A CNOT gate between multiphoton qubits encoded in two cavities

Dual-rail encoding with superconducting cavities

The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computation. To this end, we introduce the circuit-Quantum Electrodynamics (QED) dual-rail qubit in which our physical qubit is encoded in the single-photon subspace, [Formula: see text], of two superconducting microwave cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are in general much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers unique capabilities. Using just one additional transmon ancilla per dual-rail qubit, we describe how to perform a gate-based set of universal operations that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors in the cavities and the transmon can be detected and converted to erasure errors in all operations, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit exhibits a favorable hierarchy of error rates and is expected to perform well below the relevant QEC thresholds with today's coherence times.

Extremal quantum correlation generation using a hybrid channel

The preservation of quantum correlations requires optimal procedures and the proper design of the transmitting channels. In this regard, we address designing a hybrid channel comprising a single-mode cavity accompanied by a super-Gaussian beam and local dephasing parts based on the dynamics of quantum characteristics. We choose two-level atoms and various functions such as traced-distance discord, concurrence, and local-quantum uncertainty to analyze the effectiveness of the hybrid channel to preserve quantum correlations along with entropy suppression discussed using linear entropy. The joint configuration of the considered fields is found to not only preserve but also generate quantum correlations even in the presence of local dephasing. Most importantly, within certain limits, the proposed channel can be readily regulated to generate maximal quantum correlations and complete suppression of the disorder. Besides, compared to the individual parts, mixing the Fock state cavity, super-Gaussian beam, and local dephasing remains a resourceful choice for the prolonged quantum correlations' preservation. Finally, we present an interrelationship between the considered two-qubit correlations' functions, showing the deviation between each two correlations and of the considered state from maximal entanglement under the influence of the assumed hybrid channel.

Demonstration of a two-bit controlled-NOT quantum-like gate using classical acoustic qubit-analogues

The Controlled-NOT (CNOT) gate is the key to unlock the power of quantum computing as it is a fundamental component of a universal set of gates. We demonstrate the operation of a two-bit C-NOT quantum-like gate using classical qubit acoustic analogues, called herein logical phi-bits. The logical phi-bits are supported by an externally driven nonlinear acoustic metamaterial composed of a parallel array of three elastically coupled waveguides. A logical phi-bit has a two-state degree of freedom associated with the two independent relative phases of the acoustic wave in the three waveguides. A simple physical manipulation involving the detuning of the frequency of one of the external drivers is shown to operate on the complex vectors in the Hilbert space of pairs of logical phi-bits. This operation achieves a systematic and predictable C-NOT gate with unambiguously measurable input and output. The possibility of scaling the approach to more phi-bits is promising.

Nanomaterials for Quantum Information Science and Engineering

Quantum information science and engineering (QISE)-which entails the use of quantum mechanical states for information processing, communications, and sensing-and the area of nanoscience and nanotechnology have dominated condensed matter physics and materials science research in the 21st century. Solid-state devices for QISE have, to this point, predominantly been designed with bulk materials as their constituents. This review considers how nanomaterials (i.e., materials with intrinsic quantum confinement) may offer inherent advantages over conventional materials for QISE. The materials challenges for specific types of qubits, along with how emerging nanomaterials may overcome these challenges, are identified. Challenges for and progress toward nanomaterials-based quantum devices are condidered. The overall aim of the review is to help close the gap between the nanotechnology and quantum information communities and inspire research that will lead to next-generation quantum devices for scalable and practical quantum applications.

Quantum control of bosonic modes with superconducting circuits

Bosonic modes have wide applications in various quantum technologies, such as optical photons for quantum communication, magnons in spin ensembles for quantum information storage and mechanical modes for reversible microwave-to-optical quantum transduction. There is emerging interest in utilizing bosonic modes for quantum information processing, with circuit quantum electrodynamics (circuit QED) as one of the leading architectures. Quantum information can be encoded into subspaces of a bosonic superconducting cavity mode with long coherence time. However, standard Gaussian operations (e.g., beam splitting and two-mode squeezing) are insufficient for universal quantum computing. The major challenge is to introduce additional nonlinear control beyond Gaussian operations without adding significant bosonic loss or decoherence. Here we review recent advances in universal control of a single bosonic code with superconducting circuits, including unitary control, quantum feedback control, driven-dissipative control and holonomic dissipative control. Various approaches to entangling different bosonic modes are also discussed.

Heralded high-fidelity quantum hyper-CNOT gates assisted by charged quantum dots inside single-sided optical microcavities

Photonic hyper-parallel quantum information processing (QIP) can simplify the quantum circuit and improve the information-processing speed, as well as reduce the quantum resource consumption and suppress the photonic dissipation noise. Here, utilizing the singly charged semiconductor quantum dot (QD) inside single-sided optical microcavity as the potentially experimental platform, we propose five schemes for heralded four-qubit hyper-controlled-not (hyper-CNOT) gates, covering all cases of four-qubit hyper-CNOT gates operated on both the polarization and spatial-mode degrees of freedom (DoFs) of a two-photon system. The novel heralding mechanism improves the fidelity of each hyper-CNOT gate to unity in principle without the strict restriction of strong coupling. The adaptability and scalability of the schemes make the hyper-CNOT gates more accessible under current experimental technologies. These heralded high-fidelity photonic hyper-CNOT gates can therefore have immense utilization potentials in high-capacity quantum communication and fast quantum computing, which are of far-reaching significance for QIP.

