Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences, and engineering. They are expected to drive a new wave of technological innovations in communication, computation, and cryptography. Quantum mechanics is fundamentally stochastic, with randomness and uncertainty deeply rooted in quantum computation, simulation, and information. Consequently, quantum algorithms are inherently probabilistic, and quantum simulation extensively uses Monte Carlo techniques. Statistics plays a crucial role in quantum computation and simulation, offering potential to revolutionize computational statistics. Classical computers can only generate pseudorandom numbers, while quantum computers can produce genuine random numbers. Quantum computers can exponentially or quadratically speed up median evaluation, Monte Carlo integration, and Markov chain simulation. This paper reviews quantum computation, quantum simulation, and quantum information. It introduces basic concepts of quantum computation and simulation, presents quantum algorithms that are much faster than classical algorithms, and provides a statistical framework for analyzing quantum algorithms and simulation. Key terms include quantum algorithm, qubit, quantum Fourier transform, quantum information, quantum mechanics, quantum Monte Carlo, quantum probability, quantum simulation, and quantum statistics. Quantum mechanics is based on the idea of using quantum devices for computation and information processing, rather than classical devices. It studies the preparation and control of quantum states for information transmission and manipulation, including quantum computation, communication, and cryptography. Quantum information science is expected to lead to a quantum computer capable of solving problems that are intractable for classical computers. Scientists have already built rudimentary quantum computers to run quantum algorithms. Quantum systems are described by their states, which are unit vectors in a complex Hilbert space. The number of complex numbers needed to describe a quantum state grows exponentially with the system size, making classical simulation difficult. Quantum systems can store and manipulate exponential numbers of complex numbers, enabling efficient simulation of quantum systems. Quantum computers can efficiently simulate quantum systems that are intractable for classical computers. Quantum mechanics is mathematically described by a Hilbert space and self-adjoint operators. A quantum system is characterized by its state and time evolution. The state is a unit vector in the Hilbert space, and the time evolution is governed by a unitary operator. A density operator describes the state of a quantum system, which can be a pure state or an ensemble of pure states. Quantum probability involves measuring observables, which are self-adjoint operators. The measurement of an observable results in a random variable with a probability distribution. The expectation and variance of the measurement results are derived from the density operator. Measuring an observable alters the quantum state. Quantum statistics involves estimating the density matrix of a quantum system based on measurements. Quantum tomography is used to reconstruct the density matrix by measuring identically prepared quantum systems. Quantum parametric statistical models are used to estimate the density matrix. Quantum computing concepts include qubits, which are quantum bits that can exist in superposition states. Qubits can be in states |0> and |1Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences, and engineering. They are expected to drive a new wave of technological innovations in communication, computation, and cryptography. Quantum mechanics is fundamentally stochastic, with randomness and uncertainty deeply rooted in quantum computation, simulation, and information. Consequently, quantum algorithms are inherently probabilistic, and quantum simulation extensively uses Monte Carlo techniques. Statistics plays a crucial role in quantum computation and simulation, offering potential to revolutionize computational statistics. Classical computers can only generate pseudorandom numbers, while quantum computers can produce genuine random numbers. Quantum computers can exponentially or quadratically speed up median evaluation, Monte Carlo integration, and Markov chain simulation. This paper reviews quantum computation, quantum simulation, and quantum information. It introduces basic concepts of quantum computation and simulation, presents quantum algorithms that are much faster than classical algorithms, and provides a statistical framework for analyzing quantum algorithms and simulation. Key terms include quantum algorithm, qubit, quantum Fourier transform, quantum information, quantum mechanics, quantum Monte Carlo, quantum probability, quantum simulation, and quantum statistics. Quantum mechanics is based on the idea of using quantum devices for computation and information processing, rather than classical devices. It studies the preparation and control of quantum states for information transmission and manipulation, including quantum computation, communication, and cryptography. Quantum information science is expected to lead to a quantum computer capable of solving problems that are intractable for classical computers. Scientists have already built rudimentary quantum computers to run quantum algorithms. Quantum systems are described by their states, which are unit vectors in a complex Hilbert space. The number of complex numbers needed to describe a quantum state grows exponentially with the system size, making classical simulation difficult. Quantum systems can store and manipulate exponential numbers of complex numbers, enabling efficient simulation of quantum systems. Quantum computers can efficiently simulate quantum systems that are intractable for classical computers. Quantum mechanics is mathematically described by a Hilbert space and self-adjoint operators. A quantum system is characterized by its state and time evolution. The state is a unit vector in the Hilbert space, and the time evolution is governed by a unitary operator. A density operator describes the state of a quantum system, which can be a pure state or an ensemble of pure states. Quantum probability involves measuring observables, which are self-adjoint operators. The measurement of an observable results in a random variable with a probability distribution. The expectation and variance of the measurement results are derived from the density operator. Measuring an observable alters the quantum state. Quantum statistics involves estimating the density matrix of a quantum system based on measurements. Quantum tomography is used to reconstruct the density matrix by measuring identically prepared quantum systems. Quantum parametric statistical models are used to estimate the density matrix. Quantum computing concepts include qubits, which are quantum bits that can exist in superposition states. Qubits can be in states |0> and |1