Topological quantum computing with a very noisy network and local error rates approaching one percent

Even and Odd Cat States of Two and Three Qubits in the Probability Representation of Quantum Mechanics

We derive the probability representation of even and odd cat states of two and three qubits. These states are even and odd superpositions of spin-1/2 eigenstates corresponding to two opposite directions along the z axis. The probability representation of even and odd cat states of an oscillating spin-1/2 particle is also discussed. The exact formulas for entangled probability distributions describing density matrices of all these states are obtained.

Virtual Photon-Mediated Quantum State Transfer and Remote Entanglement between Spin Qubits in Quantum Dots Using Superadiabatic Pulses

Spin qubits in semiconductor quantum dots are an attractive candidate for scalable quantum information processing. Reliable quantum state transfer and entanglement between spatially separated spin qubits is a highly desirable but challenging goal. Here, we propose a fast and high-fidelity quantum state transfer scheme for two spin qubits mediated by virtual microwave photons. Our general strategy involves using a superadiabatic pulse to eliminate non-adiabatic transitions, without the need for increased control complexity. We show that arbitrary quantum state transfer can be achieved with a fidelity of 95.1% within a 60 ns short time under realistic parameter conditions. We also demonstrate the robustness of this scheme to experimental imperfections and environmental noises. Furthermore, this scheme can be directly applied to the generation of a remote Bell entangled state with a fidelity as high as 97.6%. These results pave the way for fault-tolerant quantum computation on spin quantum network architecture platforms.

Distributed Quantum Error Correction for Chip-Level Catastrophic Errors

Quantum error correction holds the key to scaling up quantum computers. Cosmic ray events severely impact the operation of a quantum computer by causing chip-level catastrophic errors, essentially erasing the information encoded in a chip. Here, we present a distributed error correction scheme to combat the devastating effect of such events by introducing an additional layer of quantum erasure error correcting code across separate chips. We show that our scheme is fault tolerant against chip-level catastrophic errors and discuss its experimental implementation using superconducting qubits with microwave links. Our analysis shows that in state-of-the-art experiments, it is possible to suppress the rate of these errors from 1 per 10 s to less than 1 per month.

A Distributed Architecture for Secure Delegated Quantum Computation

In this paper, we propose a distributed secure delegated quantum computation protocol, by which an almost classical client can delegate a (dk)-qubit quantum circuit to d quantum servers, where each server is equipped with a 2k-qubit register that is used to process only k qubits of the delegated quantum circuit. None of servers can learn any information about the input and output of the computation. The only requirement for the client is that he or she has ability to prepare four possible qubits in the state of (|0〉+eiθ|1〉)/2, where θ∈{0,π/2,π,3π/2}. The only requirement for servers is that each pair of them share some entangled states (|0〉|+〉+|1〉|−〉)/2 as ancillary qubits. Instead of assuming that all servers are interconnected directly by quantum channels, we introduce a third party in our protocol that is designed to distribute the entangled states between those servers. This would simplify the quantum network because the servers do not need to share a quantum channel. In the end, we show that our protocol can guarantee unconditional security of the computation under the situation where all servers, including the third party, are honest-but-curious and allowed to cooperate with each other.

Fault-tolerant operation of a logical qubit in a diamond quantum processor

Solid-state spin qubits is a promising platform for quantum computation and quantum networks1,2. Recent experiments have demonstrated high-quality control over multi-qubit systems3-8, elementary quantum algorithms8-11 and non-fault-tolerant error correction12-14. Large-scale systems will require using error-corrected logical qubits that are operated fault tolerantly, so that reliable computation becomes possible despite noisy operations15-18. Overcoming imperfections in this way remains an important outstanding challenge for quantum science15,19-27. Here, we demonstrate fault-tolerant operations on a logical qubit using spin qubits in diamond. Our approach is based on the five-qubit code with a recently discovered flag protocol that enables fault tolerance using a total of seven qubits28-30. We encode the logical qubit using a new protocol based on repeated multi-qubit measurements and show that it outperforms non-fault-tolerant encoding schemes. We then fault-tolerantly manipulate the logical qubit through a complete set of single-qubit Clifford gates. Finally, we demonstrate flagged stabilizer measurements with real-time processing of the outcomes. Such measurements are a primitive for fault-tolerant quantum error correction. Although future improvements in fidelity and the number of qubits will be required to suppress logical error rates below the physical error rates, our realization of fault-tolerant protocols on the logical-qubit level is a key step towards quantum information processing based on solid-state spins.