Searching for Dark Matter with a Superconducting Qubit

Detection mechanisms for low mass bosonic dark matter candidates, such as the axion or hidden photon, leverage potential interactions with electromagnetic fields, whereby the dark matter (of unknown mass) on rare occasion converts into a single photon. Current dark matter searches operating at microwave frequencies use a resonant cavity to coherently accumulate the field sourced by the dark matter and a near standard quantum limited (SQL) linear amplifier to read out the cavity signal. To further increase sensitivity to the dark matter signal, sub-SQL detection techniques are required. Here we report the development of a novel microwave photon counting technique and a new exclusion limit on hidden photon dark matter. We operate a superconducting qubit to make repeated quantum nondemolition measurements of cavity photons and apply a hidden Markov model analysis to reduce the noise to 15.7 dB below the quantum limit, with overall detector performance limited by a residual background of real photons. With the present device, we perform a hidden photon search and constrain the kinetic mixing angle to ε≤1.68×10^{-15} in a band around 6.011 GHz (24.86  μeV) with an integration time of 8.33 s. This demonstrated noise reduction technique enables future dark matter searches to be sped up by a factor of 1,300. By coupling a qubit to an arbitrary quantum sensor, more general sub-SQL metrology is possible with the techniques presented in this Letter.

High-Fidelity Software-Defined Quantum Logic on a Superconducting Qudit

We present an efficient approach to achieving arbitrary, high-fidelity control of a multilevel quantum system using optimal control techniques. As an demonstration, we implement a continuous, software-defined microwave pulse to realize a 0↔2 SWAP gate that achieves an average gate fidelity of 99.4%. We describe our procedure for extracting the system Hamiltonian, calibrating the quantum and classical hardware chain, and evaluating the gate fidelity. Our work represents an alternative, fully generalizable route towards achieving universal quantum control by leveraging optimal control techniques.

Molecular Nanomagnets as Qubits with Embedded Quantum-Error Correction

We show that molecular nanomagnets have a potential advantage in the crucial rush toward quantum computers. Indeed, the sizable number of accessible low-energy states of these systems can be exploited to define qubits with embedded quantum error correction. We derive the scheme to achieve this crucial objective and the corresponding sequence of microwave/radiofrequency pulses needed for the error correction procedure. The effectiveness of our approach is shown already with a minimal S = 3/2 unit corresponding to an existing molecule, and the scaling to larger spin systems is quantitatively analyzed.

Molecular Nanomagnets as Qubits with Embedded Quantum-Error Correction

We show that molecular nanomagnets have a potential advantage in the crucial rush toward quantum computers. Indeed, the sizable number of accessible low-energy states of these systems can be exploited to define qubits with embedded quantum error correction. We derive the scheme to achieve this crucial objective and the corresponding sequence of microwave/radiofrequency pulses needed for the error correction procedure. The effectiveness of our approach is shown already with a minimal S = 3/2 unit corresponding to an existing molecule, and the scaling to larger spin systems is quantitatively analyzed.

Demonstration of Controlled-Phase Gates between Two Error-Correctable Photonic Qubits

To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in photonic fields stored in cavities. The gates are realized by dispersively coupling an ancillary superconducting qubit to these cavities and driving it to make a cyclic evolution depending on the joint photonic state of the cavities, which produces a conditional geometric phase. We first realize phase gates for photonic qubits with the logical basis states encoded in two quasiorthogonal coherent states, which have important implications for continuous-variable-based quantum computation. Then we use this geometric method to implement a controlled-phase gate between two binomially encoded logical qubits, which have an error-correctable function.

Optical Fredkin gate assisted by quantum dot within optical cavity under vacuum noise and sideband leakage

We propose a deterministic Fredkin gate which can accomplish controlled-swap operation between three-qubit states. The proposed Fredkin gate consists of a photonic system (single photon) and quantum dots (QDs) confined in single-sided cavities (two electron spin states). In our scheme, the control qubit is the polarization state of the single photon, and two electron spin states in QDs play the role of target qubits (swapped states by control qubit). The interaction between a photon and an electron of QD within the cavity (QD-cavity system) significantly affects the performance of Fredkin gate. Thus, through the analysis of the QD-cavity system under vacuum noise and sideband leakage, we demonstrate that reliable interaction and performance of the QD-cavity system with photonic state (photon) can be acquired in our scheme. Consequently, the Fredkin gate proposed in this paper can be experimentally implemented with high feasibility and efficiency.

