D-Wave and Quantum Annealing
WOMANIUM Global Quantum Media Project Initiative — Winner of Global Quantum Media Project
Introduction
D-Wave, a pioneering quantum computing company, was founded in 1999 during a time when quantum computing was still in its infancy, and the concept of a universal quantum computer remained largely theoretical. Early research indicated the potential of building an adiabatic quantum computer, especially using superconducting qubits, and its applicability to specific problem classes and optimization tasks. From the outset, D-Wave set its sights on commercialization, opting to start with a quantum annealer to address a diverse range of challenges across industries, with the ultimate goal of delivering commercial quantum computing.
First two Decades of D-Wave
Over the course of the first two decades, D-Wave devoted significant efforts to develop the essential technical foundations, including quantum chip design, cryogenics, and calibration, required to construct a large, scalable, and well-functioning quantum annealer. This culminated in the release of their first commercially available quantum computer in 2011 [1], boasting 128 qubits. Since then, the company has achieved numerous milestones and introduced a 2000-qubit quantum processor. Today, their flagship quantum computing system, “Advantage,” boasts over 5000 qubits and supports hybrid solvers that leverage both classical and quantum resources to tackle larger industrial problems.
Phases of D-Wave Advancement
D-Wave’s advancement can be summarized in four phases:
1. Speed up on benchmark problem: Demonstrating remarkable speed-ups of 100x over the best classical heuristics.
2. Speed up on physics problem: Demonstrating 3Mx speed up over classical heuristics.
3. Customer Advantage: Professional services and real-world applications with demonstrated ROI for customers like Menten AI (100x speedup), Save-on-Foods (500x speedup), and VW (80% waste reduction).
4. Quantum Advantage: Achieving “Quantum Advantage,” wherein quantum computers have a clear advantage over classical systems in solving real-world problems.
D-Wave’s Quantum Technology Milestones
D-Wave’s Advantage
D-wave’s Advantage exhibits remarkable potency and extensive connectivity, excelling in diverse areas of computation.
- It facilitates the implementation of real-world hybrid applications on a large scale, with the ability to accommodate up to one million variables.
- Employing an innovative Annealing Quantum processor design, it boasts an impressive capacity of over 5000 qubits.
- Continuous research endeavors are dedicated to enhancing coherence and connectivity, thus continually bolstering its overall capabilities.
D-Wave’s Hybrid Solvers: CQM and BQM
The application of D-Wave’s quantum computing technology revolves around its ability to support hybrid frameworks that blend classical and quantum resources. While 5000 qubits offer substantial computational power, it is still not entirely sufficient for solving real-world problems effectively. Nevertheless, it serves as a crucial component within hybrid solvers, such as the constrained quadratic hybrid model solver and binary quadratic model solver.
1.The constrained quadratic model solver stands out for its capacity to efficiently incorporate complex constraints found in industrial optimization problems, unlocking larger application possibilities with up to 100,000 inequality and equality constraints, as well as binary, integer, and real/continuous variables.
2.The binary quadratic model solver, accommodating up to 100,000 variables, enables enterprise-scale problem-solving and effectively handles problems with binary variables.
D-Wave’s Full Stack Quantum Computing Solution
1.Quantum Computers: “Advantage” boasts five generations of annealing quantum computers with an impressive capacity of up to 5000 qubits, enabling advanced and efficient problem-solving across various fields.
2.Cloud Service: Gain seamless cloud access to the D-Wave quantum computer and quantum hybrid solvers, ensuring up to 99% uptime with real-time accessibility. This cloud-based infrastructure offers unparalleled convenience and scalability for researchers and developers.
3.Developer Tools: “Advantage” equips developers with powerful open-source tools in Python, including the Leap IDE for streamlined development and optimization of quantum algorithms. These tools foster a thriving quantum computing community and are easily accessible through local downloads.
4.Professional Services: A customer-focused phase engagement model guides organizations through the quantum computing journey. From initial exploration to production deployment, the expert team ensures a smooth onboarding experience and unlocks the full potential of quantum computing applications.
D-Wave’s Three Verticals: Logistics, Pharma, and Finance
D-Wave’s quantum computing technology has made significant strides in diverse industries, particularly in solving optimization problems to enhance operational efficiency and profitability. Logistics companies, dealing with shipping container logistics, employee scheduling, farm-to-market food delivery, and last-mile vehicle routing, have greatly benefited from D-Wave’s quantum solutions.
In the pharmaceutical sector, D-Wave’s quantum computers have been pivotal in tasks such as protein folding, clinical trials, and drug discovery. These complex processes require precise optimizations, and quantum annealing has accelerated these critical endeavors.