Low-overhead fault-tolerant quantum computing using long-range connectivity

Vast numbers of qubits will be needed for large-scale quantum computing because of the overheads associated with error correction. We present a scheme for low-overhead fault-tolerant quantum computation based on quantum low-density parity-check (LDPC) codes, where long-range interactions enable many logical qubits to be encoded with a modest number of physical qubits. In our approach, logic gates operate via logical Pauli measurements that preserve both the protection of the LDPC codes and the low overheads in terms of the required number of additional qubits. Compared with surface codes with the same code distance, we estimate order-of-magnitude improvements in the overheads for processing around 100 logical qubits using this approach. Given the high thresholds demonstrated by LDPC codes, our estimates suggest that fault-tolerant quantum computation at this scale may be achievable with a few thousand physical qubits at comparable error rates to what is needed for current approaches.

Heuristic Reordering Strategy for Quantum Circuit Mapping on LNN Architectures

Because of the connection constraints of quantum devices, the quantum gate cannot operate directly on nonadjacent qubits. Quantum circuit mapping transforms a logical quantum circuit to a circuit that satisfies the connection constraints by adding SWAP gates for nonadjacent qubits. Global and local heuristic reordering strategies are proposed in this paper for quantum circuit mapping over linear nearest neighbor (LNN) architectures, which are one-dimensional topology structures, to reduce the number of SWAP gates added. Experiment results show that the average improvements of the two methods are 13.19% and 15.46%, respectively. In this paper, we consider the quantum circuit mapping problem for linear nearest neighbor (LNN) architectures. We propose a global heuristic qubit reordering optimization algorithm and a local heuristic qubit reordering optimization algorithm. Compared with the other algorithm results, the average improvements of the two methods for quantum cost are 13.19% and 15.46%, respectively. The two methods apply to the realization of quantum circuit neighboring over one-dimensional quantum architectures and can be extended to algorithms that work for other quantum architectures of different topologies.

Entanglement transport and a nanophotonic interface for atoms in optical tweezers

The realization of an efficient quantum optical interface for multi-qubit systems is an outstanding challenge in science and engineering. Using two atoms in individually-controlled optical tweezers coupled to a nanofabricated photonic crystal cavity, we demonstrate entanglement generation, fast non-destructive readout, and full quantum control of atomic qubits. The entangled state is verified in free space after being transported away from the cavity by encoding the qubits into long-lived states and using dynamical decoupling. Our approach bridges quantum operations at an optical link and in free space by a coherent one-way transport, potentially enabling an integrated optical interface for atomic quantum processors.

Spin-photon module for scalable network architecture in quantum dots

Reliable information transmission between spatially separated nodes is fundamental to a network architecture for scalable quantum technology. Spin qubit in semiconductor quantum dots is a promising candidate for quantum information processing. However, there remains a challenge to design a practical path from the existing experiments to scalable quantum processor. Here we propose a module consisting of spin singlet-triplet qubits and single microwave photons. We show a high degree of control over interactions between the spin qubit and the quantum light field can be achieved. Furthermore, we propose preparation of a shaped single photons with an efficiency of 98%, and deterministic quantum state transfer and entanglement generation between remote nodes with a high fidelity of 90%. This spin-photon module has met the threshold of particular designed error-correction protocols, thus provides a feasible approach towards scalable quantum network architecture.

Unitary and Nonunitary Quantum Cellular Automata with Rydberg Arrays

We propose a physical realization of quantum cellular automata (QCA) using arrays of ultracold atoms excited to Rydberg states. The key ingredient is the use of programmable multifrequency couplings which generalize the Rydberg blockade and facilitation effects to a broader set of nonadditive, unitary and nonunitary (dissipative) conditional interactions. Focusing on a 1D array we define a set of elementary QCA rules that generate complex and varied quantum dynamical behavior. Finally, we demonstrate theoretically that Rydberg QCA is ideally suited for variational quantum optimization protocols and quantum state engineering by finding parameters that generate highly entangled states as the steady state of the quantum dynamics.

