超导非绝热几何量子计算及其优化控制

为实现量子门的高保真度和强鲁棒性,提出基于超导量子电路体系的非绝热几何量子计算方案.仅通过对超导比特施加含时共振微波驱动的方式,可以在超导比特上实现任意的单比特几何量子门.同时,在2个电容耦合的超导比特体系中,非平庸的2比特几何量子门也可以类似地实现.结果表明:提出的非绝热几何量子计算方案不仅对几何量子操作具有较好的鲁棒性,还可以与优化控制技术兼容,进一步增强量子门的鲁棒性.该方案的提出使容错固态量子计算的研究与发展向前迈出了重要的一步.     

Realization of three-qubit quantum error correction with superconducting circuits

Quantum computers could be used to solve certain problems exponentially faster than classical computers, but are challenging to build because of their increased susceptibility to errors. However, it is possible to detect and correct errors without destroying coherence, by using quantum error correcting codes. The simplest of these are three-quantum-bit (three-qubit) codes, which map a one-qubit state to an entangled three-qubit state; they can correct any single phase-flip or bit-flip error on one of the three qubits, depending on the code used. Here we demonstrate such phase- and bit-flip error correcting codes in a superconducting circuit. We encode a quantum state, induce errors on the qubits and decode the error syndrome--a quantum state indicating which error has occurred--by reversing the encoding process. This syndrome is then used as the input to a three-qubit gate that corrects the primary qubit if it was flipped. As the code can recover from a single error on any qubit, the fidelity of this process should decrease only quadratically with error probability. We implement the correcting three-qubit gate (known as a conditional-conditional NOT, or Toffoli, gate) in 63 nanoseconds, using an interaction with the third excited state of a single qubit. We find 85?±?1 per cent fidelity to the expected classical action of this gate, and 78?±?1 per cent fidelity to the ideal quantum process matrix. Using this gate, we perform a single pass of both quantum bit- and phase-flip error correction and demonstrate the predicted first-order insensitivity to errors. Concatenation of these two codes in a nine-qubit device would correct arbitrary single-qubit errors. In combination with recent advances in superconducting qubit coherence times, this could lead to scalable quantum technology.     

Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits

Quantum computation requires quantum logic gates that use the interaction within pairs of quantum bits (qubits) to perform conditional operations. Superconducting qubits may offer an attractive route towards scalable quantum computing. In previous experiments on coupled superconducting qubits, conditional gate behaviour and entanglement were demonstrated. Here we demonstrate selective execution of the complete set of four different controlled-NOT (CNOT) quantum logic gates, by applying microwave pulses of appropriate frequency to a single pair of coupled flux qubits. All two-qubit computational basis states and their superpositions are used as input, while two independent single-shot SQUID detectors measure the output state, including qubit-qubit correlations. We determined the gate's truth table by directly measuring the state transfer amplitudes and by acquiring the relevant quantum phase shift using a Ramsey-like interference experiment. The four conditional gates result from the symmetry of the qubits in the pair: either qubit can assume the role of control or target, and the gate action can be conditioned on either the 0-state or the 1-state. These gates are now sufficiently characterized to be used in quantum algorithms, and together form an efficient set of versatile building blocks.     

Generation of three-qubit entangled states using superconducting phase qubits

Entanglement is one of the key resources required for quantum computation, so the experimental creation and measurement of entangled states is of crucial importance for various physical implementations of quantum computers. In superconducting devices, two-qubit entangled states have been demonstrated and used to show violations of Bell's inequality and to implement simple quantum algorithms. Unlike the two-qubit case, where all maximally entangled two-qubit states are equivalent up to local changes of basis, three qubits can be entangled in two fundamentally different ways. These are typified by the states |GHZ>= (|000+?|111>)/ sqrt [2] and |W>= (|001>?+?|010>?+?|100>)/ sqrt [3]. Here we demonstrate the operation of three coupled superconducting phase qubits and use them to create and measure |GHZ> and |W>states. The states are fully characterized using quantum state tomography and are shown to satisfy entanglement witnesses, confirming that they are indeed examples of three-qubit entanglement and are not separable into mixtures of two-qubit entanglement.     

