical counterpart, it is unlik...

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...

t-stochastic neighbor embedding (t-SNE) is a nonparametric 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 th...

Current quantum computers are limited in the number of qubits and coherence time, constraining the algorithms executable with sufficient fidelity. The variational quantum eigensolver (VQE) is an algorithm to find an approximate ground state of a quantum system and is expected to work on even such a device. The deep VQE [K. Fujii, et al., arXiv:2007...

Variational quantum algorithms (VQAs) 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 VQAs can maintain quantum advantage under the intrinsic noise of the NISQ devices, which deteriorates the quantumness. Here we prop...

The implementation of time-evolution operators on quantum circuits is important for quantum simulation. However, the standard method, Trotterization, requires a huge number of gates to achieve desirable accuracy. Here, we propose a local variational quantum compilation (LVQC) algorithm, which allows us to accurately and efficiently compile time-evo...

Quantum-inspired singular value decomposition (SVD) is a technique to perform SVD in logarithmic time with respect to the dimension of a matrix, given access to the matrix embedded in a segment-tree data structure. The speedup is possible through the efficient sampling of matrix elements according to their norms. Here, we apply it to extreme learni...

The implementation of time-evolution operators, called Hamiltonian simulation, is one of the most promising usage of quantum computers that can fully exploit their computational powers. For time-independent Hamiltonians, the qubitization has recently established efficient realization of time-evolution, with achieving the optimal computational resou...

Variational quantum algorithms are considered to be appealing applications of near-term quantum computers. However, it has been unclear whether they can outperform classical algorithms or not. To reveal their limitations, we must seek a technique to benchmark them on large-scale problems. Here we propose a perturbative approach for efficient benchm...

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...

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 a variational quantum eigensolver (VQE) with a reduction in the system dimension, where the interactions between divided subsystems are taken as an effective Hamiltonian expanded...

In the early years of fault-tolerant quantum computing (FTQC), it is expected that the available code distance and the number of magic states will be restricted due to the limited scalability of quantum devices and the insufficient computational power of classical decoding units. Here, we integrate quantum error correction and quantum error mitigat...

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...

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...

DOI:https://doi.org/10.1103/PhysRevApplied.16.029901

Quantum systems have an exponentially large degree of freedom in the number of particles and hence provide a rich dynamics that could not be simulated on conventional computers. Quantum reservoir computing is an approach to use such a complex and rich dynamics on the quantum systems as it is for temporal machine learning. In this chapter, we explai...

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...

Recent developments in reservoir computing based on spintronics technology are described here. The rapid growth of brain-inspired computing has motivated researchers working in a broad range of scientific field to apply their own technologies, such as photonics, soft robotics, and quantum computing, to brain-inspired computing. A relatively new tec...

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...

Noise in quantum operations often negates the advantage of quantum computation. However, most classical simulations of quantum computers calculate the ideal probability amplitudes by either storing full state vectors or using sophisticated tensor-network contractions. Here we investigate sampling-based classical simulation methods for noisy quantum...

Variational quantum algorithms (VQAs) are expected to become a practical application of near-term noisy quantum computers. Although the effect of the noise crucially determines whether a VQA works or not, the heuristic nature of VQAs makes it difficult to establish analytic theories. Analytic estimations of the impact of the noise are urgent for se...

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...

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...

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 a sequential minimal optimization method for quantum-classical hybrid algorithms, which converges faster, robust against statistical error, and hyperparameter-free. Specifically, the optimization problem of the parameterized quantum circuits is divided into solvable subproblems by considering only a subset of the parameters. In fact, if...

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...

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 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 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) 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...

We propose a sequential minimal optimization method for quantum-classical hybrid algorithms, which converges faster, is robust against statistical error, and is hyperparameter-free. Specifically, the optimization problem of the parameterized quantum circuits is divided into solvable subproblems by considering only a subset of the parameters. In fac...

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...

The one-clean-qubit model (or the deterministic quantum computation with one quantum bit model) is a restricted model of quantum computing where all but a single input qubits are maximally mixed. It is known that the probability distribution of measurement results on three output qubits of the one-clean-qubit model cannot be classically efficiently...

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...

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...

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...

Instantaneous quantum polynomial-time (IQP) computation is a class of quantum computation consisting only of commuting two-qubit gates and is not universal in the sense of standard quantum computation. Nevertheless, it has been shown that if there is a classical algorithm that can simulate IQP efficiently, the polynomial hierarchy (PH) collapses at...

The one-clean qubit model (or the DQC1 model) is a restricted model of quantum computing where only a single qubit of the initial state is pure and others are maximally mixed. Although the model is not universal, it can efficiently solve several problems whose classical efficient solutions are not known. Furthermore, it was recently shown that if t...

What happens if in QMA the quantum channel between Merlin and Arthur is noisy? It is not difficult to show that such a modification does not change the computational power as long as the noise is not too strong so that errors are correctable with high probability, since if Merlin encodes the witness state in a quantum error-correction code and send...

Blind quantum computation (BQC) allows a client, who only possesses relatively poor quantum devices, to delegate universal quantum computation to a server, who has a fully fledged quantum computer, in such a way that the server cannot know the client's input, quantum algorithm, and output. In the existing verification schemes of BQC, any suspicious...

This paper investigates the power of polynomial-time quantum computation in which only a very limited number of qubits are initially clean in the |0> state, and all the remaining qubits are initially in the totally mixed state. No initializations of qubits are allowed during the computation, nor intermediate measurements. The main results of this p...