New Passive Quantum Error Correction Could Be The Breakthrough for Large Scale Quantum Computers

Researchers led by Prof. David DiVincenzo from Forschungszentrum Jülich and RWTH Aachen University, and partners from the University of Basel and QuTech Delft, have now proposed a design for a quantum computer circuit with passive error correction. Such a circuit would already be inherently fault protected and could significantly accelerate the construction of a quantum computer with a large number of qubits.

Above – A new qubit design combines a gyrator with superconducting circuits to intrinsically protect the qubit from noise.

Usually, several imperfect qubits are combined to form a so-called logical qubit. Quantum error correction codes, or QEC codes for short, thus make it possible to detect errors and subsequently correct them, so that the quantum information is preserved over a longer period of time. The old techniques work in a similar way to active noise cancellation in headphones: In a first step, any fault is detected. Then, a corrective operation is performed to remove the error and restore the information to its original pure form.

This is very complex and can take hundreds of qubits to make one logical qubit. Typically, complex error-correcting electronics are required for each qubit, making it difficult to build circuits with many qubits, as required to build a universal quantum computer.

The proposed design for a superconducting circuit has a kind of built-in error correction. The circuit is designed in such a way that it is already inherently protected against environmental noise while still controllable. The concept thus bypasses the need for active stabilization in a highly hardware-efficient manner, and would therefore be a promising candidate for a future large-scale quantum processor that has a large number of qubits.

Physics X – A Superconducting Qubit that Protects Itself

This strategy, known as the Gottesman-Kitaev-Preskill (GKP) code, was proposed in 2001. However, implementing it with superconducting circuits has so far been impossible because it requires a large magnetic field. The newly proposed architecture circumvents this obstacle by employing a synthetic magnetic field, pushing the GKP protocol closer to a possible realization.

Even if one physical qubit is disrupted by noise, the information carried by the logical qubit will not be corrupted. In the “exotic-state” approach to QEC, each computational unit is a single oscillator, and the logical bits are represented by two special states of the oscillator, called nontrivial states, that are robust against local noise. The exotic-state technique employs continuous-variable systems, such as electromagnetic modes, which are initialized in states that are either robust by themselves (passive QEC) or can be stabilized via operations that do not affect the logical qubit (active QEC).

The GKP strategy is one example of the exotic-state approach. In the GKP code, the exotic states are called grid states, which are superpositions of an oscillator’s position eigenstates. The robustness to noise in an active GKP protocol stems from the fact that small shifts in the momentum and position of the oscillator can be identified and corrected before they can corrupt the logical information. An experimental demonstration of grid states was recently realized in a superconducting circuit architecture with an active QEC protocol [3]. A GKP code with passive QEC, however, has not yet been demonstrated. Compared to active QEC, which requires complicated operations for error recovery, a passive QEC approach promises to be more efficient and could be advantageous for scaling up to larger computing architectures, as it requires fewer physical units.

A prototypical implementation of a passive GKP code involves an electron confined to two dimensions in a large magnetic field. Realizing such a passive GKP-code design with superconducting circuit architectures is not straightforward. The design would require a magnetic field to interact with microwave photons.

Rymarz and colleagues have proposed a way of utilizing synthetic magnetic fields, allowing for a superconducting qubit realization of the GKP code. They propose a system in which two superconducting anharmonic oscillators, called fluxonium circuits, are coupled via a gyrator, a device that can invert the current-voltage characteristics of a circuit element (Fig. 1). The asymmetric response of the gyrator implies a breaking of time-reversal symmetry like that produced by a magnetic field. The team shows that the ground states of the system correspond to the GKP “code words”—the grid states that are used to encode the logical information. The huge advantage here is that the logical qubit is constructed from the ground states of the system—in which the system will reside if no external energy is supplied. Leaving the ground state would corrupt the logical qubit, but it comes with an energy penalty, so the protection is naturally built in.

The researchers show that the proposed superconducting circuit simulates the model of an electron confined to a two-dimensional plane and subjected to a magnetic field. As such, the circuit’s energies resemble those of a quantum oscillator with discrete energy levels. For a given magnetic flux, the lowest-energy states can be used to encode the GKP code words.

Realizing GKP code words using superconducting circuits is especially promising, as it makes it relatively straightforward to implement a subset of logic gates called Clifford gates, which are required for fault-tolerant computation. The realization of an intrinsically robust computation unit is only the first step on the complex path towards fault-tolerant quantum computation.

SOURCES- APS Physics, Juelich
Written by Brian Wang,