Beyond Qubits: Unlocking the Third State in Quantum Processors

By Alex Hill, Senior Quantum Systems Engineer

Qubits are the basic building block of a quantum processor, and are so named because they represent a continuum of complex superpositions of two basic quantum states. The power of qubits comes in part from their ability to encode significantly more information than a classical bit — an infinite set of states between 0 and 1. In mathematical terms, quantum gates that manipulate the state of individual qubits are unitary operators drawn from SU(2).

Rigetti’s superconducting quantum processors are based on the transmon design [1]. Each physical qubit is an anharmonic oscillator, meaning that the energy gaps between subsequent qubit energy states decrease as the qubit climbs higher up the state ladder. We typically only address the first two states, 0 and 1 (in the literature, sometimes referred to as g(round) and e(xcited)); however, the design of our qubits supports even higher states. The simple structure of the transmon energy levels gives superconducting qubits the unique ability to address many of these states in a single circuit.

Adding just one additional state turns our qubits into qutrits, which can not only increase the amount of information encoded in a single element, but also enables techniques that can dramatically decrease readout errors [2]. Recent work at Rigetti has shown how qutrit-qutrit gates can reduce the cost of decomposing three-qubit gates (CCPHASE) into basic two-qubit components [3]. This is in part due to the much larger state space accessible using qutrits — single qutrit operations live in SU(3), while two-qutrit operations live in SU(9) — a more than twofold increase in dimensionality over the two-qubit case.

Qutrits — the three-dimensional extension to qubits — are able to encode over 2x the information over typical two-state operations.

Why not push to even higher states? In practice, the dephasing rate of superconducting qudits increases significantly as you climb to higher and higher levels of the transmon. The coherence time of the just second excited state (|2>), however, can be on the order of many microseconds — long enough to perform useful computations.

Rigetti now offers experimental access to qutrit operations through Quil-T, our pulse-level extension to Quil. In addition to the standard suite of qubit calibrations, users will have access to a new set of gates between the first and second states of the qutrit for most locations around our devices.

Consider the following simple QUIL program:

0   DECLARE ro BIT[1]
1   RX(pi) 0
2   RX_12(pi) 0
3   MEASURE 0 ro[0]

In this circuit, we flip a qutrit to the first excited state (line 1) and then the second state (line 2) before reading out (line 3).The final measurement, however, will still return a value of 0 or 1, as this program doesn’t specify how the the QPU should classify all three states. To unlock the full power of the higher state space, we can leverage Quil-T to manipulate the unclassified readout data from our qutrits. We show how to extract and classify unclassified data from your Quil-T experiments, use qutrit gates in a circuit, and perform some basic qutrit readout error mitigation in a companion Jupyter notebook available through QCS (https://docs.rigetti.com/qcs/).

Accessing the third state in our processors is useful for researchers exploring the cutting edge of quantum computing, quantum physics [4] and those interested in traditional, qubit-based algorithms alike. With carefully-chosen readout parameters, for example, classification performance can be significantly better when choosing between |2> and |0>, rather than the default classification between |0> and |1>. We use this technique to dramatically reduce readout errors — in some cases up to 60% — by adapting our readout system to decide between the best-distinguished qutrit states. We have enabled this enhanced readout scheme for all users on qubits where the higher-level gates are available.

References

[1] Koch, J., Yu, T. M., Gambetta, J., Houck, A. A., Schuster, D. I., Majer, J., Blais, A., Devoret, M. H., Girvin, S. M., & Schoelkopf, R. J. (2007). Charge-insensitive qubit design derived from the Cooper pair box. Physical Review A — Atomic, Molecular, and Optical Physics, 76(4), 042319. https://doi.org/10.1103/PhysRevA.76.042319

[2] Mallet, F., Ong, F. R., Palacios-Laloy, A., Nguyen, F., Bertet, P., Vion, D., & Esteve, D. (2009). Single-shot qubit readout in circuit quantum electrodynamics. Nature Physics, 5(11), 791–795. https://doi.org/10.1038/nphys1400

[3] Hill, A. D., Hodson, M. J., Didier, N., & Reagor, M. J. (2021). Realization of arbitrary doubly-controlled quantum phase gates. https://arxiv.org/abs/2108.01652v1

[4] Blok, M. S., Ramasesh, V. V., Schuster, T., O’Brien, K., Kreikebaum, J. M., Dahlen, D., Morvan, A., Yoshida, B., Yao, N. Y., & Siddiqi, I. (2021). Quantum Information Scrambling on a Superconducting Qutrit Processor. Physical Review X, 11(2), 021010. https://doi.org/10.1103/PhysRevX.11.021010

Editor’s note: This post was updated at 9:15am PT, December 15, 2021 to include the addition of a fourth reference.