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Developing a platform for linear mechanical quantum computing
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Abstract
Linear optical quantum computing provides a desirable approach to quantum computing, with a short list of required elements. The similarity between photons and phonons points to the interesting potential for linear mechanical quantum computing (LMQC), using phonons in place of photons. While single-phonon sources and detectors have been demonstrated, a phononic beamsplitter element remains an outstanding requirement. Here we demonstrate such an element, using two superconducting qubits to fully characterize a beamsplitter with single phonons. We further use the beamsplitter to demonstrate two-phonon interference, a requirement for two-qubit gates, completing the toolbox needed for LMQC. This advance brings linear quantum computing to a fully solid-state system, along with straightforward conversion between itinerant phonons and superconducting qubits.
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Distributing quantum entanglement on a chip is a crucial step toward realizing scalable quantum processors. Using traveling phonons—quantized guided mechanical wave packets—as a medium to transmit quantum states is now gaining substantial attention due to their small size and low propagation speed compared to other carriers, such as electrons or photons. Moreover, phonons are highly promising candidates to connect heterogeneous quantum systems on a chip, such as microwave and optical photons for long-distance transmission of quantum states via optical fibers. Here, we experimentally demonstrate the feasibility of distributing quantum information using phonons by realizing quantum entanglement between two traveling phonons and creating a time-bin–encoded traveling phononic qubit. The mechanical quantum state is generated in an optomechanical cavity and then launched into a phononic waveguide in which it propagates for around 200 micrometers. We further show how the phononic, together with a photonic qubit, can be used to violate a Bell-type inequality.
Acoustic waves at microwave frequencies are widely used in wireless communication and are potential information carriers in quantum applications. However, most acoustic devices are passive components, and the development of phononic integrated circuits is limited by the inability to control acoustic waves in a low-loss, scalable manner. Here we report the electrical control of gigahertz travelling acoustic waves at room temperature and millikelvin temperatures. We achieve phase modulation by tuning the elasticity of a lithium niobate acoustic waveguide via the electro-acoustic effect. This phase modulator is then used to build an acoustic frequency shifter based on serrodyne phase modulation, and phase modulators in a Mach–Zehnder interferometer configuration are used to create an electro-acoustic amplitude modulator. By tailoring the phase matching between acoustic and quasi-travelling electric fields, we achieve reconfigurable non-reciprocal modulation with a non-reciprocity of over 40 dB. To illustrate the potential of the approach in quantum applications, we show that our electro-acoustic modulator can provide coherent modulation of single-phonon-level acoustic waves at 50 mK.
The ability to create, manipulate and detect non-classical states of light has been key for many recent achievements in quantum physics and for developing quantum technologies. Achieving the same level of control over phonons, the quanta of vibrations, could have a similar impact, in particular on the fields of quantum sensing and quantum information processing. Here we present a crucial step towards this level of control and realize a single-mode waveguide for individual phonons in a suspended silicon microstructure. We use a cavity–waveguide architecture, where the cavity is used as a source and detector for the mechanical excitations while the waveguide has a free-standing end to reflect the phonons. This enables us to observe multiple round trips of phonons between the source and the reflector. The long mechanical lifetime of almost 100 μs demonstrates the possibility of nearly lossless transmission of single phonons over, in principle, tens of centimetres. Our experiment demonstrates full on-chip control over travelling single phonons strongly confined in the directions transverse to the propagation axis, potentially enabling a time-encoded multimode quantum memory at telecommunications wavelength and advanced quantum acoustics experiments.
Precisely engineered mechanical oscillators keep time, filter signals and sense motion, making them an indispensable part of the technological landscape of today. These unique capabilities motivate bringing mechanical devices into the quantum domain by interfacing them with engineered quantum circuits. Proposals to combine microwave-frequency mechanical resonators with superconducting devices suggest the possibility of powerful quantum acoustic processors1–3. Meanwhile, experiments in several mechanical systems have demonstrated quantum state control and readout4,5, phonon number resolution6,7 and phonon-mediated qubit–qubit interactions8,9. At present, these acoustic platforms lack processors capable of controlling the quantum states of several mechanical oscillators with a single qubit and the rapid quantum non-demolition measurements of mechanical states needed for error correction. Here we use a superconducting qubit to control and read out the quantum state of a pair of nanomechanical resonators. Our device is capable of fast qubit–mechanics swap operations, which we use to deterministically manipulate the mechanical states. By placing the qubit into the strong dispersive regime with both mechanical resonators simultaneously, we determine the phonon number distributions of the resonators by means of Ramsey measurements. Finally, we present quantum tomography of the prepared nonclassical and entangled mechanical states. Our result represents a concrete step towards feedback-based operation of a quantum acoustic processor.