Coupling superconducting qubits via a cavity bus

Superconducting circuits are promising candidates for constructing quantum bits (qubits) in a quantum computer; single-qubit operations are now routine, and several examples of two-qubit interactions and gates have been demonstrated. These experiments show that two nearby qubits can be readily coupled with local interactions. Performing gate operations between an arbitrary pair of distant qubits is highly desirable for any quantum computer architecture, but has not yet been demonstrated. An efficient way to achieve this goal is to couple the qubits to a 'quantum bus', which distributes quantum information among the qubits. Here we show the implementation of such a quantum bus, using microwave photons confined in a transmission line cavity, to couple two superconducting qubits on opposite sides of a chip. The interaction is mediated by the exchange of virtual rather than real photons, avoiding cavity-induced loss. Using fast control of the qubits to switch the coupling effectively on and off, we demonstrate coherent transfer of quantum states between the qubits. The cavity is also used to perform multiplexed control and measurement of the qubit states. This approach can be expanded to more than two qubits, and is an attractive architecture for quantum information processing on a chip.     

Preparation and measurement of three-qubit entanglement in a superconducting circuit

Traditionally, quantum entanglement has been central to foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can have results at odds with classical behaviour. These discrepancies grow exponentially with the number of entangled particles. With the ample experimental confirmation of quantum mechanical predictions, entanglement has evolved from a philosophical conundrum into a key resource for technologies such as quantum communication and computation. Although entanglement in superconducting circuits has been limited so far to two qubits, the extension of entanglement to three, eight and ten qubits has been achieved among spins, ions and photons, respectively. A key question for solid-state quantum information processing is whether an engineered system could display the multi-qubit entanglement necessary for quantum error correction, which starts with tripartite entanglement. Here, using a circuit quantum electrodynamics architecture, we demonstrate deterministic production of three-qubit Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88 per cent, measured with quantum state tomography. Several entanglement witnesses detect genuine three-qubit entanglement by violating biseparable bounds by 830?±?80 per cent. We demonstrate the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code. The integration of this encoding with decoding and error-correcting steps in a feedback loop will be the next step for quantum computing with integrated circuits.     

Demonstration of conditional gate operation using superconducting charge qubits

Following the demonstration of coherent control of the quantum state of a superconducting charge qubit, a variety of qubits based on Josephson junctions have been implemented. Although such solid-state devices are not currently as advanced as microscopic qubits based on nuclear magnetic resonance and ion trap technologies, the potential scalability of the former systems--together with progress in their coherence times and read-out schemes--makes them strong candidates for the building block of a quantum computer. Recently, coherent oscillations and microwave spectroscopy of capacitively coupled superconducting qubits have been reported; the next challenging step towards quantum computation is the realization of logic gates. Here we demonstrate conditional gate operation using a pair of coupled superconducting charge qubits. Using a pulse technique, we prepare different input states and show that their amplitude can be transformed by controlled-NOT (C-NOT) gate operation, although the phase evolution during the gate operation remains to be clarified.     

Experimental one-way quantum computing

Standard quantum computation is based on sequences of unitary quantum logic gates that process qubits. The one-way quantum computer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantum computation and more generally how we think about quantum physics. This new model requires qubits to be initialized in a highly entangled cluster state. From this point, the quantum computation proceeds by a sequence of single-qubit measurements with classical feedforward of their outcomes. Because of the essential role of measurement, a one-way quantum computer is irreversible. In the one-way quantum computer, the order and choices of measurements determine the algorithm computed. We have experimentally realized four-qubit cluster states encoded into the polarization state of four photons. We characterize the quantum state fully by implementing experimental four-qubit quantum state tomography. Using this cluster state, we demonstrate the feasibility of one-way quantum computing through a universal set of one- and two-qubit operations. Finally, our implementation of Grover's search algorithm demonstrates that one-way quantum computation is ideally suited for such tasks.     

