An official website of the United States government
Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and synthesize it with fault-tolerant protocols by combining bosonic quantum error correction (QEC) and advanced quantum control techniques. We introduce essential building blocks of error-corrected gadgets by leveraging ancilla-assisted bosonic operations using a generalized variant of path-independent quantum control. Using these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single-photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction requires only dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Moreover, each error-corrected bosonic qubit is comprised of only a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic QEC in the full fault-tolerant setting. We numerically demonstrate the feasibility of our schemes using current experimental parameters in the circuit-QED platform. Finally, we present a hardware-efficient architecture for fault-tolerant quantum computing by concatenating the four-legged cat qubits with an outer qubit code utilizing only beam-splitter couplings. Our estimates suggest that the overall noise threshold can be reached using existing hardware. These developed fault-tolerant schemes extend beyond their applicability to four-legged cat qubits and can be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits.
more »
« less
Quantum capacity and codes for the bosonic loss-dephasing channel
Bosonic qubits encoded in continuous-variable systems provide a promising alternative to two-level qubits for quantum computation and communication. So far, photon loss has been the dominant source of errors in bosonic qubits, but the significant reduction of photon loss in recent bosonic qubit experiments suggests that dephasing errors should also be considered. However, a detailed understanding of the combined photon loss and dephasing channel is lacking. Here, we show that, unlike its constituent parts, the combined loss-dephasing channel is non-degradable, pointing towards a richer structure of this channel. We provide bounds for the capacity of the loss-dephasing channel and use numerical optimization to find optimal single-mode codes for a wide range of error rates.
more »
« less
- PAR ID:
- 10384653
- Date Published:
- Journal Name:
- Quantum
- Volume:
- 6
- ISSN:
- 2521-327X
- Page Range / eLocation ID:
- 821
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Bosonic pure-loss channel, which represents the process of photons decaying into a vacuum environment, has zero quantum capacity when the channel’s transmissivity is less than 50%. Modeled as a beam splitter interaction between the system and its environment, the performance of bosonic pure-loss channel can be enhanced by controlling the environment state. We show that by choosing the ideal Gottesman-Kitaev-Preskill (GKP) states for the system and its environment, perfect transmission of quantum information through a beam splitter is achievable at arbitrarily low transmissivities. Our explicit constructions allow for experimental demonstration of the improved performance of a quantum channel through passive environment assistance, which is potentially useful for quantum transduction where the environment state can be naturally controlled. In practice, it is crucial to consider finite-energy constraints, and high-fidelity quantum communication through a beam splitter remains achievable with GKP states at the few-photon level.more » « less
-
Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. Here, we introduce a fault-tolerant hybrid quantum computation by building on the advantages of both discrete-variable (DV) and continuous-variable (CV) systems. In particular, we define a CV-DV hybrid qubit with a bosonic cat code and a single photon, which is implementable in current photonic platforms. Due to the cat code encoded in the CV part, the predominant loss errors are readily correctable without multiqubit encoding, while the logical basis is inherently orthogonal due to the DV part. We design fault-tolerant architectures by concatenating hybrid qubits and an outer DV quantum error-correction code such as a topological code, exploring their potential merit in developing scalable quantum computation. We demonstrate by numerical simulations that our scheme is at least an order of magnitude more resource efficient compared to all previous proposals in photonic platforms, allowing us to achieve a record-high loss threshold among existing CV and hybrid approaches. We discuss the realization of our approach not only in all-photonic platforms but also in other hybrid platforms including superconducting and trapped-ion systems, which allows us to find various efficient routes toward fault-tolerant quantum computing.more » « less
-
Bosonic channels describe quantum-mechanically many practical communication links such as optical, microwave, and radiofrequency. We investigate the maximum rates for the bosonic multiple access channel (MAC) in the presence of thermal noise added by the environment and when the transmitters utilize Gaussian state inputs. We develop an outer bound for the capacity region for the thermal-noise lossy bosonic MAC. We additionally find that the use of coherent states at the transmitters is capacity-achieving in the limits of high and low mean input photon numbers. Furthermore, we verify that coherent states are capacity-achieving for the sum rate of the channel. In the non-asymptotic regime, when a global mean photon-number constraint is imposed on the transmitters, coherent states are the optimal Gaussian state. Surprisingly however, the use of single-mode squeezed states can increase the capacity over that afforded by coherent state encoding when each transmitter is photon number constrained individually.more » « less
-
null (Ed.)Abstract The decoherence effects experienced by the qubits of a quantum processor are generally characterized using the amplitude damping time ( T 1 ) and the dephasing time ( T 2 ). Quantum channel models that exist at the time of writing assume that these parameters are fixed and invariant. However, recent experimental studies have shown that they exhibit a time-varying (TV) behaviour. These time-dependant fluctuations of T 1 and T 2 , which become even more pronounced in the case of superconducting qubits, imply that conventional static quantum channel models do not capture the noise dynamics experienced by realistic qubits with sufficient precision. In this article, we study how the fluctuations of T 1 and T 2 can be included in quantum channel models. We propose the idea of time-varying quantum channel (TVQC) models, and we show how they provide a more realistic portrayal of decoherence effects than static models in some instances. We also discuss the divergence that exists between TVQCs and their static counterparts by means of a metric known as the diamond norm. In many circumstances this divergence can be significant, which indicates that the time-dependent nature of decoherence must be considered, in order to construct models that capture the real nature of quantum devices.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.22331/q-2022-09-29-821
