We consider quantum error-correction codes for multimode bosonic systems, such as optical fields, that are affected by amplitude damping. Such a process is a generalization of an erasure channel. We demonstrate that the most accessible method of transforming optical systems with the help of passive linear networks has limited usefulness in preparing and manipulating such codes. These limitations stem directly from the recoverability condition for one-photon loss. We introduce a three-photon code protecting against the first order of amplitude damping, i.e. a single photon loss, and discuss its preparation using linear optics with single-photon sources and conditional detection. Quantum state and process tomography in the code subspace can be implemented using passive linear optics and photon counting. An experimental proof-of-principle demonstration of elements of the proposed quantum error correction scheme for a one-photon erasure lies well within present technological capabilites.
Superconducting qubits are sensitive to a variety of loss mechanisms including dielectric loss from interfaces. By changing the physical footprint of the qubit it is possible to modulate sensitivity to surface loss. Here we show a systematic study of planar superconducting transmons of differing physical footprints to optimize the qubit design for maximum coherence. We find that qubits with small footprints are limited by surface loss and that qubits with large footprints are limited by other loss mechanisms which are currently not understood.
It was shown that using multiphoton qubits, a nearly deterministic Bell-state measurement can be performed with linear optics and on-off photodetectors [Phys. Rev. Lett. 114, 113603 (2015)]. However, multiphoton qubits are generally more fragile than single-photon qubits under a lossy environment. In this paper, we propose and analyze a scheme to teleport multiphoton-qubit information using hybrid entanglement with a loss-tolerant carrier qubit. We consider three candidates for the carrier qubit: a coherent-state qubit, a single-photon polarization qubit, and a vacuum-and-single-photon qubit. …
Entangling operations are a necessary tool for large-scale quantum information processing, but experimental imperfections can prevent current schemes from reaching sufficient fidelities as the number of qubits is increased. Here it is shown numerically how multi-toned generalizations of standard trapped-ion entangling gates can simultaneously be made robust against noise and mis-sets of the frequencies of the individual qubits. This relaxes the degree of homogeneity required in the trapping field, making physically larger systems more practical.
We compare three different types of optical qubits for information transfer via quantum teleportation and direction transmission under photon losses. The three types of qubits are (1) qubits using the vacuum and the single-photon (VSP) states, (2) single-photon qubits using polarization degrees of freedom, i.e., polarized single-photon (PSP) qubits, and (3) coherent-state qubits that use two coherent states with opposite phases as the qubit basis. Our analysis shows that the teleportation scheme outperforms the direct transmission for most of cases as far as fidelities are concerned. Overall, …
Experimental validation and control of quantum traits for an open quantum system are important for any quantum information purpose. We consider a traveling atom qubit as a quantum memory with adjustable velocity inside a leaky cavity, adopting a quantum witness as a figure of merit for quantumness assessment. We show that this model constitutes an inherent physical instance where the quantum witness does not work properly if not suitably optimized. We then supply the optimal intermediate blind measurements which make the quantum witness a faithful tester of quantum coherence. We thus find that…
High-precision manipulation of multi-qubit quantum systems requires strictly clocked and synchronized multi-channel control signals. However, practical Arbitrary Waveform Generators (AWGs) always suffer from random signal jitters and channel latencies that induces non-ignorable state or gate operation errors. In this paper, we analyze the average gate error caused by clock noises, from which an estimation formula is derived for quantifying the control robustness against clock noises. This measure is then employed for finding robust controls via a homotopic optimization algorithm. We also intro…
The loss of qubits - the elementary carriers of quantum information - poses one of the fundamental obstacles towards large-scale and fault-tolerant quantum information processors. In this work, we experimentally demonstrate a complete toolbox and the implementation of a full cycle of qubit loss detection and correction on a minimal instance of a topological surface code. This includes a quantum non-demolition measurement of a qubit loss event that conditionally triggers a restoration procedure, mapping the logical qubit onto a new encoding on the remaining qubits. The demonstrated methods, imp…
We investigate the performance of quantum teleportation under a lossy environment using two different types of optical hybrid qubits. One is the hybrid of the vacuum and single-photon states with coherent states and the other is the hybrid of polarized single-photon states with coherent states. We have shown that the hybrid qubit using vacuum and single-photon states is generally more robust to photon loss effects compared to the one using the photon polarization with respect to fidelities and success probabilities of quantum teleportation.
