Quantum teleportation is OptQC's most important technology. Quantum teleportation has a long history. Theoretically proposed in the 1990s, conditional quantum teleportation was demonstrated by Zeilinger et al. in 1997, and deterministic quantum teleportation was demonstrated the following year in 1998 by OptQC Director and Founder, Professor Akira Furusawa.

Although the term quantum teleportation is often associated with the Sci-fi  "instantaneous travel," the reality is that it is not an instantaneous travel. The concept of quantum teleportation was born from the question of whether quantum information can be copied. While we can naturally duplicate the information we see in everyday life (e.g., this text), same task in quantum information is prohibited by the very structure of quantum mechanics, and simple duplication is not possible. Also, in quantum mechanics, measurement causes the quantum state to collapse to classical information. Once this collapse of the wave packet occurs, it is no longer quantum information, but classical information. Therefore, it is not possible to look into the quantum information and create the same quantum information based on the measurement results.

Quantum teleportation is a technique that reconstructs the same quantum state at a distance without looking directly at this quantum information. This is described as "teleportation" because it can be viewed as the quantum information disappears from one place and reappears in another place. Since the quantum information is not directly measured, there is no collapse of the wave packet, and the properties of the quantum information are retained. This technology can be further broken down into three elements: quantum entanglement, bell measurement, and feedforward operation. These three technological elements are the basic technology for most applications of quantum technology, and it is no exaggeration to say that if you conquer quantum teleportation, you conquer quantum computers.

OptQC's optical quantum computer is based on this quantum teleportation, and by perfecting each element, we are trying to realize a large-scale, high-speed, optical quantum computer that can handle both digital and analog information.

Quantum entanglement refers to relationships between multiple quantum modes (a continuous-variable version of qubits) that cannot be considered as separate entities and cannot be explained by classical physics (i.e., our everyday intuition). This inability to separate them is the key point. For example, with the multiple objects that we normally see, while they are in contact or exerting forces on each other, there is indeed a relationship. However, as soon as those events are no longer present, there should be no relationship between them. On the other hand, once quantum entanglement occurs, no matter how far apart they are, they cannot be considered as separate entities unless an external factor (disturbance, noise, etc.) eliminates the quantum entanglement. Moreover, only when all the information of all the quantum modes is available do we have the complete information. The concept of quantum entanglement is so contrary to our everyday senses and to the way we thought about physics before quantum mechanics took hold that Einstein, Podolsky, and Rosen argued in 1935 that quantum mechanics itself, which predicts the existence of this quantum entanglement, is an incomplete theory. This is the so-called EPR paradox. The existence of quantum entanglement has been shown experimentally many times and its existence has been accepted, although some parts of it continue to be studied in modern times because of the fundamental nature of quantum mechanics.

How this quantum entanglement relates to quantum teleportation is that when two quantum modes of quantum entanglement are generated, as represented in the figure, the individual quantum modes alone do not provide complete information, but rather only noise-like information. However, when both quantum modes are brought together, complete quantum information is available. Therefore, by mixing the information you want to quantum teleport with one of the modes of the quantum entanglements and measuring it (this is called Bell measurement and is described below), you can quantum teleport the input quantum state to the output via this strong relationship of quantum entanglement, without directly looking into the quantum information.

The generation of quantum entanglement is a major challenge in any physical system. This is because, while a single quantum mode requires isolation from the outside world and various other controls, quantum entanglement requires a strong relationship between multiple delicate quantum modes. Fortunately, quantum entanglement is much easier to generate in light than in other physical systems, and in the quantum teleportation diagram, quantum entanglement can be generated deterministically simply by interfering a quantum light source called squeezed light, with a partially transparent mirror. The technology to control the generation of this squeezed light and the interference of the light is of course indispensable, but the strength of an optical quantum computer is that it can realize quantum entanglement with a comparatively simple system.

OptQC consists of core members who are well versed not only in two-mode quantum entanglement, but also in quantum light sources for generating large-scale quantum entanglement, interferometer phase control, quantum entanglement measurements, and other technologies related to quantum entanglement.

In quantum teleportation, once the input state and the two-mode quantum entanglement are prepared, the input mode and one of the modes of the entanglement are interfered on a partially transparent mirror. Subsequently, measurements are made on both modes. This series of measurements is called a bell measurement. The reason why we do this kind of measurement is that we want to perform quantum teleportation via the relationship of the two-mode entanglement. Therefore, if we make a measurement that define a relationship between the input and one of the mode of the entanglement, the information can be transmitted without looking into the input information. This is related to the fact that when we look at one half of the quantum entanglement, it is incomplete information; by mixing this incomplete information with the input information, we can determine the relationship between the two without having to look into the quantum information in the input state.

In the case of an optical quantum computer, if you make a Bell measurement with a qubit instead of a quantum mode, the measurement will not necessarily succeed, but will fail with a significant probability and can only be conditional. With quantum modes, on the other hand, one can make Bell measurements deterministically and quantum teleportation succeeds unconditionally.

This Bell measurement, which corresponds to the projection of two quantum modes onto quantum entanglement, corresponds to the projection onto various quantum entanglements, depending on the measurement results of those two measuring instruments. The configuration of the system for this projection measurement to quantum entanglement is very simple and can be realized with a partially transmitting mirror and two homodyne detectors (also called balance detectors). This homodyne measuring device is a technique often used in optical communications. However, in the field of optical communications, we are dealing with classical light, which can be amplified to achieve the high speed needed for high-speed communication at the expense of quantum efficiency. For the homodyne detectors used in optical quantum computers, it is necessary to achieve high quantum efficiency and high speed at the same time, and there are only a very limited number of groups in the world that have this technology.

