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The secret behind Google's quantum supremacy: How random circuits can become verification tools?
Quantum Random Circuits (QRC) is a concept that incorporates random elements into local unit operations and measurements of quantum circuits. This idea is similar to the random matrix theory, which solves non-solvable problems that are difficult to analyze by averaging the result sets. This addition of randomness brings a variety of possible advantages to the circuit, including: (i) Verifying quantum computers: Google used this method when claiming quantum supremacy in 2019; (ii) Understanding quantum Universal structures of nonequilibrium and thermal processes in multibody dynamics.
Basic structure of quantum random circuit
General quantum circuits are composed of qubits, unit gates and measurements. The time evolution of quantum circuits is discrete, and the state system evolves gradually through unit operators.
Time evolution starts from the initial time, then
U(t;0) = U_t U_{t-1} ⋯ U_3 U_2 U_1is represented, where the unit operator of each step is represented by a local unit gate connecting the pair of qubits.In quantum information theory, the number of qubits
nrepresents the width of the circuit, and its depthdis the number of layers of unit gates.
A quantum circuit can be viewed as a tensor network, where each purple box is a local unit gate operating on two qubits. As time evolves on the grid, the final unit time evolution can be achieved by shrinking the index of the qubit.
Randomness of measurement
In quantum mechanics, the nature of measurements is stochastic, which means that circuits of the same structure (same qubits and gates) will produce different results in different runs. This randomness must be distinguished from random operations.
The results of each measurement can be different, forming a record like a random walk, and in many-body systems, the situation is further complicated by the interconnection between qubits.
Applications and Challenges
Verification of short-term quantum computers
The current era of quantum computing we are in is called the "Noisy Intermediate Scale Quantum (NISQ)" era, which means that current quantum computers are not fault-tolerant and are not large enough to achieve quantum advantage. We need to find several characteristics of the task: (i) difficult for classical computers; (ii) experimentally feasible on recent devices.
To this end, researchers are focusing on "sampling problems." For example, boron sampling has a strong theoretical foundation, but its experimental challenges are huge; random circuit sampling shows higher feasibility. In its claim of quantum supremacy, Google used a Sycamore processor to perform the sampling in much less time than a classical computer.
Thermalization of non-equilibrium and quantum many-body dynamics
In quantum many-body dynamics, elucidating how entanglements spread over time is a key problem that needs to be solved. Through the study of quantum random circuits, the results show that tangle growth under noise has a universal structure. Quantum stochastic circuits provide an experimental platform to explore and understand these processes.
Conclusion
With the advancement of quantum computing technology, the application scope of random circuits is also expanding, which may have a profound impact on many fields. However, these developments also face many challenges. Can future quantum computers truly realize the potential to surpass classical computing?