Using a fluxonium qubit with in situ tunability of its Josephson energy, we characterize its energy relaxation at different flux biases as well as different Josephson energy values. The relaxation rate at qubit energy values, ranging more than one order of magnitude around the thermal energy $k_B T$, can be quantitatively explained by a combination of dielectric loss and $1/f$ flux noise with a crossover point. The amplitude of the $1/f$ flux noise is consistent with that extracted from the qubit dephasing measurements at the flux sensitive points. In the dielectric loss dominant regime, the l…
The surface code cannot be used when qubits vanish during computation; instead, a variant known as the topological cluster state is necessary. It has a gate error threshold of $0.75% and only requires nearest-neighbor interactions on a 2D array of qubits. Previous work on loss tolerance using this code only considered qubits vanishing during measurement. We begin by also including qubit loss during two-qubit gates and initialization, and then additionally consider interaction errors that occur when neighbors attempt to entangle with a qubit that isn't there. In doing so, we show that even our …
Einstein-Podolsky-Rosen steering refers to the quantum phenomenon whereby the state of a system held by one party can be "steered" into different states at the will of another, distant, party by performing different local measurements. Although steering has been demonstrated in a number of experiments involving qubits, the question of which two-qubit states are steerable remains an open theoretical problem. Here, we derive a necessary condition for any two-qubit state to be steerable when the steering party suffers from a given probability of qubit loss. Our main result finds application in on…
Connectivity-induced surface-loss penalty in superconducting qubit-coupler lattices
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）
High-quality-factor 3D cavities in superconducting circuits are ideal candidates for bosonic logical qubits as their fidelity is limited only by the low photon loss rate. However, the transmon qubits that are used to manipulate bosonic qubits result in the emergence of additional relaxation and dephasing channels. In this work, a numerical study is performed to elucidate the effect of the various loss channels on the performance of logical gates on a bosonic qubit. A gate error model is developed that encapsulates the loss mechanisms for arbitrary gate operations and predicts experimentally ac…
Entanglement in quantum systems is usually degraded by interaction with the environment. From time to time, some parties of a multipartite entangled system may become decoherent with other parties of the system due to the interference with the environment. In this situation, it is interesting to know how much information the residual system would keep on carrying. In this paper, as a starting point for any entangled system, we investigate the property of the 2 x N x M state with qubit being disentangled, which is characterized by the measurement of robustness.
We study the problem of optimal preparation of a bipartite entangled state, which remains entangled the longest time under action of local qubit noises. We show that for unital noises such a state is always maximally entangled, whereas for nonunital noises, it is not. We develop a decomposition technique relating nonunital and unital qubit channels, based on which we find the explicit form of the ultimately robust state for general local noises. We illustrate our findings by amplitude damping processes at finite temperature, for which the ultimately robust state remains entangled up to two tim…
Analytical formulas are presented for simplified but useful qubit geometries that predict surface dielectric loss when its thickness is much less than the metal thickness, the limiting case needed for real devices. These formulas can thus be used to precisely predict loss and optimize the qubit layout. Surprisingly, a significant fraction of surface loss comes from the small wire that connects the Josephson junction to the qubit capacitor. Tapering this wire is shown to significantly lower its loss. Also predicted are the size and density of the two-level state (TLS) spectrum from individual s…
Hybrid systems consisting of different types of qubits are promising for building quantum computers if they combine useful properties of their constituent qubits. However, they also pose additional challenges if one type of qubits is more susceptible to environmental noise than the others. Dynamical decoupling can help to protect such systems by reducing the decoherence due to the environmental noise, but the protection must be designed such that it does not interfere with the control fields driving the logical operations. Here, we test such a protection scheme on a quantum register consisting…
In this work, we investigate the controlled teleportation protocol using optical qubits within the single-rail logic. The protocol makes use of an entangled tripartite state shared by the controller and two further parties (users) who will perform standard teleportation. The goal of the protocol is to guarantee that the teleportation is successful only with the permission of the controller. Optical qubits based on either superpositions of vacuum and single-photon states or superposition of coherent states are employed here to encode a tripartite maximal slice state upon which the protocol is b…
Josephson junctions form the essential non-linearity for almost all superconducting qubits. The junction is formed when two superconducting electrodes come within $\sim$1 nm of each other. Although the capacitance of these electrodes is a small fraction of the total qubit capacitance, the nearby electric fields are more concentrated in dielectric surfaces and can contribute substantially to the total dissipation. We have developed a technique to experimentally investigate the effect of these electrodes on the quality of superconducting devices. We use $λ$/4 coplanar waveguide resonators to emu…
We present a family of loss-tolerant quantum strong coin flipping protocols; each protocol differing in the number of qubits employed. For a single qubit we obtain a bias of 0.4, reproducing the result of Berlín et al. [Phys. Rev. A 80, 062321 (2009)], while for two qubits we obtain a bias of 0.3975. Numerical evidence based on semi-definite programming indicates that the bias continues to decrease as the number of qubits is increased but at a rapidly decreasing rate.