In the finance industry, D-Wave’s quantum computing capabilities have proven highly effective in optimizing portfolio risk, return, and marketing campaigns. Additionally, quantum computing aids in fraud detection, enabling quick analysis of vast datasets to identify and prevent fraudulent activities.
Two outstanding examples of D-Wave’s commercial applications include the quantum-hybrid e-commerce driver auto-scheduler (QEDA) at Pattison Food Group, significantly reducing manual scheduling time while accommodating driver preferences, and the Savant X HONE optimization engine at the Port of Los Angeles, which expedited container delivery and increased cargo handling capacity, leading to substantial efficiency gains. D-Wave’s quantum computing technology continues to empower businesses with innovative solutions to complex optimization challenges, fueling progress across industries.
Quantum Annealing
Quantum computing is fundamentally an algorithm that leverages quantum mechanical effects to seek the ground state of a Hamiltonian, akin to finding the global minimum of an objective function from a computer science perspective. This algorithm proves highly adept at solving optimization problems, as it aligns with classical approaches that model problems through energy landscapes, searching for the lowest point representing the optimal solution.
Quantum annealing employs quantum mechanical effects to identify the global minimum of an objective function, rendering it a natural solver for optimization problems. At its core, quantum annealing relies on the adiabatic theorem, which dictates that if a quantum system is initialized in the ground state of a Hamiltonian and evolves gradually into a new Hamiltonian over time, it will eventually reach the ground state of the final Hamiltonian. This concept of ground state computation facilitates the solution of complex problems through the construction and evolution of appropriate Hamiltonians.
Quantum Annealing-Different Perspective
Examining the concept of quantum annealing from a different perspective, we observe the 2D representation of the 3D energy function and wave function on a previous slide. The energy function, represented by the black curve, corresponds to the 3D plot’s essence, while the blue dotted curve signifies the wave function, determining the probability of the quantum system landing in different states across the energy landscape.
Initially, during the annealing process, when the system is initialized with a simple Hamiltonian, the wave function localizes around local minima, indicating a high probability of being in the ground state. As annealing progresses, the energy function changes, leading to multiple minima and narrow barriers, causing the wave function to spread out and delocalize across these minima. However, as the anneal continues and quantum dynamics slow, the wave function relocalizes, ideally around the global minimum, signifying a higher probability of the quantum processing unit (QPU) being in the global minimum state. At this point, the anneal yields a classical state with a sequence of spins, devoid of further quantum effects, effectively resembling a classical system.
Transverse Field Ising Hamiltonian
Quantum annealing is effectively described by a mathematical model known as the Transverse Field Ising Hamiltonian. This model involves two distinct components: the Transverse Field Hamiltonian and the Problem Hamiltonian. The Transverse Field Hamiltonian is responsible for the quantum effects during the annealing process, representing the initial simple Hamiltonian. As the annealing progresses, the two components of the Hamiltonian are combined, fully characterizing the Problem Hamiltonian. In the Problem Hamiltonian, the terms are associated with sigma z, while h and J are user-defined biases and couplings between qubits, representing the relationships between them in the problem domain.
Additionally, an anneal schedule is essential in defining how the quantum system evolves over time. The anneal schedule is plotted on the x-axis, normalized to an anneal parameter ranging from zero to one, representing the duration of the anneal. On the y-axis, the energy strength of the Transverse Field Hamiltonian (blue curve) and the Problem Hamiltonian (green curve) are depicted. The quantum annealing process begins with the QPU initialized in a state of superposition, where the quantum contribution dominates and the problem Hamiltonian is turned off. As the anneal progresses, the Transverse Field is gradually turned off, while the problem Hamiltonian is turned on, leading to the crossover region where quantum dynamics significantly impact the problem-solving process. .
After the crossover point, the qubits freeze into classical states, and at the end of the anneal, the final state of the qubits can be read out.
Quantum Annealing — Individual Qubit Level
Zooming in on the individual qubit level, we can characterize a single qubit using a double-well potential. This energy function describes the possibility of the qubit ending up in a spin-up or spin-down state, which is further mapped to binary variables.
The barrier between the wells corresponds to the Transverse Field, which is gradually raised during the annealing process. User-defined biases (H values) tilt the potential, favoring one state over the other. Moreover, the quadratic term (J) represents the relationship between two qubits, where they either agree or disagree on their final states.