High-speed linear optics quantum computing using active feed-forward

As information carriers in quantum computing, photonic qubits have the advantage of undergoing negligible decoherence. However, the absence of any significant photon-photon interaction is problematic for the realization of non-trivial two-qubit gates. One solution is to introduce an effective nonlinearity by measurements resulting in probabilistic gate operations. In one-way quantum computation, the random quantum measurement error can be overcome by applying a feed-forward technique, such that the future measurement basis depends on earlier measurement results. This technique is crucial for achieving deterministic quantum computation once a cluster state (the highly entangled multiparticle state on which one-way quantum computation is based) is prepared. Here we realize a concatenated scheme of measurement and active feed-forward in a one-way quantum computing experiment. We demonstrate that, for a perfect cluster state and no photon loss, our quantum computation scheme would operate with good fidelity and that our feed-forward components function with very high speed and low error for detected photons. With present technology, the individual computational step (in our case the individual feed-forward cycle) can be operated in less than 150 ns using electro-optical modulators. This is an important result for the future development of one-way quantum computers, whose large-scale implementation will depend on advances in the production and detection of the required highly entangled cluster states.     

Universal quantum computation with the exchange interaction

Various physical implementations of quantum computers are being investigated, although the requirements that must be met to make such devices a reality in the laboratory at present involve capabilities well beyond the state of the art. Recent solid-state approaches have used quantum dots, donor-atom nuclear spins or electron spins; in these architectures, the basic two-qubit quantum gate is generated by a tunable exchange interaction between spins (a Heisenberg interaction), whereas the one-qubit gates require control over a local magnetic field. Compared to the Heisenberg operation, the one-qubit operations are significantly slower, requiring substantially greater materials and device complexity--potentially contributing to a detrimental increase in the decoherence rate. Here we introduced an explicit scheme in which the Heisenberg interaction alone suffices to implement exactly any quantum computer circuit. This capability comes at a price of a factor of three in additional qubits, and about a factor of ten in additional two-qubit operations. Even at this cost, the ability to eliminate the complexity of one-qubit operations should accelerate progress towards solid-state implementations of quantum computation.     

Experimental demonstration of a robust,high-fidelity geometric two ion-qubit phase gate

Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum computation. Dynamical gates have been proposed in the context of trapped ions; however, geometric phase gates (which change only the phase of the physical qubits) offer potential practical advantages because they have higher intrinsic resistance to certain small errors and might enable faster gate implementation. Here we demonstrate a universal geometric pi-phase gate between two beryllium ion-qubits, based on coherent displacements induced by an optical dipole force. The displacements depend on the internal atomic states; the motional state of the ions is unimportant provided that they remain in the regime in which the force can be considered constant over the extent of each ion's wave packet. By combining the gate with single-qubit rotations, we have prepared ions in an entangled Bell state with 97% fidelity-about six times better than in a previous experiment demonstrating a universal gate between two ion-qubits. The particular properties of the gate make it attractive for a multiplexed trap architecture that would enable scaling to large numbers of ion-qubits.     

基于STQ系统的一个四比特簇态制备方案

Transmon比特通过电容与一个超导TLR(transmission line resonator)耦合。本文采用Transmon比特与TLR之间有更强的耦合常量,提出了一个在STQ(superconducting transmon qubit)系统中制备四比特纠缠簇态(cluster state)的简单方案。与已有的方案相比,此方案有更长的消相干时间。又由于Transmon比特和TLR有以上的属性,此方案在实验上更可行。     

Coherent dynamics of a flux qubit coupled to a harmonic oscillator

In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits (qubits). Single-qubit operations, direct coupling between two qubits and the realization of a quantum gate have been reported. However, complex manipulation of entangled states-such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments and cavity quantum electrodynamics-has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system.     

