4 quantum bits simulate a high-fidelity circuit 8 times larger Pan, Zhu et al. propose circuit cutting scheme

Although recent quantum computing devices are still limited by the number and quality of quantum bits in the so-called NISQ era, the advantages of quantum computing have been demonstrated experimentally. Moreover, hybrid architectures for quantum and classical computing have emerged as prime examples for demonstrating NISQ applications in which low-depth quantum circuits are repeatedly applied. To further scale up the problems that can be solved by NISQ devices, the number of physical quantum bits can be reduced by "cutting" the quantum circuit into different parts.

Recently, Jianwei Pan, Xiaobo Zhu, Chengzhi Peng, and Wenkang Weng from the University of Science and Technology of China (USTC) have experimentally demonstrated a new circuit cutting method: using only four physical superconducting quantum bits, they successfully simulated linear cluster states involving up to 33 quantum bits, and achieved higher circuit fidelity. A preprinted paper, "Experimental Simulation of Larger Quantum Circuits with Fewer Superconducting Quantum Bits," has been submitted to the ArXiV website.

01 Applications in the NISQ Era: The Need for Smaller Quantum Devices

Quantum computing offers potentially higher speedups than classical computing for many applications, such as factorization, unstructured search, and quantum simulations. However, these applications require quantum computers to be fault-tolerant, which current quantum technologies are not yet able to do: we have just entered the era of noise-containing intermediate-scale quanta (NISQ), which means that the number of physical quantum bits is substantial in the computational space, but they are error-prone, or noisy. Recent experimental demonstrations of quantum computing involve about 50-60 quantum bits. Although they may already exceed the limits of classical supercomputers in terms of memory size; the error-prone noise gate limits the depth of quantum circuits running on current quantum devices and constitutes a major obstacle to practical applications.

Therefore, it makes practical sense to solve big problems with smaller quantum devices, even in exchange for using more classical resources.

This topic can be roughly divided into two branches; one at the algorithmic level and the other at the circuit level. The former involves breaking down a large problem into smaller subproblems, each of which is solved by a small quantum computer. This includes the quantized classical divide and conquer algorithm to solve combinatorial optimization problems; and the deep variational quantum algorithmic framework - which is suitable for modeling physical systems with weak interactions between subsystems. The circuit-level solution is to decompose a large quantum circuit into smaller parts, implement each part independently, and finally use a classical computer to combine the computational results.

02Circuit cutting scheme: simulating linear cluster states of superconducting quantum biton circuits

This time, this Chinese team chose to solve this problem from the circuit level. The team experimentally implemented a tomography-like circuit cutting scheme to simulate large linear-cluster states. Due to the symmetry of linear-cluster states, the team ended up only needing to run subcircuits of up to four superconducting quantum bits, and the simulated linear-cluster states could be scaled up to 33 quantum bits.

A cluster state is a series of highly entangled states that can be used to implement measurement-based quantum computation. That is, only measurements of the cluster states are needed to perform universal quantum computation; where the linear cluster state is a specific example of a cluster state where all the quantum bits are aligned in one dimension.

To analyze the performance, the team also used a stabilizer technique to estimate a lower limit of fidelity. This was then compared to the fidelity bounds obtained in previous work on the direct preparation of 12 quantum bit states. Using the circuit-cut scheme, the experimental fidelity bounds for the 4-qubit simulation of the 12-qubit cluster state can reach 0.734, which is about 19% higher than previous experiments simulated directly on a 12-qubit superconducting processor.

This experimental result indicates that the circuit cut scheme has the potential to become a standard tool in NISQ applications.

(a)Example diagram of the circuit cut scheme. The quantum circuit on the left is cut at the red cross and split into two subcircuits. The original circuit can be simulated by combining the quantum measurement statistics of the two subcircuits at different bases and with different inputs. (b) The simplified density matrix of the first two quantum bits can be decomposed into pictures. (c) Left: a 12-bit linear cluster state; right: a 12-bit linear cluster state can be simulated by combining the measurement data of these two subcircuits.

(a)Processor structure diagram with the quantum bits of Q3 to Q6 selected by the team as the 4-quantum-bit subcircuit and the quantum bits of Q4 to Q6 as the 3-quantum-bit subcircuit. (b) Measurement benchmark waveforms of the 4-quantum-bit subcircuit. (c) Measurement reference waveform of the 3-quantum-bit subcircuit.

(a)Comparison of expectations from a 12-quantum-bit circuit (orange) and a circuit-cutting scheme by running a smaller quantum circuit (blue) with 64 expectations per group, all of which have an ideal value of 1. (b) Simulation of fidelity (blue) and processing time (red) for large linear cluster states using the same experimental data for a 4-quantum-bit and 3-quantum-bit circuit. The circuit cut experiment was repeated 25 times, and the error bars in both subplots indicate fluctuations due to repeated experiments.

03The future: exploiting the full potential of circuit cutting to determine the optimal cutting point

In this work, the team experimentally demonstrated a circuit-cutting scheme and simulated larger linear cluster states that scale in size up to 33 quantum bits, using up to 4 quantum bits. With 12 quantum bits, a higher fidelity is achieved compared to previous work in which 12 quantum bits states were prepared directly, providing corroboration for the applicability of the circuit cut scheme.

In the NISQ era, the simulation of large quantum circuits with small quantum devices is a promising direction. Currently, several circuit-cutting schemes exist; further experimental benchmarking of these schemes is necessary to assess their applicability in practice. On the other hand, although circuit cutting schemes provide systematic methods for cutting quantum circuits into small pieces, at present, there is no general method for determining the optimal cutting point. Thus, the team concludes, "the potential of circuit cutting has not been fully exploited."

Link to paper：

https://arxiv.org/abs/2207.14142