# Analog Quantum Computing

Analog Quantum Computing is a form of quantum computing that uses continuous variables to represent and manipulate quantum information. Unlike digital quantum computing, which relies on discrete qubits and gates, analog quantum computing operates on continuous quantum states and employs continuous transformations. It's a versatile approach with applications in quantum simulation, optimization, and more.

One of the primary applications of analog quantum computing is quantum simulation. Quantum simulators are specialized devices that mimic the behavior of complex quantum systems, such as molecules or materials. By tuning the parameters of the analog quantum system, researchers can study the properties and dynamics of the target system. This has significant implications for chemistry, physics, and materials science.

Analog quantum computing often involves continuous variables, such as the position and momentum of quantum particles. Quantum operations are implemented through continuous interactions, such as laser-induced couplings or magnetic field gradients. This continuous nature allows for a more direct mapping between the quantum computer and the physical system being simulated or solved.

Analog quantum computing offers some advantages, including the potential for more natural and efficient simulations of certain quantum systems. It may also require fewer resources compared to digital quantum computing for specific tasks. However, it also presents challenges, such as sensitivity to noise and errors, difficulty in error correction, and limitations in the types of problems that can be addressed.

Hybrid approaches that combine analog and digital quantum computing are being explored to leverage the strengths of both paradigms. Research in analog quantum computing continues to advance, with ongoing work in developing new techniques, improving error mitigation, and exploring novel applications. It's an area that contributes to the broader landscape of quantum computing and offers unique insights and capabilities.

Analog Quantum Computing represents a distinct approach to quantum information processing, emphasizing continuous interactions and transformations. It provides a valuable tool for studying complex quantum systems and solving problems that are challenging for classical computers. The ongoing exploration of analog quantum computing enriches the diversity of quantum technologies and expands the possibilities for quantum research and applications.

## What is Analog Quantum Computing?

This definition is important, because the answers to a Stack Exchange Computer Science question “Is Quantum Computer analog?” indicates that this is not well understood, or at least it wasn’t at the time the question was asked. Some answers were more about **analog computer vs quantum computer**, which demonstrates a fundamental misunderstanding of what quantum computers are. Because of the widespread use of digital mode, this might still be an issue today. And to potentially add to the confusion, an analog quantum computer might be referred to as a quantum simulator.

The difference between an **analog quantum computer** and a **digital quantum computer** is abstraction. The digital mode adds a layer above the analog mode that makes the quantum computer a little more user friendly. Circuits and gates are relatively easy to teach, and programming one is not far removed from classical programming. Even though quantum computers are inherently parallel, a quantum circuit shows a discrete series of operations that are executed sequentially, not unlike classical computer instructions. Interestingly, these digital gate operations are compiled into analog operations, because that’s how a quantum computer actually works.

Analog mode may seem like **advanced quantum computing**, because it’s noticeably unfamiliar. Instead of discrete steps of any kind, there may be as few as one relatively-long step. It’s probably impossible to do anything meaningful with one classical instruction, true random number generation could arguably count as a meaningful single digital mode instruction, but analog mode can solve certain real-world problems with a single instruction.

The most significant difference is that analog mode might end up being quicker to “quantum advantage.” Digital gate operations are associated with errors that limit the practicality of quantum computers until these errors can be suppressed, detected, and corrected. Quantum circuits with any meaningful applications also often have a number of operations that exceed the duration that today’s quantum computers can retain quantum information, which produces meaningless results.

## Analog vs. Digital Quantum Computing

Quantum computing has three modes: analog, digital, and hybrid digital-analog. Each has its own advantages and disadvantages, which can be summarized as follows:

### Analog Quantum Computing

- There is a problem Hamiltonian, which is a concept that can be avoided in digital mode, depending on the target application.
- The quantum state is changing continuously, as it does in nature.
- There is a small number of user-definable parameters, which actually makes it simpler than deep quantum circuits with dozens, hundreds, or even thousands of operations.
- It’s easier to implement architecturally, as digital mode can potentially add several layers to the full stack, each of which need to be designed, developed, tested, and troubleshot.

### Digital Quantum Computing

- Digital mode has become the most common presentation of quantum computing to general audiences, with quantum circuits being far more common than pulse schedules.
- The textbook quantum algorithms, such as Shor’s and Grover’s, as well as most other well-known quantum algorithms, are designed to be implemented in digital mode.
- Gates evolve the quantum state in potentially long sequences of discrete timesteps.
- Gates may evolve only parts of a quantum state.
- Every single-qubit gate introduces a small chance of introducing an error, while multi-qubit gates, which are essential, are particularly error prone.
- For general audiences, far more books and tutorials are available for digital mode.

### Hybrid Quantum Computing

- From a user’s perspective, it looks and feels like digital mode.
- Software converts the quantum circuit to a pulse schedule and optimizes it, as opposed to using the default pulses that would otherwise result from compilation.

In summary, all quantum computers are inherently analog. Digital mode is arguably easier-to-use, but has its drawbacks in error rates and coherence times. Hybrid approaches seek to leverage the advantages of both: the relative ease-of-use of digital mode with the performance of analog mode.

It’s worth noting that while far more educational material exists for digital mode, making it easier to learn in one sense, QuEra makes comparable educational materials available for analog mode. There are also online workshops, during which the instructor answers any attendee questions that may arise.

## Applications of Analog Quantum Computing

Because quantum circuits are ultimately compiled into pulses for execution, all digital mode applications are also applicable to analog mode. The following applications, therefore, are some of those that are particularly well-suited for analog mode:

### Quantum Optimization

- Maximum Independent Set (MIS): antenna placement, store locations, etc.
- Maximum Clique: financial portfolio optimization, social networks, etc.
- Minimum vertex cover: network security, financial networks, economic analysis, etc.
- Minimum Dominating Set: 5G networks, document summarization, etc.
- Graph coloring: task scheduling, map labeling, wireless channel allocation, etc.
- Quadratic Unconstrained Binary Optimization (QUBO): credit scoring, etc.
- Integer factorization: cryptography, divisibility rules, simplifying fractions, etc.

### Quantum Machine Learning

- Reservoir machine learning: temporal data processing and classification
- Classification: MNIST digit recognition, natural language processing, etc.

And, as stated at the outset,

### Quantum Simulation

- Flexible excitation and drive parameters to simulate the Hamiltonian

This is not an exhaustive list, and the list can be expected to grow over time. For example, a project titled “Analog vs digital quantum computing for certain optimization problems” by a research team at Fysisk institutt of the Universitetet I Oslo proposes to compare analog mode quantum annealing to digital mode Quantum Approximate Optimization Algorithm (QAOA) for NP-hard MaxCut problems. At least part of the goal is to determine if either or both has the potential to realize computational advantages. Due to the limitations of quantum annealing, a better analog modality would be neutral atoms, so that could be a topic of further research.

Finally, a ScienceDirect paper titled “Quantum Analog Computing” discusses another approach to hybrid digital-analog mode using recurrent neural networks (QRNN). With this approach, the computation is analog, but the algorithm includes the classical feedback loops, mid-circuit measurements, and reset operations that are sometimes found in digital mode. Therefore, it’s not just proposing converting digital to analog, but rather truly incorporating the features of both.