Decoherence-protected quantum gates for a hybrid solid-state spin register

Protecting the dynamics of coupled quantum systems from decoherence by the environment is a key challenge for solid-state quantum information processing. An idle quantum bit (qubit) can be efficiently insulated from the outside world by dynamical decoupling, as has recently been demonstrated for individual solid-state qubits. However, protecting qubit coherence during a multi-qubit gate is a non-trivial problem: in general, the decoupling disrupts the interqubit dynamics and hence conflicts with gate operation. This problem is particularly salient for hybrid systems, in which different types of qubit evolve and decohere at very different rates. Here we present the integration of dynamical decoupling into quantum gates for a standard hybrid system, the electron-nuclear spin register. Our design harnesses the internal resonance in the coupled-spin system to resolve the conflict between gate operation and decoupling. We experimentally demonstrate these gates using a two-qubit register in diamond operating at room temperature. Quantum tomography reveals that the qubits involved in the gate operation are protected as accurately as idle qubits. We also perform Grover's quantum search algorithm, and achieve fidelities of more than 90% even though the algorithm run-time exceeds the electron spin dephasing time by two orders of magnitude. Our results directly allow decoherence-protected interface gates between different types of solid-state qubit. Ultimately, quantum gates with integrated decoupling may reach the accuracy threshold for fault-tolerant quantum information processing with solid-state devices.     

Realization of quantum error correction

Scalable quantum computation and communication require error control to protect quantum information against unavoidable noise. Quantum error correction protects information stored in two-level quantum systems (qubits) by rectifying errors with operations conditioned on the measurement outcomes. Error-correction protocols have been implemented in nuclear magnetic resonance experiments, but the inherent limitations of this technique prevent its application to quantum information processing. Here we experimentally demonstrate quantum error correction using three beryllium atomic-ion qubits confined to a linear, multi-zone trap. An encoded one-qubit state is protected against spin-flip errors by means of a three-qubit quantum error-correcting code. A primary ion qubit is prepared in an initial state, which is then encoded into an entangled state of three physical qubits (the primary and two ancilla qubits). Errors are induced simultaneously in all qubits at various rates. The encoded state is decoded back to the primary ion one-qubit state, making error information available on the ancilla ions, which are separated from the primary ion and measured. Finally, the primary qubit state is corrected on the basis of the ancillae measurement outcome. We verify error correction by comparing the corrected final state to the uncorrected state and to the initial state. In principle, the approach enables a quantum state to be maintained by means of repeated error correction, an important step towards scalable fault-tolerant quantum computation using trapped ions.     

Demonstration of an all-optical quantum controlled-NOT gate

The promise of tremendous computational power, coupled with the development of robust error-correcting schemes, has fuelled extensive efforts to build a quantum computer. The requirements for realizing such a device are confounding: scalable quantum bits (two-level quantum systems, or qubits) that can be well isolated from the environment, but also initialized, measured and made to undergo controllable interactions to implement a universal set of quantum logic gates. The usual set consists of single qubit rotations and a controlled-NOT (CNOT) gate, which flips the state of a target qubit conditional on the control qubit being in the state 1. Here we report an unambiguous experimental demonstration and comprehensive characterization of quantum CNOT operation in an optical system. We produce all four entangled Bell states as a function of only the input qubits' logical values, for a single operating condition of the gate. The gate is probabilistic (the qubits are destroyed upon failure), but with the addition of linear optical quantum non-demolition measurements, it is equivalent to the CNOT gate required for scalable all-optical quantum computation.     