Strong Coupling of Two Individually Controlled Atoms via a Nanophotonic Cavity

We demonstrate photon-mediated interactions between two individually trapped atoms coupled to a nanophotonic cavity. Specifically, we observe collective enhancement when the atoms are resonant with the cavity and level repulsion when the cavity is coupled to the atoms in the dispersive regime. Our approach makes use of individual control over the internal states of the atoms and their position with respect to the cavity mode, as well as the light shifts to tune atomic transitions individually, allowing us to directly observe the anticrossing of the bright and dark two-atom states. These observations open the door for realizing quantum networks and studying quantum many-body physics based on atom arrays coupled to nanophotonic devices.

A silicon quantum-dot-coupled nuclear spin qubit

Single nuclear spins in the solid state are a potential future platform for quantum computing^1-3, because they possess long coherence times^4-6 and offer excellent controllability⁷. Measurements can be performed via localized electrons, such as those in single atom dopants^8,9 or crystal defects^10-12. However, establishing long-range interactions between multiple dopants or defects is challenging^13,14. Conversely, in lithographically defined quantum dots, tunable interdot electron tunnelling allows direct coupling of electron spin-based qubits in neighbouring dots^15-20. Moreover, the compatibility with semiconductor fabrication techniques²¹ may allow for scaling to large numbers of qubits in the future. Unfortunately, hyperfine interactions are typically too weak to address single nuclei. Here we show that for electrons in silicon metal-oxide-semiconductor quantum dots the hyperfine interaction is sufficient to initialize, read out and control single ²⁹Si nuclear spins. This approach combines the long coherence times of nuclear spins with the flexibility and scalability of quantum dot systems. We demonstrate high-fidelity projective readout and control of the nuclear spin qubit, as well as entanglement between the nuclear and electron spins. Crucially, we find that both the nuclear spin and electron spin retain their coherence while moving the electron between quantum dots. Hence we envision long-range nuclear-nuclear entanglement via electron shuttling³. Our results establish nuclear spins in quantum dots as a powerful new resource for quantum processing.

Deterministic teleportation of a quantum gate between two logical qubits

A quantum computer has the potential to efficiently solve problems that are intractable for classical computers. However, constructing a large-scale quantum processor is challenging because of the errors and noise that are inherent in real-world quantum systems. One approach to addressing this challenge is to utilize modularity-a strategy used frequently in nature and engineering to build complex systems robustly. Such an approach manages complexity and uncertainty by assembling small, specialized components into a larger architecture. These considerations have motivated the development of a quantum modular architecture, in which separate quantum systems are connected into a quantum network via communication channels^1,2. In this architecture, an essential tool for universal quantum computation is the teleportation of an entangling quantum gate^3-5, but such teleportation has hitherto not been realized as a deterministic operation. Here we experimentally demonstrate the teleportation of a controlled-NOT (CNOT) gate, which we make deterministic by using real-time adaptive control. In addition, we take a crucial step towards implementing robust, error-correctable modules by enacting the gate between two logical qubits, encoding quantum information redundantly in the states of superconducting cavities⁶. By using such an error-correctable encoding, our teleported gate achieves a process fidelity of 79 per cent. Teleported gates have implications for fault-tolerant quantum computation³, and when realized within a network can have broad applications in quantum communication, metrology and simulations^1,2,7. Our results illustrate a compelling approach for implementing multi-qubit operations on logical qubits and, if integrated with quantum error-correction protocols, indicate a promising path towards fault-tolerant quantum computation using a modular architecture.

A CNOT gate between multiphoton qubits encoded in two cavities

Entangling gates between qubits are a crucial component for performing algorithms in quantum computers. However, any quantum algorithm must ultimately operate on error-protected logical qubits encoded in high-dimensional systems. Typically, logical qubits are encoded in multiple two-level systems, but entangling gates operating on such qubits are highly complex and have not yet been demonstrated. Here we realize a controlled NOT (CNOT) gate between two multiphoton qubits in two microwave cavities. In this approach, we encode a qubit in the high-dimensional space of a single cavity mode, rather than in multiple two-level systems. We couple two such encoded qubits together through a transmon, which is driven by an RF pump to apply the gate within 190 ns. This is two orders of magnitude shorter than the decoherence time of the transmon, enabling a high-fidelity gate operation. These results are an important step towards universal algorithms on error-corrected logical qubits.

