D Wave is a Canadian based quantum computing firm whose main goal is to develop quantum computers which uses quantum annealing properties.
Let’s talk a bit about Quantum annealers:
Quantum annealers are a types of quantum computers developed by D Wave system and the term “Ocean” is an open-source SDE kit which runs in D Wave quantum computers. Ocean is not a python programming language. But it has python packages developed by D-Wave company.
Now, we ask the question? Why specifically the company has developed “Ocean”? Because D-Wave determined to solve optimization problems.
Now, what in the world is optimization problem?
Optimization means finding the best solution among the available solutions.
Image Source: Combinatorial Optimization Using Binary Decision Diagrams | NTT Technical Review (ntt-review.jp)
In the above example, there were 3 solutions available but picked up the first solution because this matches the combination of food tiems with 300 yen.
Now, how to achieve this optimization? By means of quantum annealers.
Quantum annealers naturally returns the lower energy solutions [1]. With the help of Quantum physics optimization problems can be mapped to energy minimization problem. The fundamental rule of physics is: everything tends to seek minimum energy state. For example, Objects slide down, hot things cool down over time. The same is applicable for quantum physics as well.
Image source: What is Quantum Annealing? — D-Wave System Documentation documentation (dwavesys.com)
Quantum annealing uses the properties of quantum physics to find the lower energy state of a problem thus finding the near-optimal or optimal set of solutions.
Sampling problems:
For machine learning issues where you wish to construct a probabilistic model of reality, sampling from a variety of low-energy states and defining the energy landscape are helpful. The samples provide data about the model state for a particular set of parameters, which can be used to enhance the model.
Sampling from energy-based distributions is a computationally intensive task that is an excellent match for the way that the D-Wave quantum computer solves problems; that is, by seeking low-energy states [2].
How Quantum Annealing works in D-Wave QPU’s:
Image source: What is Quantum Annealing? — D-Wave System Documentation documentation (dwavesys.com)
Qubits are the lowest energy states of the superconducting loops that make up the D-Wave QPU. These states have a circulating current and a corresponding magnetic field.
Here, due to Superposition qubits can be in 0 and 1 state at the same time. The below energy diagram has only one valley.
Image source: What is Quantum Annealing? — D-Wave System Documentation documentation (dwavesys.com)
During annealing process, the barrier is raised which makes the energy diagram as a double well potential.
The left lower valley is ‘0’ state and right lower valley is ‘1’.
Image source: What is Quantum Annealing? — D-Wave System Documentation documentation (dwavesys.com)
At the end of the quantum annealing process, each qubit collapses from a superposition state into either 0 or 1 (a classical state).
Image source: What is Quantum Annealing? — D-Wave System Documentation documentation (dwavesys.com)
The qubit states end up in either 0 or 1.
But with the help of external magnetic field, we can control the state of qubit. The programmable quantity that controls the external magnetic field is called a bias, and the qubit minimizes its energy in the presence of the bias. The qubit which ends in lower well is the final output.
The real power is to link the quantum states. This can be achieved by coupler. Quantum Entanglement process is used here. A coupler can make two qubits tend to end up in the same state — both 0 or both 1 — or it can make them tend to be in opposite states. Like a qubit bias, the correlation weights between coupled qubits can be programmed by setting a coupling strength. Together, the programmable biases and weights are the means by which a problem is defined in the D-Wave quantum computer.
Image source: What is Quantum Annealing? — D-Wave System Documentation documentation (dwavesys.com)
As stated, each qubit has a bias and qubits interact via the couplers. When formulating a problem, users choose values for the biases and couplers. The biases and couplings define an energy landscape, and the D-Wave quantum computer finds the minimum energy of that landscape: this is quantum annealing.
Complexity increases when the number of qubits increases.
In summary, the systems starts with a set of qubits, each in a superposition state of 0 and 1. They are not yet coupled. When they undergo quantum annealing, the couplers and biases are introduced and the qubits become entangled. At this point, the system is in an entangled state of many possible answers. By the end of the anneal, each qubit is in a classical state that represents the minimum energy state of the problem, or one very close to it. All of this happens in D-Wave quantum computers in a matter of microseconds.
Usage of Ocean software:
Ocean software automates the mapping from the linear and quadratic coefficients of a quadratic model to qubit bias and coupling values set on the QPU, you should understand it if you are using QPU solvers directly because it has implications for the problem-graph size and solution quality.
The D-Wave QPU is a lattice of interconnected qubits. While some qubits connect to others via couplers, the D-Wave QPU is not fully connected [2].
To know more about its architecture, kindly refer the below link:
D-Wave QPU Architecture: Topologies — D-Wave System Documentation documentation (dwavesys.com)
So, today we have seen quantum annealers concept in a comprehensive way along with the qubit orientation in D-Wave as well as some physics and graphs behind it. Thus, optimization problems can be solved more efficiently with the help of D-Wave Ocean systems.
References:
[1] What is Quantum Annealing? — D-Wave System Documentation documentation (dwavesys.com)
[2] D-Wave QPU Architecture: Topologies — D-Wave System Documentation documentation (dwavesys.com)