Members of OptQC have homodyne measurement and bell measurement techniques to read out quantum information of quantum modes with high accuracy and speed, and can observe various quantum states and quantum entanglement.

In the quantum teleportation circuit shown in the figure, after the results of the bell measurement are obtained, a displacement operation is performed according to the measured value. The reason why this operation is necessary is that the values of the measurement results of the Bell measurement corresponds to a variety of different quantum entanglements. Depending on this measurement results,  the output state is not the input state itself, but rather the input state with the quantum operations applied according to the measurement values. However, if this extra operations can be removed for any measurement results, quantum teleportation will succeed for all measurement results. It is the ability to implement this feedforward operation that makes quantum teleportation with quantum modes deterministic.

At first glance, the importance of this feedforward operation is difficult to recognize. The reason for this is that most of feedforward processes appear to be simply processing classical values with classical computers and then reverting back to quantum operations. Perhaps this is why there many researches in which the feedforward operation is replaced by conditioning on the measured values of bell measurements without actually performing the feedforward operation. While this may not be a problem at the research level, such an approach is not acceptable in the implementation of a quantum computer. Also, this feedforward operation is actually very important. For example, in the method of implementing an fault-tolerant quantum computer, the key issue is how to feedforward the classical information about where the error is in the quantum computer back to the quantum state after obtaining the classical information. Moreover, this feedforward operation will be the most limiting factor for the overall computation speed of the quantum computer.

The core members of OptQC have been working on quantum teleportation for many years and have deeper understanding of feedforward technology more than anyone else in the world, and we understand how feedforward operations can be developed to realize an optical quantum computer.

A processor in a quantum computer performs quantum operations on the input qubit or quantum mode to obtain and measure the quantum state corresponding to the result of the calculation. Quantum processors vary depending on the physical system, but there are several important parameters. The first parameter ois how accurately the quantum operation can be performed. This parameter is often expressed as the fidelity of the quantum gate in quantum computers using qubits. The second parameter is how many quantum operations can be performed on how many inputs. The definition of this parameter is not just the number of qubits or quantum modes, but also how many interactions can be performed between those qubits or quantum modes. For example, if you have a million qubits that cannot interact, that is not much different from what you can do with one qubit. How much input can be processed is sometimes expressed in terms of how scalable it is.

Many quantum computers struggle with this scalability, and even when small-scale demonstrations and algorithms are possible, extension of that methodology do not guarantee practical quantum computer. In optical quantum computer, we have tackled this scalability problem earlier than in other physical systems. This is because by applying optical telecommunication technology, which supports the vast exchange of information in today's information society, to optical quantum computers, it is possible to handle large-scale quantum information with a small number of elements. Light has various degrees of freedom such as frequency, time, spatial mode, and polarization, and by multiplexing these degrees of freedom, large-capacity information communication that supports the social infrastructure is possible.

OptQC uses a multiplexing technique called time-domain multiplexing to achieve large-scale quantum computation. The quantum information of light is stored in a temporally localized pulses of light, which are generated sequentially, entering the quantum processor or interacting with light pulses at different timing, and finally being read out by sequentially via measurement. This method requires the fewest number of elements because the light pulses enter the quantum processor in sequence on their own, but it also requires high-speed handling of the quantum information because it must process the quantum information of the light pulses that come in one after another in succession.

OptQC members pioneered this quantum information and and its high-speed processing from an early stage and have always been at the forefront of high-speed quantum information processing.

In order to develop quantum teleportation into quantum computation, the two-mode quantum entanglement used in quantum teleportation must be changed to something else. As the input is output via quantum entanglement in quantum teleportation, quantum entanglement can be viewed as a kind of wiring for quantum information processing, and any quantum manipulation can be implemented by measurement-basis switching (see below) as long as the necessary wiring for input and output is in place. Such a quantum entanglement of multi-quantum modes that has the necessary structure for any quantum operations is called a two-dimensional clustered state.

After Dr. Shota Yokoyama generate 1D cluster state in 2013, in fact, one of our founders, Dr. Warit Asavanant, was the first person in the world to realize this 2D cluster state in 2019 using the time-domain multiplexing technique. Since then, this time-domain multiplexed 2D cluster state technique has been further developed. Only the OptQC members are able to generate such quantum entangled states with high quality.

In quantum teleportation, the input state is output to the output side by making a bell measurement. In fact, by changing how we do the measurement (in technical terms, the measurement basis) of this bell measurement, it is possible to output not the same state as the input state, but a state in which the input state is subjected to quantum operation according to the measurement basis. This method of quantum computation using quantum entanglement and changing the measurement basis is called measurement-based quantum computation, and the OptQC approach is to realize a quantum processor by combining two-dimensional clusters and this measurement basis switching. In the time-domain multiplexing method, quantum information enters the processor sequentially as optical pulses, so the measurement basis switching must also switch at the speed of the interval between the optical pulses. The speed, accuracy, and manner of this switching itself corresponds to the physics-level programming of the optical quantum computer, and is a very important technique.

The core members of OptQC were the first in the world to pioneer this technology and have accumulated a variety of know-how.