Kerr Parametric Oscillators: The Key to Faster, More Efficient Quantum Computing?

Kerr Parametric Oscillators (KPOs) stabilize the superpositions of coherent states, which can be used as qubits, the fundamental units of quantum information. KPOs are promising for hardware-efficient quantum computers, with their ability to suppress bit-flip errors. They can also be applied to quantum annealing and fault-tolerant quantum computing. Implementing KPOs in quantum computing involves a Josephson parametric oscillator and a KPO in a three-dimensional cavity. Researchers from Toshiba Corporation’s Frontier Research Laboratory have proposed methods to accelerate the elementary gates for universal quantum computation with KPO qubits, potentially leading to more efficient and faster quantum computers.

What are Kerr Parametric Oscillators (KPOs) and their Role in Quantum Computing?

Kerr Parametric Oscillators (KPOs) are devices that can stabilize the superpositions of coherent states, which can be utilized as qubits. Qubits are the fundamental units of quantum information, similar to how bits are in classical computing. KPOs are promising candidates for realizing hardware-efficient quantum computers. The stabilization of the coherent states and the suppression of bit-flip errors have been experimentally realized in superconducting circuits for the dissipative-cat qubit and the KPO qubit.

KPOs do not rely on dissipation and can be described by a simple Hamiltonian. Despite their simplicity, KPOs yield rich nonlinear dynamics such as quantum bifurcation and chaos. The quantum bifurcation can be applied to quantum annealing, and a number of its implementations have been proposed. By regarding two branches of the bifurcation as up and down-spin states, a KPO lattice can behave like an Ising model and its physics such as phase transitions has been studied.

Applications of KPOs to fault-tolerant quantum computing have also been studied. Quantum gates preserving the bias of errors mentioned above have been proposed, which can be utilized for hardware-efficient quantum error correction. Analytically engineered control methods for shortening the gate times of the bias-preserving gates have recently been proposed.

How are KPOs Implemented in Quantum Computing?

For implementing a KPO with a superconducting circuit, a Josephson parametric oscillator with low photon loss has been suggested and demonstrated experimentally. Then by using a KPO in a three-dimensional cavity, single-qubit gates have been performed. Also, tunable coupling between two KPOs has been realized. Other experiments with KPOs have been reported such as a crossover from a Duffing oscillator to a KPO, degenerate excited states, single-qubit operations and characterizations with an ancillary transmon, and reflection coefficient measurements.

For KPO qubits, elementary gates for universal quantum computation have been proposed, which are based on adiabatic evolution and consist of ZX and ZZ rotations. Experimentally, a study has demonstrated adiabatic Rz and non-adiabatic Rx, and another study has adiabatically performed both Rz and Rx. Theoretically, other kinds of gate implementations have been proposed.

What are the Challenges and Solutions in Implementing KPOs?

Shorter gate times are desirable because they can reduce errors caused by photon loss in KPOs and also enable faster computation. However, the previous adiabatic elementary gates need long gate times and otherwise diabatic transitions out of a qubit space cause leakage errors. To reduce leakage errors, control methods called shortcuts to adiabaticity (STAs) have been proposed for cat-state generation and Rzz with a phase rotation of a parametric drive. Also, a variant of the derivative removal by adiabatic gate (DRAG) technique, which is related to STAs, has been proposed for the bias-preserving gates.

To accelerate the elementary gates for universal quantum computation with KPO qubits, an approach is based on an STA called counter-diabatic terms or counterterms for short, but does not use the exact counterterms which are often experimentally infeasible. Instead, the counterterms are first approximated by experimentally feasible terms, and then the pulse shapes for the gate operations are numerically optimized. As a result, the gate operations become faster by 2-6 times for Rz, 60 times for Rzz, and 2-6 times for Rx, keeping high gate fidelities.

What are the Implications of this Research?

This research by Taro Kanao and Hayato Goto from Toshiba Corporation’s Frontier Research Laboratory Corporate Research Development Center in Japan, published in the Physical Review Research journal, shows that the proposed methods can achieve speedups compared to adiabatic ones by up to six times with high gate fidelities of 99.9%. These methods are thus expected to be useful for quantum computers with KPOs.

The findings of this research could have significant implications for the development of quantum computing technology. By accelerating the elementary gates for universal quantum computation with KPO qubits, the researchers have demonstrated a method that could potentially lead to more efficient and faster quantum computers.

The research also contributes to the broader understanding of quantum computing and the role of KPOs in this field. It provides valuable insights into the challenges and potential solutions in implementing KPOs in quantum computing, which could guide future research and development efforts in this area.