A Schrödinger cat living in two boxes Wang, Chen; Gao, Yvonne Y.; Reinhold, Philip ...
Science,
05/2016, Letnik:
352, Številka:
6289
Journal Article
Recenzirano
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Quantum superpositions of distinct coherent states in a single-mode harmonic oscillator, known as "cat states," have been an elegant demonstration of Schrödinger's famous cat paradox. Here, we ...realize a two-mode cat state of electromagnetic fields in two microwave cavities bridged by a superconducting artificial atom, which can also be viewed as an entangled pair of single-cavity cat states. We present full quantum state tomography of this complex cat state over a Hilbert space exceeding 100 dimensions via quantum nondemolition measurements of the joint photon number parity. The ability to manipulate such multicavity quantum states paves the way for logical operations between redundantly encoded qubits for fault-tolerant quantum computation and communication.
Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depend on the quantity that is measured. In a partial measurement performed by an ideal ...apparatus, quantum physics predicts that the system remains in a pure state whose evolution can be tracked perfectly from the measurement record. We demonstrated this property using a superconducting qubit dispersively coupled to a cavity traversed by a microwave signal. The back-action on the qubit state of a single measurement of both signal quadratures was observed and shown to produce a stochastic operation whose action is determined by the measurement result. This accurate monitoring of a qubit state is an essential prerequisite for measurement-based feedback control of quantum systems.
Quantum computation presents a powerful new paradigm for information processing. A robust universal quantum computer can be realized with any well controlled quantum system, but a successful platform ...will ultimately require the combination of highly coherent, error-correctable quantum elements with at least one entangling operation between them
. Quantum information stored in a continuous-variable system-for example, a harmonic oscillator-can take advantage of hardware-efficient quantum error correction protocols that encode information in the large available Hilbert space of each element
. However, such encoded states typically have no controllable direct couplings, making deterministic entangling operations between them particularly challenging. Here we develop an efficient implementation of the exponential-SWAP operation
and present its experimental realization between bosonic qubits stored in two superconducting microwave cavities. This engineered operation is analogous to the exchange interaction between discrete spin systems, but acts within any encoded subspace of the continuous-variable modes. Based on a control rotation, the operation produces a coherent superposition of identity and SWAP operations between arbitrary states of two harmonic oscillator modes and can be used to enact a deterministic entangling gate within quantum error correction codes. These results provide a valuable building block for universal quantum computation using bosonic modes.
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.
We construct a new class of quantum error-correcting codes for a bosonic mode, which are advantageous for applications in quantum memories, communication, and scalable computation. These “binomial ...quantum codes” are formed from a finite superposition of Fock states weighted with binomial coefficients. The binomial codes can exactly correct errors that are polynomial up to a specific degree in bosonic creation and annihilation operators, including amplitude damping and displacement noise as well as boson addition and dephasing errors. For realistic continuous-time dissipative evolution, the codes can perform approximate quantum error correction to any given order in the time step between error detection measurements. We present an explicit approximate quantum error recovery operation based on projective measurements and unitary operations. The binomial codes are tailored for detecting boson loss and gain errors by means of measurements of the generalized number parity. We discuss optimization of the binomial codes and demonstrate that by relaxing the parity structure, codes with even lower unrecoverable error rates can be achieved. The binomial codes are related to existing two-mode bosonic codes, but offer the advantage of requiring only a single bosonic mode to correct amplitude damping as well as the ability to correct other errors. Our codes are similar in spirit to “cat codes” based on superpositions of the coherent states but offer several advantages such as smaller mean boson number, exact rather than approximate orthonormality of the code words, and an explicit unitary operation for repumping energy into the bosonic mode. The binomial quantum codes are realizable with current superconducting circuit technology, and they should prove useful in other quantum technologies, including bosonic quantum memories, photonic quantum communication, and optical-to-microwave up- and down-conversion.
We investigate cat codes that can correct multiple excitation losses and identify two types of logical errors: bit-flip errors due to excessive excitation loss and dephasing errors due to quantum ...backaction from the environment. We show that selected choices of logical subspace and coherent amplitude significantly reduce dephasing errors. The trade-off between the two major errors enables optimized performance of cat codes in terms of minimized decoherence. With high coupling efficiency, we show that one-way quantum repeaters with cat codes feature a boosted secure communication rate per mode when compared to conventional encoding schemes, showcasing the promising potential of quantum information processing with continuous variable quantum codes.