In this article the robustness of tripartite Greenberger-Horne-Zeilinger (GHZ) and W states is investigated against Dzyaloshinskii-Moriya (i.e. DM) interaction. We consider a closed system of three qubits and an environmental qubit. The environmental qubit interacts with any one of the three qubits through DM interaction. The tripartite system is initially prepared in GHZ and W states respectively. The composite four qubits system evolve with unitary dynamics. We detach the environmental qubit by tracing out from four qubits and profound impact of DM interaction is studied on the initial entan…
We investigate the performance of Grover's quantum search algorithm on a register which is subject to loss of the particles that carry the qubit information. Under the assumption that the basic steps of the algorithm are applied correctly on the correspondingly shrinking register, we show that the algorithm converges to mixed states with 50% overlap with the target state in the bit positions still present. As an alternative to error correction, we present a procedure that combines the outcome of different trials of the algorithm to determine the solution to the full search problem. The procedu…
Loss resilience of driven-dissipative remote entanglement in chiral waveguide quantum electrodynamics
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；Department of Physics, University of Chicago（芝加哥大学物理系）
We present a scheme for generating robust and persistent entanglement between qubits that do not interact and that are separated by a long and lossy transmission channel, using Markovian reservoir engineering. The proposal uses only the correlated decay into the common channel of remotely separated, driven single-photon qubit transitions. This simple scheme is generic and applicable to various experimental implementations, including circuit and cavity QED, with little experimental overhead compared with methods requiring dynamic control, initialization, measurement, or feedback. In addition to…
We present an error analysis of various tomographic protocols based on the linear inversion for the reconstruction of an unknown two-qubit state. We solve the problem of finding a tomographic protocol which is the most robust against errors in terms of the lowest value (i.e., equal to 1) of a condition number, as required by the Gastinel-Kahan theorem. In contrast, standard tomographic protocols, including those based on mutually unbiased bases, are nonoptimal for determining all 16 elements of an unknown two-qubit density matrix. Our method is based on the measurements of the 16 generalized P…
Qubit realizations based on Majorana bound states have been considered promising candidates for quantum information processing which is inherently inert to decoherence. We put the underlying general arguments leading to this conjecture to the test from an open quantum system perspective. It turns out that, from a fundamental point of view, the Majorana qubit is as susceptible to decoherence as any local paradigm of a qubit.
We propose a teleportation-based scheme to implement a universal set of quantum gates with a four-component cat code, assisted by appropriate entangled resource states and photon number resolving detection. The four-component cat code features the ability to recover from single photon loss. Here, we propose a concrete procedure to correct the single photon loss, including detecting the single photon loss event and recovering the initial states. By concatenating with standard qubit error correcting codes, we estimate the loss threshold for fault-tolerant quantum computation and obtain a signifi…
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 structu…
With the assistance of weak cross-Kerr nonlinearities, we introduce an optical scheme to fuse two small-size polarization entangled W states into a large-scale W state without qubit loss, i.e.,$\mathrm{W}_{n+m}$ state can be generated from an $n$-qubit W state and a $m$-qubit W state. To complete the fusion task, two polarization entanglement processes and one spatial entanglement process are applied. The fulfillments of the above processes are contributed by a cross-Kerr nonlinear interaction between the signal photons and a coherent state via Kerr media. We analyze the resource cost and the …
We present a general method for finding loss-tolerant teleportation on large, entangled stabilizer states using only single-qubit measurements, known as \emph{stabilizer pathfinding} (SPF). For heralded loss, SPF is shown to generate optimally loss-tolerant measurement patterns on any given stabilizer state. Furthermore, SPF also provides highly loss-tolerant teleportation strategies when qubit loss is unheralded. We provide a fast algorithm for SPF that updates continuously as a state is generated and measured, which is therefore suitable for real-time implementation on a quantum-computing de…
We construct a minimal robust controlled-NOT gate with an Ising-type interaction by which elementary two-qubit gates are implemented. It is robust against inaccuracy of the coupling strength and the obtained quantum circuits are constructed with the minimal number (N=3) of elementary two-qubit gates and several one-qubit gates. It is noteworthy that all the robust circuits can be mapped to one-qubit circuits robust against a pulse length error. We also prove that a minimal robust SWAP gate cannot be constructed with N=3, but requires N=6 elementary two-qubit gates.