All-Gaussian Universality and Fault Tolerance with the Gottesman-Kitaev-Preskill Code

The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator is particularly appealing for fault-tolerant quantum computing with bosons because Gaussian operations on encoded Pauli eigenstates enable Clifford quantum computing with error correction. We show that applying GKP error correction to Gaussian input states, such as vacuum, produces distillable magic states, achieving universality without additional non-Gaussian elements. Fault tolerance is possible with sufficient squeezing and low enough external noise. Thus, Gaussian operations are sufficient for fault-tolerant, universal quantum computing given a supply of GKP-encoded Pauli eigenstates.

Creation of superposition of arbitrary states encoded in two high-Q cavities

The principle of superposition is a key ingredient for quantum mechanics. A recent work [Phys. Rev. Lett.116, 110403 (2016)10.1103/PhysRevLett.116.110403] has shown that a quantum adder that deterministically generates a superposition of two unknown states is forbidden. Here we consider the implementation of the probabilistic quantum adder in the 3D cavity-transmon system. Our implementation is based on a three-level superconducting transmon qubit dispersively coupled to two cavities. Numerical simulations show that high-fidelity generation of the superposition of two coherent states is feasible with current circuit QED technology. Our method also works for other physical systems such as two optical cavities coupled to a three-level atom or two nitrogen-vacancy center ensembles interacted with one three-level superconducting flux qubit.

Photonic scheme of discrete quantum Fourier transform for quantum algorithms via quantum dots

We propose an optical scheme of discrete quantum Fourier transform (DQFT) via ancillary systems using quantum dots (QDs) confined in single-sided cavities (QD-cavity systems). In our DQFT scheme, the main component is a controlled-rotation k (CRk) gate, which utilizes the interactions between photons and QDs, consisting of two QD-cavity systems. Since the proposed CRk gate can be experimentally implemented with high efficiency and reliable performance, the scalability of multi-qubit DQFT scheme can also be realized through the simple composition of the proposed CRk gates via the QD-cavity systems. Subsequently, in order to demonstrate the performance of the CRk gate, we analyze the interaction between a photon and a QD-cavity system, and then indicate the condition to be efficient CRk gate with feasibility under vacuum noise and sideband leakage.

Parity-Assisted Generation of Nonclassical States of Light in Circuit Quantum Electrodynamics

We propose a method to generate nonclassical states of light in multimode microwave cavities. Our approach considers two-photon processes that take place in a system composed of N extended cavities and an ultrastrongly coupled light–matter system. Under specific resonance conditions, our method generates, in a deterministic manner, product states of uncorrelated photon pairs, Bell states, and W states in different modes on the extended cavities. Furthermore, the numerical simulations show that the generation scheme exhibits a collective effect which decreases the generation time in the same proportion as the number of extended cavity increases. Moreover, the entanglement encoded in the photonic states can be transferred towards ancillary two-level systems to generate genuine multipartite entanglement. Finally, we discuss the feasibility of our proposal in circuit quantum electrodynamics. This proposal could be of interest in the context of quantum random number generator, due to the quadratic scaling of the output state.

Asymmetric controlled bidirectional remote preparation of two- and three-qubit equatorial state

In this paper, a novel asymmetric controlled bidirectional remote preparation scheme is proposed. In our scheme, Alice and Bob are not only the senders but also the receivers with the control of Charlie. By using the eleven-qubit entangled state as the quantum channel, Alice prepares an arbitrary two-qubit equatorial state for Bob and Bob prepares an arbitrary three-qubit equatorial state for Alice simultaneously. Firstly, we give the construction process of the quantum channel. Secondly, the whole recovery operations are given. Alice and Bob can recover the prepared state determinately. Thirdly, we consider the effect of the noisy environment (amplitude-damping and phase-damping) in our scheme and calculate the fidelities of the output states. Finally, since our scheme does not need additional operations and auxiliary qubits, the efficiency of our scheme is higher than that of the previous schemes.

Experimental Engineering of Arbitrary Qudit States with Discrete-Time Quantum Walks

The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk dynamics represents a valid tool in the task of engineering arbitrary quantum states. Here we affirm such potential in a linear-optics platform that realizes discrete-time quantum walks in the orbital angular momentum degree of freedom of photons. Different classes of relevant qudit states in a six-dimensional space are prepared and measured, confirming the feasibility of the protocol. Our results represent a further investigation of quantum walk dynamics in photonics platforms, paving the way for the use of such a quantum state-engineering toolbox for a large range of applications.

Fault-tolerant detection of a quantum error

A critical component of any quantum error-correcting scheme is detection of errors by using an ancilla system. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information. We demonstrate a fault-tolerant error-detection scheme that suppresses spreading of ancilla errors by a factor of 5, while maintaining the assignment fidelity. The same method is used to prevent propagation of ancilla excitations, increasing the logical qubit dephasing time by an order of magnitude. Our approach is hardware-efficient, as it uses a single multilevel transmon ancilla and a cavity-encoded logical qubit, whose interaction is engineered in situ by using an off-resonant sideband drive. The results demonstrate that hardware-efficient approaches that exploit system-specific error models can yield advances toward fault-tolerant quantum computation.

Achieving the Heisenberg limit in quantum metrology using quantum error correction

Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed that suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.