Cloud-based quantum hardware providers: Where to run your quantum algorithms

Having designed your initial quantum algorithm, the logical next step is to determine where you can execute it. To address this, it is essential to first identify the type of quantum algorithm you have developed, as there are various paradigms within quantum computing. 

Gate-based quantum computing

This is the most well-known paradigm. In this model, information is processed using qubits and quantum gates, similar to how classical bits and logic gates function in traditional computing. Quantum gates manipulate the quantum states of qubits, enabling superpositions, entanglement, and complex transformations. By arranging these gates into circuits, gate-based quantum computers can execute various quantum machine learning algorithms, such as quantum neural networks or kernel methods.  

Quantum gates, such as the Hadamard, Pauli-X, Pauli-Y, Pauli-Z, and CNOT gates, are fundamental building blocks in this paradigm. The Hadamard gate, for example, creates superpositions, allowing a qubit to exist simultaneously in both its |0⟩ and |1⟩ states. The Pauli-X gate acts as a quantum NOT gate, flipping the state of a qubit, while the Pauli-Y and Pauli-Z gates introduce phase shifts. The CNOT gate, or controlled NOT gate, is a two-qubit gate that entangles qubits, a crucial resource for quantum computing. Quantum circuits are the combination of various quantum gates, arranged to perform useful transformations to the initial qubits. For example, the following two-qubit circuit transforms the initial |00⟩ state to a superposition of all basis states: |00⟩ + |01⟩ - |10⟩ - |11⟩. 

The underlying hardware for these quantum computers varies. Superconducting qubits, which rely on superconducting circuits to create and manipulate qubits, are used by companies such as IBM, Rigetti, and Google. These qubits are cooled to near absolute zero temperatures to maintain their quantum states. Trapped ions, utilized by companies like IonQ and Quantinuum, involve trapping ions in electromagnetic fields and using lasers to manipulate their quantum states. Neutral atoms, employed by companies such as QuEra and Pasqal, use optical tweezers to trap and manipulate atoms. All these quantum computers can be accessed on the cloud, providing researchers and developers worldwide the opportunity to run their quantum algorithms on state-of-the-art quantum hardware. 

Continuous variable model

This paradigm, primarily employed by Xanadu, offers a distinct approach to quantum computing. Instead of using qubits, this model utilizes qumodes. Unlike qubits, which are binary and can represent either 0 or 1 (or a superposition of both), qumodes can take on a continuous range of values from 0 to a certain number n. This continuous variable approach allows for more complex and richer quantum state superpositions, providing a different set of advantages and challenges compared to the qubit-based model.  

Quantum computers operating under this paradigm are implemented using photonics, the fundamental particles of light, as the carriers of information. These photons can be manipulated using various optical components such as beam splitters, phase shifters, and squeezers to create and transform quantum states. One of the significant advantages of photonic quantum computers is that they can operate at room temperature, unlike many qubit-based systems that require extremely low temperatures to maintain quantum coherence. Additionally, photonic systems are less susceptible to certain types of noise and decoherence, making them potentially more stable and scalable for specific applications. 

Xanadu, a leading company in this field, has been at the forefront of developing photonic quantum computers. They have introduced hardware such as the Borealis and Strawberry Fields platforms, which enable the implementation of continuous variable quantum algorithms. These platforms provide tools for quantum machine learning, optimization, and simulation tasks. 

Quantum annealing 

In quantum annealing, qubits represent the variables of an optimization problem, with the problem encoded in the system's energy landscape. This process involves slowly cooling the system from a high-energy state to its lowest energy configuration, which corresponds to the optimal solution of the problem. Quantum annealing leverages the principles of quantum mechanics, such as tunneling and superposition, to explore and traverse the energy landscape more efficiently than classical methods. 

The annealing process begins with all qubits initialized in a superposition of states, representing all possible solutions simultaneously. As the system gradually evolves, it explores the energy landscape defined by the problem's Hamiltonian. The goal is to reach the ground state, where the energy is minimized, representing the optimal solution to the optimization problem. Quantum tunneling allows the system to escape local minima and continue searching for the global minimum, enhancing the probability of finding the best solution. 

This quantum computing paradigm is well-suited for optimization problems, such as protein folding, genetic sequence alignment and clinical trial optimization.  

D-Wave Systems is a leading provider of quantum annealing machines. These machines consist of thousands of qubits, interconnected in a complex architecture that allows for the encoding and solving of large-scale optimization problems. They can be accessed via the cloud, allowing researchers and businesses worldwide to leverage quantum annealing for solving complex optimization problems. 

Quantum-inspired algorithms  

Quantum-inspired algorithms run on classical hardware, such as GPUs, but draw inspiration from the principles of quantum mechanics. These algorithms leverage quantum concepts to enhance the performance of classical computations, providing innovative solutions to complex problems. One prominent example of quantum-inspired algorithms is tensor networks, which are graphical representations of tensors inspired by quantum operators. 

Tensor networks decompose high-dimensional tensors into a network of lower-dimensional tensors connected by edges, making it easier to manage and compute with large datasets. This decomposition allows for efficient representation and manipulation of data, reducing the computational complexity associated with high-dimensional spaces.

These quantum-inspired algorithms can run efficiently on classical GPUs, taking advantage of the parallel processing capabilities of these devices. Moreover, quantum-inspired algorithms have the potential to scale on quantum computers as the hardware matures. This scalability ensures that quantum-inspired algorithms will continue to provide advantages both now, on classical hardware, and in the future, on quantum hardware.