Abstract Coherence times for superconducting qubits have greatly improved over time. Moreover, small logical qubit architectures using engineered dissipation have shown great promise for further improvements in the coherence of a logical qubit manifold comprised of few physical qubits. Nevertheless, optimal working parameters for small logical qubits are generally not well understood. This work presents several approaches to finding preferential parameter configurations by looking at three different cases of increasing complexity. We begin by looking at state stabilization of a single qubit using dissipation via coupling to a lossy object. We look at the limiting factors in this approach to error correction, and how we address those by numerically optimizing the parametric coupling strength with the lossy object having an effective time-varying dissipation rate—we call this a pulse-reset cycle. We then translate this approach to more efficient state stabilization to an abstracted three-qubit flip code, and end by looking at the very small logical qubit (VSLQ). By using these techniques, we can further increase logical state lifetimes for different architectures. We show significant advantages in using a pulse-reset cycle over numerically optimized, fixed parameter spaces.
Abstract Coherence times for superconducting qubits have greatly improved over time. Moreover, small logical qubit architectures using engineered dissipation have shown great promise for further improvements in the coherence of a logical qubit manifold comprised of few physical qubits. Nevertheless, optimal working parameters for small logical qubits are generally not well understood. This work presents several approaches to finding preferential parameter configurations by looking at three different cases of increasing complexity. We begin by looking at state stabilization of a single qubit using dissipation via coupling to a lossy object. We look at the limiting factors in this approach to error correction, and how we address those by numerically optimizing the parametric coupling strength with the lossy object having an effective time-varying dissipation rate—we call this a pulse-reset cycle. We then translate this approach to more efficient state stabilization to an abstracted three-qubit flip code, and end by looking at the very small logical qubit (VSLQ). By using these techniques, we can further increase logical state lifetimes for different architectures. We show significant advantages in using a pulse-reset cycle over numerically optimized, fixed parameter spaces.
One of the largest obstacles to building a quantum computer is gate error, where the physical evolution of the state of a qubit or group of qubits during a gate operation does not match the intended unitary transformation. Gate error stems from a combination of control errors and random single qubit errors from interaction with the environment. While great strides have been made in mitigating control errors, intrinsic qubit error remains a serious problem that limits gate fidelity in modern qubit architectures. Simultaneously, recent developments of small error-corrected logical qubit devices promise significant increases in logical state lifetime, but translating those improvements into increases in gate fidelity is a complex challenge. In this Letter, we construct protocols for gates on and between small logical qubit devices which inherit the parent device's tolerance to single qubit errors which occur at any time before or during the gate. We consider two such devices, a passive implementation of the three-qubit bit flip code, and the author's own [E. Kapit, Phys. Rev. Lett. 116, 150501 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.150501] very small logical qubit (VSLQ) design, and propose error-tolerant gate sets for both. The effective logical gate error rate in these models displays superlinear error reduction with linear increases in single qubit lifetime, proving that passive error correction is capable of increasing gate fidelity. Using a standard phenomenological noise model for superconducting qubits, we demonstrate a realistic, universal one- and two-qubit gate set for the VSLQ, with error rates an order of magnitude lower than those for same-duration operations on single qubits or pairs of qubits. These developments further suggest that incorporating small logical qubits into a measurement based code could substantially improve code performance.
We can encode a qubit in the energy levels of a quantum system.Relaxation and other dissipation processes lead to decay of the fidelity of this stored information.Is it possible to preserve the quantum information for a longer time by introducing additional drives and dissipation?The existence of autonomous quantum error correcting codes answers this question in the positive.Nonetheless, discovering these codes for a real physical system, i.e., finding the encoding and the associated driving fields and bath couplings, remains a challenge that has required intuition and inspiration to overcome.In this work, we develop and demonstrate a computational approach based on adjoint optimization for discovering autonomous quantum error correcting codes given a Hamiltonian description of a physical system.We implement an optimizer that searches for a logical subspace and control parameters to better preserve quantum information.We demonstrate our method on a system of a harmonic oscillator coupled to a lossy qubit, and find that varying the Hamiltonian distance in Fock space-a proxy for the control hardware complexity-leads to discovery of different and new error correcting schemes.We discover what we call the √ 3 code, realizable with a Hamiltonian distance d = 2, and propose a hardware-efficient implementation based on superconducting circuits.
