While gate-based quantum computers capture most of the attention, alternative computing paradigms are emerging that blend quantum effects, probabilistic processes, and classical computation. These hybrid approaches—including quantum annealing, thermodynamic computing, and probabilistic circuits—offer different trade-offs and may prove more practical for specific applications than full-scale fault-tolerant quantum computers.

For detailed information on specific approaches:

• Quantum Computing - Quantum Annealing - Deep dive into D-Wave's quantum annealing approach
• Quantum Computing - Thermodynamic Computing - Extropic's probabilistic computing approach
• Quantum Computing - Hybrid Quantum-Classical Systems - Combining quantum and classical processors

The Hybrid Computing Landscape

Traditional quantum computing aims for universal, fault-tolerant quantum computers that can run any quantum algorithm. However, this goal remains decades away. In the meantime, several hybrid approaches are showing promise:

1. Quantum Annealing - Uses quantum fluctuations to find optimal solutions (D-Wave)
2. Thermodynamic Computing - Uses probabilistic circuits to sample from energy landscapes (Extropic)
3. Hybrid Quantum-Classical - Combines quantum and classical processors
4. Analog Quantum Simulators - Specialized quantum systems for specific problems

These approaches often map optimization problems onto energy landscapes, making them natural applications for spin glass physics. See Spin Glasses for background on how these energy landscapes work.

Quantum Annealing: D-Wave's Approach

Quantum annealing is a specialized form of quantum computing that uses quantum fluctuations to find the global minimum of optimization problems. D-Wave Systems has commercialized this approach with systems containing thousands of qubits.

Key Points:

• Uses quantum tunneling to escape local minima in energy landscapes
• Implements programmable spin glass Hamiltonians
• Specialized for optimization problems (not universal quantum computing)
• Commercial availability through D-Wave Leap cloud platform

For a comprehensive deep dive, see Quantum Computing - Quantum Annealing.

Thermodynamic Computing: Extropic's Approach

Extropic is pioneering thermodynamic computing using probabilistic circuits. Instead of quantum effects, their hardware directly samples from programmable probability distributions using energy-based models.

Key Points:

• Uses energy-based models (EBMs) with Boltzmann distributions
• Hardware naturally evolves toward low-energy states
• Particularly suited for generative AI and optimization
• Deep connections to spin glass physics

For a comprehensive deep dive, see Quantum Computing - Thermodynamic Computing.

Connections to Spin Glass Physics

Both quantum annealing and thermodynamic computing have deep connections to spin glass physics:

Spin Glasses as Optimization Landscapes

Spin glasses are disordered magnetic systems with rugged energy landscapes—exactly the kind of landscapes that optimization algorithms must navigate. The Hamiltonian:

$\mathcal{H} = -\sum_{\langle i,j \rangle} J_{ij} \sigma_i \sigma_j$

where $J_{ij}$ are random couplings, creates frustration and many local minima. This structure appears in:

• Traveling Salesman Problem - Can be mapped to spin glass form
• Neural network training - Loss landscapes resemble spin glasses
• Protein folding - Energy landscapes share spin glass characteristics
• Combinatorial optimization - Many NP-hard problems have spin glass-like structure

For more on this connection, see Markov Chains, Traveling Salesman and Spin Glasses.

Quantum vs. Classical Annealing

Classical simulated annealing (see Simulated Annealing) uses thermal fluctuations to explore energy landscapes:

• Probability of accepting moves: $P \propto \exp(-\Delta E / T)$
• Gets trapped in local minima at low temperature
• Requires careful cooling schedules

Quantum annealing (D-Wave's approach) uses quantum tunneling:

• Can tunnel through energy barriers even at zero temperature
• Quantum fluctuations provide alternative to thermal fluctuations
• Potentially faster for certain problem classes

For more on quantum spin glasses, see Quantum Spin Glass.