We show that piezoelectric strain actuation of acoustomechanical interactions can produce large phase velocity changes in an existing quantum phononic platform: aluminum nitride on suspended silicon. Using finite element analysis, we demonstrate a piezo-acoustomechanical phase shifter waveguide capable of producing ±π phase shifts for GHz frequency phonons in 10s of μm with 10s of volts applied. Then, using the phase shifter as a building block, we demonstrate several phononic integrated circuit elements useful for quantum information processing. In particular, we show how to construct programmable multi-mode interferometers for linear phononic processing and a dynamically reconfigurable phononic memory that can switch between an ultra-long-lifetime state and a state strongly coupled to its bus waveguide. From the master equation for the full open quantum system of the reconfigurable phononic memory, we show that it is possible to perform read and write operations with over 90% quantum state transfer fidelity for an exponentially decaying pulse.
Surface acoustic waves are commonly used in classical electronics applications, and their use in quantum systems is beginning to be explored, as evidenced by recent experiments using acoustic Fabry–Pérot resonators. Here we explore their use for quantum communication, where we demonstrate a single-phonon surface acoustic wave transmission line, which links two physically separated qubit nodes. Each node comprises a microwave phonon transducer, an externally controlled superconducting variable coupler, and a superconducting qubit. Using this system, precisely shaped individual itinerant phonons are used to coherently transfer quantum information between the two physically distinct quantum nodes, enabling the high-fidelity node-to-node transfer of quantum states as well as the generation of a two-node Bell state. We further explore the dispersive interactions between an itinerant phonon emitted from one node and interacting with the superconducting qubit in the remote node. The observed interactions between the phonon and the remote qubit promise future quantum-optics-style experiments with itinerant phonons.
Using the deterministic, on-demand generation of two entangled phonons, we demonstrate a quantum eraser protocol in a phononic interferometer where the which-path information can be heralded during the interference process. Omitting the heralding step yields a clear interference pattern in the interfering half-quanta pathways; including the heralding step suppresses this pattern. If we erase the heralded information after the interference has been measured, the interference pattern is recovered, thereby implementing a delayed-choice quantum erasure. The test is implemented using a closed surface acoustic wave communication channel into which one superconducting qubit can emit itinerant phonons that the same or a second qubit can later recapture. If the first qubit releases only half of a phonon, the system follows a superposition of paths during the phonon propagation: either an itinerant phonon is in the channel or the first qubit remains in its excited state. These two paths are made to constructively or destructively interfere by changing the relative phase of the two intermediate states, resulting in a phase-dependent modulation of the first qubit’s final state, following interaction with the half-phonon. A heralding mechanism is added to this construct, entangling a heralding phonon with the signaling phonon. The first qubit emits a phonon herald conditioned on the qubit being in its excited state, with no signaling phonon, and the second qubit catches this heralding phonon, storing which-path information which can either be read out, destroying the signaling phonon’s self-interference, or erased.
High-index-contrast optical waveguides are crucial for the development of photonic integrated circuits with complex functionalities. Despite many similarities between optical and acoustic waves, high-acoustic-index-contrast phononic waveguides remain elusive, preventing intricate manipulation of phonons on par with its photonic counterpart. Here, we present the realization of such phononic waveguides and the formation of phononic integrated circuits through exploiting a gallium-nitride-on-sapphire platform, which provides strong confinement and control of phonons. By demonstrating key building blocks analogous to photonic circuit components, we establish the functionality and scalability of the phononic circuits. Moreover, the unidirectional excitation of propagating phononic modes allows the exploration of unconventional spin-orbit interaction of phonons in this circuit platform, which opens up the possibility of novel applications such as acoustic gyroscopic and non-reciprocal devices. Such phononic integrated circuits could provide an invaluable resource for both classical and quantum information processing.
Phononic quantum networks feature distinct advantages over photonic networks for on-chip quantum communications, providing a promising platform for developing quantum computers with robust solid-state spin qubits. Large mechanical networks including one-dimensional chains of trapped ions, however, have inherent and well-known scaling problems. In addition, chiral phononic processes, which are necessary for conventional phononic quantum networks, are difficult to implement in a solid-state system. To overcome these seemingly unsolvable obstacles, we have developed a new network architecture that breaks a large mechanical network into small and closed mechanical subsystems. This architecture is implemented in a diamond phononic nanostructure featuring alternating phononic crystal waveguides with specially designed band gaps. The implementation also includes nanomechanical resonators coupled to color centers through phonon-assisted transitions as well as quantum state transfer protocols that can be robust against the thermal environment.