Dissipatively stabilized cat qubits provide a promising route toward fault-tolerant quantum computation, exhibiting exponential suppression of bit-flip errors with increasing phase-space separation of the logical states, while incurring only a linear increase in phase-flip errors. Existing implementations rely on engineered two-photon dissipation via nonlinear coupling to a lossy environment, an approach largely confined to superconducting platforms and limited by spurious decay channels and finite dissipation rates. Here, we propose a fundamentally different stabilization paradigm based on repeated interactions with an auxiliary two-level system mediated by a quadratic Hamiltonian, enabling dissipative stabilization without reservoir engineering. Our approach overcomes key limitations of existing schemes and is compatible with a wider class of experimental platforms. Furthermore, it preserves the noise bias and extends to squeezed cat qubits, rendering single-photon loss errors partially correctable.
Cat qubits, for which logical |0⟩ and |1⟩ are coherent states |±α⟩ of a harmonic mode, offer a promising route towards quantum error correction. Using dissipation to our advantage so that photon pairs of the harmonic mode are exchanged with single photons of its environment, it is possible to stabilize the logical states and exponentially increase the bit-flip time of the cat qubit with the photon number |α|2 . A large two-photon dissipation rate κ2 ensures fast qubit manipulation and short error-correction cycles, which are instrumental to correct the remaining phase-flip errors in a repetition code of cat qubits. Here, we introduce and operate an autoparametric superconducting circuit that couples a mode containing the cat qubit to a lossy mode whose frequency is set at twice that of the cat mode. This passive coupling does not require a parametric pump, and it reaches a rate κ2/2π≈2 MHz . With such a strong two-photon dissipation, bit-flip errors of the autoparametric cat qubit are prevented for a characteristic time up to 0.3 s with only a mild impact on phase-flip errors. In addition, we illustrate how the phase of a quantum superposition between |α⟩ and |−α⟩ can be arbitrarily changed by driving the harmonic mode while keeping the engineered dissipation active. Published by the American Physical Society 2024
Quantum computing crucially relies on maintaining quantum coherence for the duration of a calculation. Bosonic quantum error correction protects this coherence by encoding qubits into superpositions of noise-resilient oscillator states. In the case of the Kerr-cat qubit (KCQ), these states derive their stability from being the quasi-degenerate ground states of an engineered Hamiltonian in a driven nonlinear oscillator. KCQs are experimentally compatible with on-chip architectures and high-fidelity operations, making them promising candidates for a scalable bosonic quantum processor. However, their bit-flip time must increase further to fully leverage these advantages. Here, we present direct evidence that the bit-flip time in a KCQ is limited by leakage out of the qubit manifold and experimentally mitigate this process. We coherently control the leakage population and measure it to be > 9%, twelve times higher than in the undriven system. We then cool this population back into the KCQ manifold with engineered dissipation, identify conditions under which this suppresses bit-flips, and demonstrate increased bit-flip times up to 3.6 milliseconds. By employing both Hamiltonian confinement and engineered dissipation, our experiment combines two paradigms for Schrödinger-cat qubit stabilization. Our results elucidate the interplay between these stabilization processes and indicate a path towards fully realizing the potential of these qubits for quantum error correction.
Superconducting qubits are among the most promising platforms for building a quantum computer. However, individual qubit coherence times are not far past the scalability threshold for quantum error correction, meaning that millions of physical devices would be required to construct a useful quantum computer. Consequently, further increases in coherence time are very desirable. In this Letter, we blueprint a simple circuit consisting of two transmon qubits and two additional lossy qubits or resonators, which is passively protected against all single-qubit quantum error channels through a combination of continuous driving and engineered dissipation. Photon losses are rapidly corrected through two-photon drive fields implemented with driven superconducting quantum interference device couplings, and dephasing from random potential fluctuations is heavily suppressed by the drive fields used to implement the multiqubit Hamiltonian. Comparing our theoretical model to published noise estimates from recent experiments on flux and transmon qubits, we find that logical state coherence could be improved by a factor of 40 or more compared to the individual qubit T_{1} and T_{2} using this technique. We thus demonstrate that there is substantial headroom for improving the coherence of modern superconducting qubits with a fairly modest increase in device complexity.