Experimental implementation of heat-bath algorithmic cooling using solid-state nuclear magnetic resonance

The counter-intuitive properties of quantum mechanics have the potential to revolutionize information processing by enabling the development of efficient algorithms with no known classical counterparts. Harnessing this power requires the development of a set of building blocks, one of which is a method to initialize the set of quantum bits (qubits) to a known state. Additionally, fresh ancillary qubits must be available during the course of computation to achieve fault tolerance. In any physical system used to implement quantum computation, one must therefore be able to selectively and dynamically remove entropy from the part of the system that is to be mapped to qubits. One such method is an 'open-system' cooling protocol in which a subset of qubits can be brought into contact with an external system of large heat capacity. Theoretical efforts have led to an implementation-independent cooling procedure, namely heat-bath algorithmic cooling. These efforts have culminated with the proposal of an optimal algorithm, the partner-pairing algorithm, which was used to compute the physical limits of heat-bath algorithmic cooling. Here we report the experimental realization of multi-step cooling of a quantum system via heat-bath algorithmic cooling. The experiment was carried out using nuclear magnetic resonance of a solid-state ensemble three-qubit system. We demonstrate the repeated repolarization of a particular qubit to an effective spin-bath temperature, and alternating logical operations within the three-qubit subspace to ultimately cool a second qubit below this temperature. Demonstration of the control necessary for these operations represents an important step forward in the manipulation of solid-state nuclear magnetic resonance qubits.     

Clifford代数与量子逻辑门

以 Clifford代数为工具 ,讲座量子比特 ( Qubit)与量子逻辑门 (量子非门 ,Hadamard门 ,量子受控非门 ,Toffoli门等 )的有关性质。     

Controlled exchange interaction between pairs of neutral atoms in an optical lattice

Ultracold atoms trapped by light offer robust quantum coherence and controllability, providing an attractive system for quantum information processing and for the simulation of complex problems in condensed matter physics. Many quantum information processing schemes require the manipulation and deterministic entanglement of individual qubits; this would typically be accomplished using controlled, state-dependent, coherent interactions among qubits. Recent experiments have made progress towards this goal by demonstrating entanglement among an ensemble of atoms confined in an optical lattice. Until now, however, there has been no demonstration of a key operation: controlled entanglement between atoms in isolated pairs. Here we use an optical lattice of double-well potentials to isolate and manipulate arrays of paired (87)Rb atoms, inducing controlled entangling interactions within each pair. Our experiment realizes proposals to use controlled exchange coupling in a system of neutral atoms. Although 87Rb atoms have nearly state-independent interactions, when we force two atoms into the same physical location, the wavefunction exchange symmetry of these identical bosons leads to state-dependent dynamics. We observe repeated interchange of spin between atoms occupying different vibrational levels, with a coherence time of more than ten milliseconds. This observation demonstrates the essential component of a neutral atom quantum SWAP gate (which interchanges the state of two qubits). Its 'half-implementation', the root SWAP gate, is entangling, and together with single-qubit rotations it forms a set of universal gates for quantum computation.     

A scalable quantum computer with ions in an array of microtraps

Quantum computers require the storage of quantum information in a set of two-level systems (called qubits), the processing of this information using quantum gates and a means of final readout. So far, only a few systems have been identified as potentially viable quantum computer models--accurate quantum control of the coherent evolution is required in order to realize gate operations, while at the same time decoherence must be avoided. Examples include quantum optical systems (such as those utilizing trapped ions or neutral atoms, cavity quantum electrodynamics and nuclear magnetic resonance) and solid state systems (using nuclear spins, quantum dots and Josephson junctions). The most advanced candidates are the quantum optical and nuclear magnetic resonance systems, and we expect that they will allow quantum computing with about ten qubits within the next few years. This is still far from the numbers required for useful applications: for example, the factorization of a 200-digit number requires about 3,500 qubits, rising to 100,000 if error correction is implemented. Scalability of proposed quantum computer architectures to many qubits is thus of central importance. Here we propose a model for an ion trap quantum computer that combines scalability (a feature usually associated with solid state proposals) with the advantages of quantum optical systems (in particular, quantum control and long decoherence times).