Thermodynamic Sampling

Thermodynamic computing (Extropic's approach) directly samples from the equilibrium distribution:

• Samples from $P(\mathbf{x}) \propto \exp(-E(\mathbf{x})/T)$
• Natural evolution toward low-energy states
• Hardware implements the sampling process directly

This is similar to Markov chain Monte Carlo methods used to study spin glasses (see Markov Chains, Traveling Salesman and Spin Glasses), but implemented in hardware rather than software.

Hybrid Quantum-Classical Computing

Hybrid quantum-classical systems combine quantum and classical processors, using quantum processors to evaluate cost functions while classical optimizers adjust parameters. This approach is particularly useful in the NISQ era.

Key Applications:

• Variational Quantum Eigensolver (VQE) - Finding ground states of molecules
• Quantum Approximate Optimization Algorithm (QAOA) - Combinatorial optimization
• Quantum Machine Learning - Training quantum neural networks

For detailed information, see Quantum Computing - Hybrid Quantum-Classical Systems.

Comparison of Approaches

Approach	Mechanism	Best For	Current Status
Gate-based Quantum	Quantum gates, superposition, entanglement	General quantum algorithms	NISQ era, limited scale
Quantum Annealing	Quantum tunneling through energy landscape	Optimization, sampling	Commercial (D-Wave)
Thermodynamic Computing	Probabilistic sampling from energy landscape	Generative AI, optimization	Early commercial (Extropic)
Hybrid Quantum-Classical	Quantum + classical optimization	NISQ applications	Active research

The Future of Hybrid Computing

Hybrid approaches are likely to play a crucial role in the near-term future of quantum computing:

1. Specialization - Different problems may require different approaches
2. Pragmatism - Hybrid systems can be built with current technology
3. Energy efficiency - Physical evolution may be more efficient than explicit computation
4. Complementarity - Quantum and classical processors can work together

As we move toward fault-tolerant quantum computing, hybrid approaches will continue to provide practical solutions for specific problems. Understanding the connections to spin glass physics helps explain why these approaches work and when they're most effective.

Conclusion

Hybrid computing approaches—quantum annealing, thermodynamic computing, and hybrid quantum-classical systems—offer alternative paths to quantum advantage. By leveraging energy landscapes, probabilistic processes, and physical evolution, these approaches can solve optimization and sampling problems more efficiently than classical methods alone.

The deep connections to spin glass physics illuminate why these approaches work: many computational problems have energy landscapes similar to spin glasses, and understanding how physical systems navigate these landscapes informs algorithm design.

Whether through quantum tunneling (D-Wave), probabilistic sampling (Extropic), or hybrid systems, these approaches demonstrate that there are multiple paths to computational advantage beyond universal quantum computers.

Exploring Further

For more background on the physics underlying these approaches:

• Spin Glasses - Overview of spin glass physics and energy landscapes
• Quantum Spin Glass - Quantum extensions and quantum annealing
• Simulated Annealing - Classical optimization inspired by spin glasses
• Markov Chains, Traveling Salesman and Spin Glasses - Computational methods and connections to optimization

For information about quantum computing companies and tools, see:

• Quantum Computing - Companies and Tools - Overview of major quantum computing platforms

Learning Resources

Quantum Annealing

• D-Wave Learning Resources - Official tutorials and documentation on quantum annealing: docs.dwavesys.com
• Ocean SDK Documentation - Learn to program D-Wave quantum annealers: docs.ocean.dwavesys.com
• D-Wave Leap - Cloud platform with tutorials and examples: cloud.dwavesys.com/leap

Spin Glass Physics and Optimization

• Statistical Mechanics Courses (MIT OpenCourseWare) - Free course materials on statistical mechanics and spin glasses: ocw.mit.edu
• Optimization Algorithms (Coursera) - Courses on optimization methods including simulated annealing: coursera.org

Thermodynamic Computing

• Energy-Based Models - Research papers and resources on energy-based models in machine learning
• Probabilistic Computing - Emerging field resources on probabilistic and thermodynamic computing approaches