Silicon quantum processor with robust long-distance qubit couplings

Practical quantum computers require a large network of highly coherent qubits, interconnected in a design robust against errors. Donor spins in silicon provide state-of-the-art coherence and quantum gate fidelities, in a platform adapted from industrial semiconductor processing. Here we present a scalable design for a silicon quantum processor that does not require precise donor placement and leaves ample space for the routing of interconnects and readout devices. We introduce the flip-flop qubit, a combination of the electron-nuclear spin states of a phosphorus donor that can be controlled by microwave electric fields. Two-qubit gates exploit a second-order electric dipole-dipole interaction, allowing selective coupling beyond the nearest-neighbor, at separations of hundreds of nanometers, while microwave resonators can extend the entanglement to macroscopic distances. We predict gate fidelities within fault-tolerance thresholds using realistic noise models. This design provides a realizable blueprint for scalable spin-based quantum computers in silicon.Quantum computers will require a large network of coherent qubits, connected in a noise-resilient way. Tosi et al. present a design for a quantum processor based on electron-nuclear spins in silicon, with electrical control and coupling schemes that simplify qubit fabrication and operation.

Design and characterization of an integrated surface ion trap and micromirror optical cavity

We have fabricated and characterized laser-ablated micromirrors on fused silica substrates for constructing stable Fabry-Perot optical cavities. We highlight several design features which allow these cavities to have lengths in the 250-300 μm range and be integrated directly with surface ion traps. We present a method to calculate the optical mode shape and losses of these micromirror cavities as functions of cavity length and mirror shape, and confirm that our simulation model is in good agreement with experimental measurements of the intracavity optical mode at a test wavelength of 780 nm. We have designed and tested a mechanical setup for dampening vibrations and stabilizing the cavity length, and explore applications for these cavities as efficient single-photon sources when combined with trapped Yb171⁺ ions.

A photonic platform for donor spin qubits in silicon

Donor spins in silicon are highly competitive qubits for upcoming quantum technologies, offering complementary metal-oxide semiconductor compatibility, coherence (T₂) times of minutes to hours, and simultaneous initialization, manipulation, and readout fidelities near ~99.9%. This allows for many quantum error correction protocols, which will be essential for scale-up. However, a proven method of reliably coupling spatially separated donor qubits has yet to be identified. We present a scalable silicon-based platform using the unique optical properties of "deep" chalcogen donors. For the prototypical ⁷⁷Se⁺ donor, we measure lower bounds on the transition dipole moment and excited-state lifetime, enabling access to the strong coupling limit of cavity quantum electrodynamics using known silicon photonic resonator technology and integrated silicon photonics. We also report relatively strong photon emission from this same transition. These results unlock clear pathways for silicon-based quantum computing, spin-to-photon conversion, photonic memories, integrated single-photon sources, and all-optical switches.

Multispecies Trapped-Ion Node for Quantum Networking

Trapped atomic ions are a leading platform for quantum information networks, with long-lived identical qubit memories that can be locally entangled through their Coulomb interaction and remotely entangled through photonic channels. However, performing both local and remote operations in a single node of a quantum network requires extreme isolation between spectator qubit memories and qubits associated with the photonic interface. We achieve this isolation by cotrapping ^{171}Yb^{+} and ^{138}Ba^{+} qubits. We further demonstrate the ingredients of a scalable ion trap network node with two distinct experiments that consist of entangling the mixed species qubit pair through their collective motion and entangling a ^{138}Ba^{+} qubit with an emitted visible photon.

Fault-tolerant error correction with the gauge color code

The constituent parts of a quantum computer are inherently vulnerable to errors. To this end, we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a universal set of computational operations with the minimal cost in quantum resources remains an important and ongoing challenge. One proposal of significant recent interest is the gauge color code. Notably, this code may offer a reduced resource cost over other well-studied fault-tolerant architectures by using a new method, known as gauge fixing, for performing the non-Clifford operations that are essential for universal quantum computation. Here we examine the gauge color code when it is subject to noise. Specifically, we make use of single-shot error correction to develop a simple decoding algorithm for the gauge color code, and we numerically analyse its performance. Remarkably, we find threshold error rates comparable to those of other leading proposals. Our results thus provide the first steps of a comparative study between the gauge color code and other promising computational architectures.

