# the quantum analog revolution

if quantum is inherently analog, then what is "quantum analog?" allow us to explain...

1

the realization of computation

Computing on devices can be thought of as a process used to obtain an answer to a particular problem by exploiting the dynamical properties of the device. In a sense, all computation (whether digital, analog, etc.) is based on analogy, or a systematic relationship, between the states of a computing device and those in the primary system.

In all computation, the relevant mathematical structure of the problem is realized in the physical states and processes of the computation device, the only difference is how direct this realization is. Therefore any computing paradigm, whether analog, digital or quantum, is at its heart a mathematical study. The systematic relationship between the computing physical system and the primary one has led infinityQ to develop a new computational approach, called quantum analog computing.

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analog: representing physical systems with mathematics

Analog computers have a long history prior to the digital age and have been applied to an extensive variety of fields. Analog computation refers to an analogy, or systematic relationship, between the physical processes in the computing device and those in the system it is modelling/describing. An analog computer is therefore an analogy of the particular system it is set to describe. The physical quantities of the analog device follow the same mathematical laws as the physics in the system under study.

In analog computers, rather than operating through the manipulation of numbers as digital computers do, numbers emerge as a result of measurements of physical parameters. Analog computers use continuously adjustable quantities of the system in order to codify a given problem. The time evolution of the voltage waveform of the analog computer represents the encoding of the solution of a given problem. Electronic components (physical devices) are used to sum, multiply, and integrate physical quantities like these signals. These components are connected in a way that the voltages of the analog computer are related by the same mathematical equations as the original physical variables. One of the advantages of analog systems is the ability to connect these components in a variety of ways, depending on the physical system under consideration. Other advantages to consider: speed, inherent natural parallelism, and its small size. These advantages stem from the fact that analog computations are close to the physical processes that realize them. In principle, any mathematically described physical process can be used for analog computation.

3

the three categories of quantum computation

In a well-known lecture in 1982 Richard Feynman proposed a quantum machine, capable of simulating quantum physics. He posited that, since nature is not classical, to simulate natural phenomena one would need a device which operates on quantum mechanical principles. These computing devices would exploit quantum mechanical properties such as superposition and entanglement. The promise of quantum computing is the delivery of more efficient computation, especially for certain types of computationally intensive problems.

GATE PARADIGM

The most widely known one is the gate paradigm which is analogous to the binary logic gates in classical computers. Quantum information is processed by means of quantum gates, implementing complex circuits to achieve practical functionalities with the promise of incredible advantages over classical computing. Today, most quantum devices are able to apply several gates in sequence. For solving interesting problems, long gate sequences will be required, leading to long operation time and large errors. To keep the error level to a certain minimum, substantial external active control systems are necessary, making the problem of scaling to more than several qubits extremely challenging.

ADIABATIC

The adiabatic model is pursued on the theory that the architecture may have a certain inherent fault tolerance due to resistance to slowly varying control error. Moreover, the energy gap may provide inherent resistance to noise, due to stray couplings to the environment, for example, if noiseless qubits are developed. In adiabatic quantum computing, the computation starts from an initial Hamiltonian with an easy to construct ground state. The Hamiltonian is then gradually varied into a final Hamiltonian, whose ground state encodes the solution to the computational problem. It has been theoretically shown that adiabatic quantum computing is as powerful as the circuit-based approach, but it brings with it a significant cost in terms of additional physical qubits (just like in the gate paradigm).

CONTINUOUS VARIABLE (CV)

In the CV model, quantum information is encoded in an infinite-dimensional bosonic mode (photons). Its computational power is similar to the circuit model. A qubit is realized by means of a polarization state of a photon since the latter is not as plagued by decoherence as other quantum systems. An intrinsic limitation of this architecture is the need to achieve interaction between photons for multi-qubit control, which requires strong optical nonlinearities.

WHY "QUANTUM" IS A BUZZWORD

"In fairness, one needs to ask whether the promised speed increase obtained by the quantum computer is actually a result of the quantum mechanics, or is a result of the use of parallel analog computation." - D Ferry, 2001

Practical quantum computing is dependent on the development of better (noiseless) qubits, better interconnects, improved control, and error correction. As a result, one can perform accurate computations with hundreds of digits after the decimal. Since it will be capable of dealing with such numbers efficiently (something digital computers above a certain digit cannot), a quantum computer can in theory solve problems computationally intractable with digital computers.

Ferry, furthermore, examines a qubit as an analog quantity, showing that in certain processes the real speed up comes from the analog quantities and advantages and "not from the use of quantum mechanics."

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the current digital approach has some gaps that quantum technologies can fill

Today, the main computational device is the digital computer, which has become omnipresent in our daily routines. For decades, increased computational power and energy efficiency has been obtained by shrinking transistors and putting more of them in microchips. Yet, by the mid-2000s transistor miniaturization had led to such narrow gaps between them that current leakage occurred, reducing energy efficiency gains and increasing the risk of overheating due to the presence of a natural upper bound on how rapidly heat waste can be removed.

A workaround to mitigate those limitations has been the development of many-core architectures and vectorization practices, although they are hindered in terms of Amdahl’s law. Even specialized architectures, such as GPUs, are limited by clock cycles due to parasitic capacitances, as well as certain energy barriers. The consequent slowing of Moore’s law has prompted the need to develop new computing technology.

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quantum + analog = soulmates

An analog device can be used to demonstrate quite clearly multiple facets of the mathematics of quantum mechanics since an analog device computes by exploiting physical phenomena directly. Such a physical system can be realized through an appropriate analog device capable of simulating the corresponding NP-complete problem. Indeed, one could say the reason for the growing attraction of quantum computing comes from its analog nature, that is, its ability to physically simulate quantum probabilities.

infinityQ has developed a new computational approach, called quantum analog computing. It is analog in two ways. First, it relies on analogies with quantum systems. Second, it employs analog electronics. In practical terms, this means that instead of dealing with actual atoms or molecules (which are extremely sensitive to the external environment) to carry out quantum computations, we use analog circuits to achieve certain quantum computing capabilities. Each analog circuit (or analog qubit) is mathematically equivalent to (or are doppelgängers of) an atom in lambda-configuration. More specifically, the analog system represents the dynamics of an electron in an atom irradiated by two laser beams (known as pumping and probe), which couple the two ground states to their common excited state. More specifically, the analog system represents the dynamics of an electron in an atom irradiated by two laser beams (known as pumping and probe), which couple the two ground states to their common excited state.

One of the important consequences of this approach is that the need for error correction also disappears. To attenuate noise, one can utilize several possible options such as: feedback loops, appropriate use of energy, resources (time and space) to increase precision by averaging state variables, by adaptations, and others. All computations were performed at room temperature and were not affected by a detrimental noise. To perform useful computations, the ensemble of analog circuits interacts collectively to solve a certain problem. To achieve this, infinityQ has used a concept known as collective computing that can be realized by means of reservoir computing.

infinityQ’s device utilizes the concept of collective computing to connect its qubits in an all-to-all topology allowing the problem to be solved to be codified into the topology of the device. The computation proceeds until a stationary regime is reached.

The stationary regime represents the solution of the problem.