In this paper, we compare single-photon qubits and hybrid qubits as information carriers through quantum teleportation using a Gaussian continuous-variable channel. A hybrid qubit in our study is in the form of entanglement between a coherent state and a single photon. We find that hybrid qubits outperform photonic qubits when coherent amplitudes of the hybrid qubits are as low as $α\lesssim 1$, while photonic qubits yield better results for larger amplitudes. We analyze effects of photon losses, and observe that the overall character of teleportation for different qubits remains the same alth…
We investigate a scheme for topological quantum computing using optical hybrid qubits and make an extensive comparison with previous all-optical schemes. We show that the photon loss threshold reported by Omkar {\it et al}. [Phys. Rev. Lett. 125, 060501 (2020)] can be improved further by employing postselection and multi-Bell-state-measurement based entangling operation to create a special cluster state, known as Raussendorf lattice for topological quantum computation. In particular, the photon loss threshold is enhanced up to $5.7\times10^{-3}$, which is the highest reported value given a rea…
Dynamical decoupling is a technique that protects qubits against noise. The ability to preserve quantum coherence in the presence of noise is essential for the development of quantum devices. Here the Rigetti quantum computing platform was used to test different dynamical decoupling sequences. The performance of the sequences was characterized by Quantum Process Tomography and analyzed using the quantum channels formalism. It is shown that dynamical decoupling can reduce qubit dephasing but cannot protect against spontaneous emission. Furthermore, from process tomography results, it was also p…
In single-qubit quantum secret sharing, a secret is shared between N parties via manipulation and measurement of one qubit at a time. Each qubit is sent to all N parties in sequence; the secret is encoded in the first participant's preparation of the qubit state and the subsequent participants' choices of state rotation or measurement basis. We present a protocol for single-qubit quantum secret sharing using polarization entanglement of photon pairs produced in type-I spontaneous parametric downconversion. We investigate the protocol's security against eavesdropping attack under common experim…
Exquisite quantum control has now been achieved in small ion traps, in nitrogen-vacancy centres and in superconducting qubit clusters. We can regard such a system as a universal cell with diverse technological uses from communication to large-scale computing, provided that the cell is able to network with others and overcome any noise in the interlinks. Here we show that loss-tolerant entanglement purification makes quantum computing feasible with the noisy and lossy links that are realistic today: With a modestly complex cell design, and using a surface code protocol with a network noise thre…
Graph codes play an important role in photonic quantum technologies as they provide significant protection against qubit loss, a dominant noise mechanism. Here, we develop methods to analyse and optimise measurement-based tolerance to qubit loss and computational errors for arbitrary graph codes. Using these tools we identify optimised codes with up to 12 qubits and asymptotically-large modular constructions. The developed methods enable significant benefits for various photonic quantum technologies, as we illustrate with novel all-photonic quantum repeater states for quantum communication and…
Transferring quantum information between distant nodes of a network is a key capability. This transfer can be realized via remote state preparation where two parties share entanglement and the sender has full knowledge of the state to be communicated. Here we demonstrate such a process between heterogeneous nodes functioning with different information encodings, i.e., particle-like discrete-variable optical qubits and wave-like continuous-variable ones. Using hybrid entanglement of light as a shared resource, we prepare arbitrary coherent-state superpositions controlled by measurements on the …
