What is a quantum processor? How it works

A quantum processor is the central processing unit of a quantum computer, designed to operate and control quantum bits (qubits) to perform computational tasks. Unlike classical processors that operate on bits representing definite 0 or 1 states, quantum processors influence the principles of quantum mechanics, such as superposition and entanglement, to achieve potentially exponential speedups for certain types of computations.

Fundamental Principles of Quantum Processors

A qubit is the heart of the quantum processor. Similar to a classical bit, a qubit has two possible basis states, typically denoted as |0⟩ and |1⟩ using Dirac notation. However, a qubit can also exist in a superposition, which is a linear combination of both |0⟩ and |1⟩ simultaneously. This means a qubit can be in a state that is neither definitively 0 nor 1, but rather a probabilistic combination of both. A string of n qubits can store 2ⁿ bits of information due to superposition, allowing quantum computers to represent exponentially more values than their classical counterparts. For instance, four classical bits can represent a number between 0 and 15, but four qubits can represent all these integers at the same time.

Another quantum property applied by quantum processors is entanglement. When two or more qubits are entangled, their quantum states become linked, such that the state of one qubit instantly influences the state of the others, regardless of the distance separating them. Measuring one entangled qubit will reveal the state of the other entangled qubits. This interconnection allows for complex correlations and parallel processing of information.

Quantum processors operate qubits using quantum gates (or qugates). These are similar to classical logic gates (like AND, OR, NOT) but operate on the quantum states of qubits. A quantum gate is a unitary transformation that changes the superposition and entanglement of qubits. The sequence of quantum gates applied to a set of qubits forms a quantum circuit, which represents a quantum algorithm.

Differences between Quantum processors and Classical Processors

The difference between quantum and classical processors lies in how they represent and process information. Classical computers store information as bits that are either 0 or 1 with 100% probability. They operate on these bits using logic gates in a sequential manner. In contrast, quantum processors utilize qubits that can exist in a probabilistic superposition of 0 and 1. Quantum computation controls the parallel nature of superposition, allowing quantum computers to potentially explore a huge computational space at the same time. Furthermore, entanglement enables intricate connections between qubits, leading to computational advantages for specific problems.

The concept of “quantum parallelism” arises from the ability of a quantum computer to operate on a superposition of many inputs at once. This allows for the concurrent evaluation of a function for multiple input values, a feat impossible for classical computers with a single operation. Deutsch showed that this quantum parallelism can lead to new algorithms and complexity classes. Shor’s algorithm for factorization, which is polynomial in time on a quantum computer compared to the exponential time required on a classical Turing computer, dramatically illustrates this potential. Grover’s database search algorithm demonstrates a quadratic speedup over classical search algorithms.

Architecture and Components

A quantum computing system, including the quantum processor, is envisioned as a full-stack architecture. This stack typically includes:

• Application Level: The high-level problem or task to be solved.
• Algorithmic Logic: The quantum algorithm designed to solve the problem. This is expressed in a quantum programming language.
• Quantum Programming Language and Compiler: High-level quantum programming languages (such as Q#, Qiskit, Cirq, OpenQL, Quipper, Scaffold, Silq, QCL, QML, Ket) allow programmers to express quantum algorithms. Compilers translate these high-level instructions into a sequence of low-level quantum instructions that the quantum processor can execute. Intermediate representations like cQASM and eQASM may be used.
• Micro-architecture: Defines the set of quantum instructions that the physical quantum hardware can execute.
• Physical Qubit Layer (Quantum Hardware): This is the actual quantum processor where qubits are physically realized and operated.

Controlling the qubits that operate quantum gates requires classy control systems. Quantum code compilers translate high-level computational instructions into machine code to control the quantum hardware.

Programming and Control

Programming quantum processors involves designing quantum circuits, which are sequences of quantum gates applied to qubits. This is done using quantum programming languages and software development kits (SDKs) like IBM’s Qiskit, Microsoft’s Quantum Development Kit (Q#), and Google’s Cirq. These tools provide ideas for working with qubits and quantum gates, as well as simulators for testing quantum algorithms.

Compilers play a critical role in translating high-level quantum programs into the specific instructions that can be executed on a particular quantum processor. This involves tasks such as qubit allocation, gate scheduling, and optimization for the target hardware’s architecture and connectivity limitations. Due to the high error rates in current quantum hardware, code optimization is essential to reduce the number of operations and improve the possibility of correct results.