RF SQUIDS
In the realm of quantum computing, a crucial component is the RF SQUID (Superconducting Quantum Interference Device), which can be visualized as a superconducting loop of wire. Superconductors play a vital role in quantum computing due to their unique properties. Firstly, when a superconductor is cooled below a specific temperature known as the critical temperature, it exhibits zero resistance. This property ensures that any current circulating through the superconductor does not generate heat or noise, crucial for maintaining a noise-free environment in quantum systems. Secondly, in the superconducting state, when current circulates in the loop, it does so simultaneously in both directions. This intriguing property allows magnetic flux to travel through the qubit’s body in opposing directions, creating what is known as a state of superposition.
To utilize these properties, D-Wave employs loops of wire as qubits. The qubit’s state, either spin-up or spin-down, is determined by the direction of the magnetic flux through the qubit’s body, following the principles of the right-hand rule. Despite current flowing in both directions, the magnetic flux does not cancel out but instead travels through the qubit’s body due to the superconducting loop’s configuration, effectively creating the state of superposition. In summary, the superconducting loop enables the circulation of current in both directions, resulting in magnetic flux traveling through the qubit’s body and realizing the state of superposition.
However, merely having a loop of wire would trap the qubit in a state of superposition indefinitely. To enable the qubit to reach a definitive state by the end of the annealing process, a Josephson junction is introduced. This involves creating a break in the loop and filling it with a dielectric material, allowing some current to pass through. The maximum current that can pass through this junction is called the critical current. The Josephson junction introduces a barrier, transitioning the qubit from a single-well potential state to a double-well potential state. The magnitude of the critical current determines the height of this barrier in the double well potential. Consequently, we can now create a qubit with two distinct states. Nonetheless, to move from the state of superposition to the state with a double-well potential, a tunable qubit is implemented, allowing the barrier height to be adjusted by applying a magnetic flux to the qubit’s loop.
Tunable Qubit
To achieve tunability in qubits, a single Josephson junction is replaced with a loop containing two Josephson junctions. This modification enables us to adjust the height of the barrier in the double well potential. During the annealing process, the height of the barrier can be initially set to zero, and then, over time, a magnetic flux is applied to the cJJ loop, raising the barrier height. This change in the flux through the loop alters the critical current through the Josephson junctions, effectively tuning the barrier height. Additionally, a bias is applied to a single qubit physically, which is implemented by introducing a flux through the qubit’s body. The magnitude and direction of this flux determine the preferred direction or state of the qubit’s body.
Coupling Qubits
In the quantum annealing process, it is essential to encode relationships between qubits, and this is achieved through the implementation of a coupler. The coupler is designed as a qubit-like device shown in red, resembling the ordinary qubit in structure, but with different parameters. It possesses a monostable energy function. Applying a magnetic flux to the cCJJ (Coupled Current-Carrying Josephson Junction) loop creates mutual induction between the coupler and the adjacent qubits.
The magnitude of the magnetic flux (ϕ_sub_co) corresponds to the J value, which defines the strength of the relationship between these qubits. By adjusting the flux, different relationships can be established. When the flux is in the positive range, it creates an antiferromagnetic relationship, indicating that the two qubits want to disagree. In contrast, when the flux is in the negative range, it establishes a ferromagnetic relationship, signifying that both qubits agree and aim to have the same state at the end of the anneal. Therefore, modifying the magnitude of the flux allows us to control the type of relationship realized by the J value as defined in the user’s problem.
The Chip — Processor Layout
Processors are constructed using tiles of qubits represented by loops, and couplers indicated by dots where horizontal and vertical qubits intersect. A tile typically contains eight qubits, and additional couplers connect multiple tiles of eight qubits. The D-Wave 2000 qubit processor had each qubit coupled to six others, resulting in 16-way connectivity. However, addressing real-world problems with multiple variables and interactions required more extensive connectivity. With the development of Advantage, connectivity increased from 6 to 15, enabling each qubit to couple with 15 others. This enhanced connectivity offers greater flexibility in handling complex real-world problems, as qubits can form more relationships and manage intricate interactions effectively. Further advancements are pursued to achieve even higher connectivity levels for addressing more intricate challenges.
Quantum Annealing vs Gate-based Quantum Computing
Quantum Annealing vs QAOA
Conclusion
In summary, D-Wave is a pioneer and exclusive provider of quantum annealing solutions, leading the forefront of quantum annealing with their cutting-edge processor “Advantage,” boasting over 5000 qubits and the upcoming “Advantage 2” with more than 7000 qubits. Since 2011, their rigorous simulations have demonstrated an extraordinary speedup of up to 3 million times compared to classical techniques, showcasing the immense potential of quantum annealing for optimization problems. D-Wave’s ultimate goal is to deliver commercial quantum computing, bridging the gap between theory and real-world applications to address complex challenges across industries.
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