Repeated quantum error correction on a continuously encoded qubit by real-time feedback

Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be compatible with universal fault-tolerant computations, it is essential that states remain encoded at all times and that errors are actively corrected. Here we demonstrate such active error correction on a continuously protected logical qubit using a diamond quantum processor. We encode the logical qubit in three long-lived nuclear spins, repeatedly detect phase errors by non-destructive measurements, and apply corrections by real-time feedback. The actively error-corrected qubit is robust against errors and encoded quantum superposition states are preserved beyond the natural dephasing time of the best physical qubit in the encoding. These results establish a powerful platform to investigate error correction under different types of noise and mark an important step towards fault-tolerant quantum information processing.

Large-scale quantum information processing requires the continuous protection of quantum states against errors. Here, the authors demonstrate active quantum error correction that improves the dephasing time of quantum states using a diamond quantum processor.

Coherent control of a single ²⁹Si nuclear spin qubit

Magnetic fluctuations caused by the nuclear spins of a host crystal are often the leading source of decoherence for many types of solid-state spin qubit. In group-IV semiconductor materials, the spin-bearing nuclei are sufficiently rare that it is possible to identify and control individual host nuclear spins. This Letter presents the first experimental detection and manipulation of a single ²⁹Si nuclear spin. The quantum nondemolition single-shot readout of the spin is demonstrated, and a Hahn echo measurement reveals a coherence time of T₂=6.3(7)  ms—in excellent agreement with bulk experiments. Atomistic modeling combined with extracted experimental parameters provides possible lattice sites for the ²⁹Si atom under investigation. These results demonstrate that single ²⁹Si nuclear spins could serve as a valuable resource in a silicon spin-based quantum computer.

Deterministic coupling of a single silicon-vacancy color center to a photonic crystal cavity in diamond

Deterministic coupling of single solid-state emitters to nanocavities is the key for integrated quantum information devices. We here fabricate a photonic crystal cavity around a preselected single silicon-vacancy color center in diamond and demonstrate modification of the emitters internal population dynamics and radiative quantum efficiency. The controlled, room-temperature cavity coupling gives rise to a resonant Purcell enhancement of the zero-phonon transition by a factor of 19, coming along with a 2.5-fold reduction of the emitter's lifetime.

Quantum information. Unconditional quantum teleportation between distant solid-state quantum bits

Realizing robust quantum information transfer between long-lived qubit registers is a key challenge for quantum information science and technology. Here we demonstrate unconditional teleportation of arbitrary quantum states between diamond spin qubits separated by 3 meters. We prepare the teleporter through photon-mediated heralded entanglement between two distant electron spins and subsequently encode the source qubit in a single nuclear spin. By realizing a fully deterministic Bell-state measurement combined with real-time feed-forward, quantum teleportation is achieved upon each attempt with an average state fidelity exceeding the classical limit. These results establish diamond spin qubits as a prime candidate for the realization of quantum networks for quantum communication and network-based quantum computing.

Universal control and error correction in multi-qubit spin registers in diamond

Quantum registers of nuclear spins coupled to electron spins of individual solid-state defects are a promising platform for quantum information processing. Pioneering experiments selected defects with favourably located nuclear spins with particularly strong hyperfine couplings. To progress towards large-scale applications, larger and deterministically available nuclear registers are highly desirable. Here, we realize universal control over multi-qubit spin registers by harnessing abundant weakly coupled nuclear spins. We use the electron spin of a nitrogen-vacancy centre in diamond to selectively initialize, control and read out carbon-13 spins in the surrounding spin bath and construct high-fidelity single- and two-qubit gates. We exploit these new capabilities to implement a three-qubit quantum-error-correction protocol and demonstrate the robustness of the encoded state against applied errors. These results transform weakly coupled nuclear spins from a source of decoherence into a reliable resource, paving the way towards extended quantum networks and surface-code quantum computing based on multi-qubit nodes.