Logical qubit encoding and quantum error correction (QEC) protocols have been experimentally demonstrated in various physical systems with multiple physical qubits, generally without reaching the ...break-even point, at which the lifetime of the quantum information exceeds that of the single best physical qubit within the logical qubit. Logical operations are challenging, owing to the necessary non-local operations at the physical level, making bosonic logical qubits that rely on higher Fock states of a single oscillator attractive, given their hardware efficiency. QEC that reaches the break-even point and single logical-qubit operations have been demonstrated using the bosonic cat code. Here, we experimentally demonstrate repetitive QEC approaching the break-even point of a single logical qubit encoded in a hybrid system consisting of a superconducting circuit and a bosonic cavity using a binomial bosonic code. This is achieved while simultaneously maintaining full control of the single logical qubit, including encoding, decoding and a high-fidelity universal quantum gate set with 97% average process fidelity. The corrected logical qubit has a lifetime 2.8 times longer than that of its uncorrected counterpart. We also perform a Ramsey experiment on the corrected logical qubit, reporting coherence twice as long as for the uncorrected case.Repeated error correction creates a logical qubit encoded in the hybrid state of a superconducting circuit and a bosonic cavity, which is shown to be fully controllable under a universal single-qubit gate set.
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.
Single-photon optomechanics Nunnenkamp, A; Børkje, K; Girvin, S M
Physical review letters,
2011-Aug-05, Letnik:
107, Številka:
6
Journal Article
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Optomechanics experiments are rapidly approaching the regime where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. We show that ...in this limit the power spectrum has multiple sidebands and that the cavity response has several resonances in the resolved-sideband limit. Using master-equation simulations, we also study the crossover from the weak-coupling many-photon to the single-photon strong-coupling regime. Finally, we find non-Gaussian steady states of the mechanical oscillator when multiphoton transitions are resonant. Our study provides the tools to detect and take advantage of this novel regime of optomechanics.
The interaction of matter and light is one of the fundamental processes occurring in nature, and its most elementary form is realized when a single atom interacts with a single photon. Reaching this ...regime has been a major focus of research in atomic physics and quantum optics for several decades and has generated the field of cavity quantum electrodynamics. Here we perform an experiment in which a superconducting two-level system, playing the role of an artificial atom, is coupled to an on-chip cavity consisting of a superconducting transmission line resonator. We show that the strong coupling regime can be attained in a solid-state system, and we experimentally observe the coherent interaction of a superconducting two-level system with a single microwave photon. The concept of circuit quantum electrodynamics opens many new possibilities for studying the strong interaction of light and matter. This system can also be exploited for quantum information processing and quantum communication and may lead to new approaches for single photon generation and detection.
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DOBA, IJS, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Quantum computers, which harness the superposition and entanglement of physical states, could outperform their classical counterparts in solving problems with technological impact-such as factoring ...large numbers and searching databases. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized register of qubits, which coherently evolves into a final state containing the result of the computation. Building a quantum processor is challenging because of the need to meet simultaneously requirements that are in conflict: state preparation, long coherence times, universal gate operations and qubit readout. Processors based on a few qubits have been demonstrated using nuclear magnetic resonance, cold ion trap and optical systems, but a solid-state realization has remained an outstanding challenge. Here we demonstrate a two-qubit superconducting processor and the implementation of the Grover search and Deutsch-Jozsa quantum algorithms. We use a two-qubit interaction, tunable in strength by two orders of magnitude on nanosecond timescales, which is mediated by a cavity bus in a circuit quantum electrodynamics architecture. This interaction allows the generation of highly entangled states with concurrence up to 94 per cent. Although this processor constitutes an important step in quantum computing with integrated circuits, continuing efforts to increase qubit coherence times, gate performance and register size will be required to fulfil the promise of a scalable technology.
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DOBA, IJS, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
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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.
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.
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DOBA, IJS, IZUM, KILJ, KISLJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Recent progress in solid-state quantum information processing has stimulated the search for amplifiers and frequency converters with quantum-limited performance in the microwave range. Depending on ...the gain applied to the quadratures of a single spatial and temporal mode of the electromagnetic field, linear amplifiers can be classified into two categories (phase sensitive and phase preserving) with fundamentally different noise properties. Phase-sensitive amplifiers use squeezing to reduce the quantum noise, but are useful only in cases in which a reference phase is attached to the signal, such as in homodyne detection. A phase-preserving amplifier would be preferable in many applications, but such devices have not been available until now. Here we experimentally realize a proposal for an intrinsically phase-preserving, superconducting parametric amplifier of non-degenerate type. It is based on a Josephson ring modulator, which consists of four Josephson junctions in a Wheatstone bridge configuration. The device symmetry greatly enhances the purity of the amplification process and simplifies both its operation and its analysis. The measured characteristics of the amplifier in terms of gain and bandwidth are in good agreement with analytical predictions. Using a newly developed noise source, we show that the upper bound on the total system noise of our device under real operating conditions is three times the quantum limit. We foresee applications in the area of quantum analog signal processing, such as quantum non-demolition single-shot readout of qubits, quantum feedback and the production of entangled microwave signal pairs.
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DOBA, IJS, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Thorough control of quantum measurement is key to the development of quantum information technologies. Many measurements are destructive, removing more information from the system than they obtain. ...Quantum non-demolition (QND) measurements allow repeated measurements that give the same eigenvalue. They could be used for several quantum information processing tasks such as error correction, preparation by measurement and one-way quantum computing. Achieving QND measurements of photons is especially challenging because the detector must be completely transparent to the photons while still acquiring information about them. Recent progress in manipulating microwave photons in superconducting circuits has increased demand for a QND detector that operates in the gigahertz frequency range. Here we demonstrate a QND detection scheme that measures the number of photons inside a high-quality-factor microwave cavity on a chip. This scheme maps a photon number, n, onto a qubit state in a single-shot by means of qubit-photon logic gates. We verify the operation of the device for n=0 and 1 by analysing the average correlations of repeated measurements, and show that it is 90% QND. It differs from previously reported detectors because its sensitivity is strongly selective to chosen photon number states. This scheme could be used to monitor the state of a photon-based memory in a quantum computer.
Superconducting quantum circuits based on Josephson junctions have made rapid progress in demonstrating quantum behavior and scalability. However, the future prospects ultimately depend upon the ...intrinsic coherence of Josephson junctions, and whether superconducting qubits can be adequately isolated from their environment. We introduce a new architecture for superconducting quantum circuits employing a three-dimensional resonator that suppresses qubit decoherence while maintaining sufficient coupling to the control signal. With the new architecture, we demonstrate that Josephson junction qubits are highly coherent, with T2 ∼ 10 to 20 μs without the use of spin echo, and highly stable, showing no evidence for 1/f critical current noise. These results suggest that the overall quality of Josephson junctions in these qubits will allow error rates of a few 10(-4), approaching the error correction threshold.
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