*Alán Aspuru-Guzik, Thi Ha Kyaw, Tim Menke, Sukin Sim, Mario Krenn, and Jakob Kottmann*

Quantum computers promise to outperform their classical counterparts in several critical applications such as machine learning or factorization of large prime numbers. The original “killer application” of quantum computers is the quantum simulation of quantum mechanical systems. It promises to overcome the daunting computational overhead that grows exponentially in the size of the system. The impact of making the simulation of large quantum systems tractable could be immense: Quantum computers may one day be able to simulate new pharmaceutical compounds or high-temperature superconducting materials. On one hand, many recent approaches make near-term intermediate-scale quantum computers (NISQ) computing a contender to simulate increasingly larger systems as both the software and the hardware keep improving. Also, we know that quantum algorithms for these tasks in error-corrected quantum computers require 100,000s of high-quality qubits, which are not accessible anytime soon.

A collective effort of the large community of quantum algorithm designers is to identify new practical applications for quantum computers.

**Our team has now identified a new family of relevant applications for near-term quantum computers: The design of new quantum hardware itself. **

Quantum computers excel at simulating systems that are *quantum *in nature. Our key observation is that because quantum hardware is itself a quantum mechanical system, there will come a moment when they are too complex to be designed and studied with classical computers. At that point, we will need to employ quantum algorithms as well as quantum resources rather than classical ones to simulate new quantum hardware. In two preprints, we show how to use variations of the variational quantum eigensolver (VQE) algorithm to design new superconducting and new photonic devices, with applications to quantum computing, quantum communication, and quantum sensing.

In the first preprint, we develop methods to quantumly simulate and design new superconducting circuit-based quantum processors. The project was done in collaboration with Nicolas Sawaya and Gian Giacomo Guerreschi from Intel Labs and Will Oliver from MIT. As a proof-of-principle numerical experiment, we emulate the quantum computer-aided design process (QCAD) by considering networks of superconducting transmon qubits and computing both static and dynamic properties of these quantum processors by using quantum algorithms. A multi-level extension of the VQE algorithm is employed to find the energy states of the superconducting processor, which can aid in identifying undesired crosstalk between separate parts of the hardware chip. In addition, we use a quantum simulation technique called Suzuki-Trotter evolution to simulate the performance of gate operations on transmon circuits.

In the second preprint, we apply the concept of quantum simulation to the design of new photonic quantum hardware. We show how to reproduce photonic boson sampling results and high-dimensional multipartite entangled state generation. The direct mappings of quantum optical elements to digital quantum circuits can be seen in the figure below. The mapping onto digital quantum computers allows not only for more efficient simulation of the optical setup but also gives access to more powerful optimization techniques by emulating operations that are hard to achieve on the photonic devices. One immediate example is the direct emulation of initial photon pairs which can currently only be created by probabilistic processes on photonic hardware.

For photonics, classical optimization protocols for the topological optimization of optical setups exist. Here our approach can take over the non-topological part of the optimization by simulating and optimizing parametrized trial setups. The combination of QCAD with an effective graph-based optimization algorithm, also recently proposed by our group, appears to be a promising candidate to combine the best of the classical and quantum world. A similar quantum-classical symbiosis is possible for superconducting circuits by combining the respective QCAD algorithm with automated design software that we developed previously.

Our work opens the possibility of using one type of quantum computer to design another one. We could envision an ion trap quantum computer designing a superconducting one or vice-versa. Like in all digital design processes, the make-test-analyze design cycle for quantum hardware may be enhanced by using the proposed QCAD algorithm.

Furthermore, quantum processor design is likely to encounter a roadblock in the next few years when the size of quantum processor modules will outpace our classical simulation capabilities. We envision that the preprints that we describe in this post provide a path forward for the design of large quantum processors. Along the way, we expect to discover exciting new hardware designs and improved quantum algorithms that facilitate quantum computers’ ability to simulate their own building blocks.

We are curious about how the global creativity of the quantum community will make QCAD even more efficient and extend it to new use cases.

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