Applications of Quantum Processors

While large-scale, fault-tolerant quantum computers are still on the horizon, NISQ processors are being discovered for various applications, including:

• Cryptography: Quantum computers pose a threat to current public-key cryptography systems like RSA, as Shor’s algorithm can professionally factor large numbers, a task that is computationally impracticable for classical computers. This has encouraged research into quantum-safe cryptography (also known as post-quantum cryptography). Quantum processors can also be used for quantum key distribution (QKD), a secure method for generating cryptographic keys.
• Quantum Simulation: Feynman proposed that quantum computers could efficiently simulate complex quantum systems in physics, chemistry, and materials science, a task that is very difficult for classical computers due to the exponential growth of the Hilbert space. This could lead to innovations in drug discovery, materials design, and understanding fundamental physical miracles.
• Optimization: Quantum algorithms like the Quantum Approximate Optimization Algorithm (QAOA) and quantum annealing hold promise for solving computationally challenging optimization problems in areas such as logistics routing, financial modeling, and resource allocation. D-Wave focuses on quantum annealing processors for optimization tasks.
• Machine Learning: Quantum machine learning discovers the potential of quantum algorithms to improve or speed up machine learning tasks. This includes developing quantum neural networks, quantum support vector machines, and quantum algorithms for data analysis.
• Scientific Computing: Quantum computers have the potential to quicken various scientific computing tasks, such as solving linear equations, differential equations, and performing numerical integration.

Simulation of Quantum Processors

Due to the limited availability and noisy nature of physical quantum processors, quantum simulators play a critical role in the development and testing of quantum algorithms. Classical computers can simulate the behavior of quantum systems, allowing researchers to study and debug quantum algorithms before running them on actual quantum hardware. However, simulating large numbers of qubits becomes expensive due to the exponential growth of the state space. For instance, simulating a 50-qubit system requires storing 2⁵⁰ complex amplitudes.

High-performance computing resources enable the simulation of quantum circuits with a significant number of qubits. Quantum simulators can run on classical hardware, and some are accessible through cloud platforms.

What does a quantum processor do?

A quantum processor takes initialised qubits, applies a designed sequence of unitary quantum gates to manipulate their states (control superposition and entanglement), and finally measures the qubits to obtain classical results. This process, repeatedly controlled by a classical computer, allows quantum algorithms to potentially solve certain problems much faster than classical algorithms.

A quantum processor executes quantum algorithms by operating the states of qubits. Here’s a step-by-step of what a quantum processor does

1. Initialisation of Qubits: The quantum processor starts by initialising a set of qubits to a specific state, naturally the |0⟩ state. This initial state serves as the input for the quantum algorithm. The number of qubits available defines the size of the quantum register and effects the complexity of computations that can be performed.
2. Application of Quantum Gates: The core of the quantum computation involves applying a sequence of quantum gates to the qubits.
   • Quantum gates are unitary transformations that operate on one or more qubits, changing their quantum states. These gates are the elementary operations of a quantum algorithm, similar to logic gates in classical computing.
   • The sources mention various types of quantum gates, including single-qubit gates (like Hadamard, Pauli-X, Z) and multi-qubit gates (like Controlled-NOT (CNOT), Controlled-U, and Toffoli (CCNOT)).
   • The sequence of gates applies, the quantum algorithm being executed. This sequence is often represented as a quantum circuit.
3. Quantum Parallelism: One of the features of a quantum processor is its ability to achievement superposition, allowing it to operate on multiple input states at the same time.
   • A qubit can exist in a superposition of both |0⟩ and |1⟩ states at the same time. When quantum gates are applied to qubits in superposition, the operations are effectively performed on all the superposed states in parallel.
   • This quantum parallelism allows quantum computers to potentially explore a huge computational space with a relatively small number of qubits and operations.
4. Entanglement: Quantum processors can also create and operate entangled states between qubits.
   • Entanglement is a quantum mechanical singularity where the states of two or more qubits become correlated in such a way that they share the same chance, no matter how far apart they are.
   • Entangled qubits are critical for many quantum algorithms and improve the computational power of quantum computers.
5. Interaction with Classical Control (Hybrid Architecture): Quantum processors repeatedly operate as quantum accelerators under the control of a classical processor.
   • The classical processor can manage the overall execution flow, including setting up the quantum circuit, sending instructions to the quantum processor, and processing the measurement results.
   • Some quantum programming languages, like QCL, are designed with this hybrid architecture in mind, embedding quantum operations within a classical control flow.
6. Measurement: The final step in a quantum computation is measuring the state of the qubits.
   • Measurement is a process that collapses the quantum state of a qubit into a definite classical state (either 0 or 1). The outcome of a measurement is probabilistic, determined by the amplitudes of the qubit’s superposition state.
   • The measurement results, which are classical bits, are then read out from the quantum processor. These results are used by the classical part of the system to provide the final answer to the computational problem.
   • Some quantum algorithms may include intermediate measurements during the computation, with subsequent operations potentially depending on the results of these measurements.
7. Reversibility (Ideally): In principle, quantum operations, being based on unitary transformations, are reversible. This means that (theoretically) the initial state of the qubits can be recovered by applying the inverse sequence of operations. However, the final measurement step is inherently irreversible.