5 research outputs found
Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
Encoding quantum information into a set of harmonic oscillators is considered
a hardware efficient approach to mitigate noise for reliable quantum
information processing. Various codes have been proposed to encode a qubit into
an oscillator -- including cat codes, binomial codes and
Gottesman-Kitaev-Preskill (GKP) codes. These bosonic codes are among the first
to reach a break-even point for quantum error correction. Furthermore, GKP
states not only enable close-to-optimal quantum communication rates in bosonic
channels, but also allow for error correction of an oscillator into many
oscillators. This review focuses on the basic working mechanism, performance
characterization, and the many applications of GKP codes, with emphasis on
recent experimental progress in superconducting circuit architectures and
theoretical progress in multimode GKP qubit codes and
oscillators-to-oscillators (O2O) codes. We begin with a preliminary
continuous-variable formalism needed for bosonic codes. We then proceed to the
quantum engineering involved to physically realize GKP states. We take a deep
dive into GKP stabilization and preparation in superconducting architectures
and examine proposals for realizing GKP states in the optical domain (along
with a concise review of GKP realization in trapped-ion platforms). Finally, we
present multimode GKP qubits and GKP-O2O codes, examine code performance and
discuss applications of GKP codes in quantum information processing tasks such
as computing, communication, and sensing.Comment: 77+5 pages, 31 figures. Minor bugs fixed in v2. comments are welcome
Architectures for Multinode Superconducting Quantum Computers
Many proposals to scale quantum technology rely on modular or distributed
designs where individual quantum processors, called nodes, are linked together
to form one large multinode quantum computer (MNQC). One scalable method to
construct an MNQC is using superconducting quantum systems with optical
interconnects. However, a limiting factor of these machines will be internode
gates, which may be two to three orders of magnitude noisier and slower than
local operations. Surmounting the limitations of internode gates will require a
range of techniques, including improvements in entanglement generation, the use
of entanglement distillation, and optimized software and compilers, and it
remains unclear how improvements to these components interact to affect overall
system performance, what performance from each is required, or even how to
quantify the performance of each. In this paper, we employ a `co-design'
inspired approach to quantify overall MNQC performance in terms of hardware
models of internode links, entanglement distillation, and local architecture.
In the case of superconducting MNQCs with microwave-to-optical links, we
uncover a tradeoff between entanglement generation and distillation that
threatens to degrade performance. We show how to navigate this tradeoff, lay
out how compilers should optimize between local and internode gates, and
discuss when noisy quantum links have an advantage over purely classical links.
Using these results, we introduce a roadmap for the realization of early MNQCs
which illustrates potential improvements to the hardware and software of MNQCs
and outlines criteria for evaluating the landscape, from progress in
entanglement generation and quantum memory to dedicated algorithms such as
distributed quantum phase estimation. While we focus on superconducting devices
with optical interconnects, our approach is general across MNQC
implementations.Comment: 23 pages, white pape
Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector
International audienceIn quantum error correction, information is encoded in a high-dimensional system to protect it from the environment. A crucial step is to use natural, low-weight operations with an ancilla to extract information about errors without causing backaction on the encoded system. Essentially, ancilla errors must not propagate to the encoded system and induce errors beyond those which can be corrected. The current schemes for achieving this fault-tolerance to ancilla errors come at the cost of increased overhead requirements. An efficient way to extract error syndromes in a fault-tolerant manner is by using a single ancilla with strongly biased noise channel. Typically, however, required elementary operations can become challenging when the noise is extremely biased. We propose to overcome this shortcoming by using a bosonic-cat ancilla in a parametrically driven nonlinear cavity. Such a cat-qubit experiences only bit-flip noise and is stabilized against phase-flips. To highlight the flexibility of this approach, we illustrate the syndrome extraction process in a variety of codes such as qubit-based toric codes, bosonic cat- and Gottesman-Kitaev-Preskill (GKP) codes. Our results open a path for realizing hardware-efficient, fault-tolerant error syndrome extraction
Quantum error correction of a qubit encoded in grid states of an oscillator
Text and figures edited for clarity. The claims of the paper remain the same. Author list fixedInternational audienceQuantum bits are more robust to noise when they are encoded non-locally. In such an encoding, errors affecting the underlying physical system can then be detected and corrected before they corrupt the encoded information. In 2001, Gottesman, Kitaev and Preskill (GKP) proposed a hardware-efficient instance of such a qubit, which is delocalised in the phase-space of a single oscillator. However, implementing measurements that reveal error syndromes of the oscillator while preserving the encoded information has proved experimentally challenging: the only realisation so far relied on post-selection, which is incompatible with quantum error correction (QEC). The novelty of our experiment is precisely that it implements these non-destructive error-syndrome measurements for a superconducting microwave cavity. We design and implement an original feedback protocol that incorporates such measurements to prepare square and hexagonal GKP code states. We then demonstrate QEC of an encoded qubit with unprecedented suppression of all logical errors, in quantitative agreement with a theoretical estimate based on the measured imperfections of the experiment. Our protocol is applicable to other continuous variable systems and, in contrast with previous implementations of QEC, can mitigate all logical errors generated by a wide variety of noise processes, and open a way towards fault-tolerant quantum computation
High-On-Off-Ratio Beam-Splitter Interaction for Gates on Bosonically Encoded Qubits
Encoding a qubit in a high-quality superconducting microwave cavity offers the opportunity to perform the first layer of error correction in a single device but presents a challenge: how can quantum oscillators be controlled while introducing a minimal number of additional error channels? We focus on the two-qubit portion of this control problem by using a three-wave-mixing coupling element to engineer a programmable beam-splitter interaction between two bosonic modes separated by more than an octave in frequency, without introducing major additional sources of decoherence. Combining this with single-oscillator control provided by a dispersively coupled transmon provides a framework for quantum control of multiple encoded qubits. The beam-splitter interaction g_{bs} is fast relative to the time scale of oscillator decoherence, enabling over 10^{3} beam-splitter operations per coherence time and approaching the typical rate of the dispersive coupling χ used for individual oscillator control. Further, the programmable coupling is engineered without adding unwanted interactions between the oscillators, as evidenced by the high on-off ratio of the operations, which can exceed 10^{5}. We then introduce a new protocol to realize a hybrid controlled-swap operation in the regime g_{bs}≈χ, in which a transmon provides the control bit for the swap of two bosonic modes. Finally, we use this gate in a swap test to project a pair of bosonic qubits into a Bell state with measurement-corrected fidelity of 95.5%±0.2%