Wiring up quantum systems Girvin, S. M; Schoelkopf, R. J
Nature (London),
02/2008, Letnik:
451, Številka:
7179
Journal Article
Recenzirano
In the past two decades, scientists and engineers in a variety of disciplines have been excited by the idea of quantum information processing, in which a computation is carried out by controlling a ...complex collection of quantum objects. This idea seeks to combine two of the greatest advances in science and technology of the twentieth century.
The efficient simulation of quantum systems is a primary motivating factor for developing controllable quantum machines. For addressing systems with underlying bosonic structure, it is advantageous ...to utilize a naturally bosonic platform. Optical photons passing through linear networks may be configured to perform quantum simulation tasks, but the efficient preparation and detection of multiphoton quantum states of light in linear optical systems are challenging. Here, we experimentally implement a boson sampling protocol for simulating molecular vibronic spectra J. Huh et al., Nat. Photonics 9, 615 (2015) in a two-mode superconducting device. In addition to enacting the requisite set of Gaussian operations across both modes, we fulfill the scalability requirement by demonstrating, for the first time in any platform, a high-fidelity single-shot photon number resolving detection scheme capable of resolving up to 15 photons per mode. Furthermore, we exercise the capability of synthesizing non-Gaussian input states to simulate spectra of molecular ensembles in vibrational excited states. We show the reprogrammability of our implementation by extracting the spectra of photoelectron processes inH2O,O3,NO2, andSO2. The capabilities highlighted in this work establish the superconducting architecture as a promising platform for bosonic simulations, and by combining them with tools such as Kerr interactions and engineered dissipation, enable the simulation of a wider class of bosonic systems.
Interference experiments provide a simple yet powerful tool to unravel fundamental features of quantum physics. Here we engineer a driven, time-dependent bilinear coupling that can be tuned to ...implement a robust50∶50beam splitter between stationary states stored in two superconducting cavities in a three-dimensional architecture. With this, we realize high-contrast Hong-Ou-Mandel interference between two spectrally detuned stationary modes. We demonstrate that this coupling provides an efficient method for measuring the quantum state overlap between arbitrary states of the two cavities. Finally, we showcase concatenated beam splitters and differential phase shifters to implement cascaded Mach-Zehnder interferometers, which can control the signature of the two-photon interference on demand. Our results pave the way toward implementation of scalable boson sampling, the application of linear optical quantum computing protocols in the microwave domain, and quantum algorithms between long-lived bosonic memories.
Macroscopic mechanical objects and electromagnetic degrees of freedom can couple to each other through radiation pressure. Optomechanical systems in which this coupling is sufficiently strong are ...predicted to show quantum effects and are a topic of considerable interest. Devices in this regime would offer new types of control over the quantum state of both light and matter, and would provide a new arena in which to explore the boundary between quantum and classical physics. Experiments so far have achieved sufficient optomechanical coupling to laser-cool mechanical devices, but have not yet reached the quantum regime. The outstanding technical challenge in this field is integrating sensitive micromechanical elements (which must be small, light and flexible) into high-finesse cavities (which are typically rigid and massive) without compromising the mechanical or optical properties of either. A second, and more fundamental, challenge is to read out the mechanical element's energy eigenstate. Displacement measurements (no matter how sensitive) cannot determine an oscillator's energy eigenstate, and measurements coupling to quantities other than displacement have been difficult to realize in practice. Here we present an optomechanical system that has the potential to resolve both of these challenges. We demonstrate a cavity which is detuned by the motion of a 50-nm-thick dielectric membrane placed between two macroscopic, rigid, high-finesse mirrors. This approach segregates optical and mechanical functionality to physically distinct structures and avoids compromising either. It also allows for direct measurement of the square of the membrane's displacement, and thus in principle the membrane's energy eigenstate. We estimate that it should be practical to use this scheme to observe quantum jumps of a mechanical system, an important goal in the field of quantum measurement.
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