The Hong–Ou–Mandel (HOM) interference is one of the most fundamental quantum-mechanical effects that reveal a nonclassical behavior of single photons. Two identical photons that are incident on the input ports of an unbiased beam splitter always exit the beam splitter together from the same output port, an effect referred to as photon bunching. In this Letter, we utilize a single electro-optic phase modulator as a probabilistic frequency beam splitter, which we exploit to observe HOM interference between two photons that are in different spectral modes, yet are identical in other characteristics. Our approach enables linear optical quantum information processing protocols using the frequency degree of freedom in photons such as quantum computing techniques with linear optics.
We realize the quantum regime of a surface acoustic wave (SAW) resonator by demonstrating vacuum Rabi mode splitting due to interaction with a superconducting artificial atom. Reaching the quantum regime is physically difficult and technologically challenging since SAW devices consist of large arrays of narrow metal strips. This work paves the way for realizing analogues of quantum optical phenomena with phonons and can be useful in on-chip quantum electronics.
The experimental investigation of quantum devices incorporating mechanical resonators has opened up new frontiers in the study of quantum mechanics at a macroscopic level. Superconducting microwave circuits have proven to be a powerful platform for the realisation of such quantum devices, both in cavity optomechanics, and circuit quantum electro-dynamics (QED). While most experiments to date have involved localised nanomechanical resonators, it has recently been shown that propagating surface acoustic waves (SAWs) can be piezoelectrically coupled to superconducting qubits, and confined in high-quality Fabry-Perot cavities up to microwave frequencies in the quantum regime, indicating the possibility of realising coherent exchange of quantum information between the two systems. Here we present measurements of a device in which a superconducting qubit is embedded in, and interacts with, the acoustic field of a Fabry-Perot SAW cavity on quartz, realising a surface acoustic version of cavity quantum electrodynamics. This quantum acoustodynamics (QAD) architecture may be used to develop new quantum acoustic devices in which quantum information is stored in trapped on-chip surface acoustic wavepackets, and manipulated in ways that are impossible with purely electromagnetic signals, due to the times slower speed of travel of the mechanical waves.
We theoretically investigate quantum interference of two single photons at a lossy asymmetric beam splitter, the most general passive 2×2 optical circuit. The losses in the circuit result in a non-unitary scattering matrix with a non-trivial set of constraints on the elements of the scattering matrix. Our analysis using the noise operator formalism shows that the loss allows tunability of quantum interference to an extent not possible with a lossless beam splitter. Our theoretical studies support the experimental demonstrations of programmable quantum interference in highly multimodal systems such as opaque scattering media and multimode fibers.
We introduce a superconducting qubit architecture that combines
high-coherence qubits and tunable qubit-qubit coupling. With the ability to set
the coupling to zero, we demonstrate that this architecture is protected from
the frequency crowding problems that arise from fixed coupling. More
importantly, the coupling can be tuned dynamically with nanosecond resolution,
making this architecture a versatile platform with applications ranging from
quantum logic gates to quantum simulation. We illustrate the advantages of
dynamic coupling by implementing a novel adiabatic controlled-Z gate, at a
speed approaching that of single-qubit gates. Integrating coherence and
scalable control, our "gmon" architecture is a promising path towards
large-scale quantum computation and simulation.
Quantum logic gates must perform properly when operating on their standard input basis states, as well as when operating on complex superpositions of these states. Experiments using superconducting qubits have validated the truth table for particular implementations of e.g. the controlled-NOT gate [1,2], but have not fully characterized gate operation for arbitrary superpositions of input states. Here we demonstrate the use of quantum process tomography (QPT) [3,4] to fully characterize the performance of a universal entangling gate between two superconducting quantum bits. Process tomography permits complete gate analysis, but requires precise preparation of arbitrary input states, control over the subsequent qubit interaction, and simultaneous single-shot measurement of the output states. We use QPT to measure the fidelity of the entangling gate and to quantify the decoherence mechanisms affecting the gate performance. In addition to demonstrating a promising fidelity, our entangling gate has a on/off ratio of 300, a level of adjustable coupling that will become a requirement for future high-fidelity devices. This is the first solid-state demonstration of QPT in a two-qubit system, as solid-state process tomography has previously only been demonstrated with single qubits [5,6].
We study the implementation of quantum state transfer protocols in phonon
networks, where in analogy to optical networks, quantum information is
transmitted through propagating phonons in extended mechanical resonator arrays
or phonon waveguides. We describe how the problem of a non-vanishing thermal
occupation of the phononic quantum channel can be overcome by implementing
optomechanical multi- and continuous mode cooling schemes to create a 'cold'
frequency window for transmitting quantum states. In addition, we discuss the
implementation of phonon circulators and switchable phonon routers, which rely
on strong coherent optomechanical interactions only, and do not require strong
magnetic fields or specific materials. Both techniques can be applied and
adapted to various physical implementations, where phonons coupled to spin or
charge based qubits are used for on-chip networking applications.
Short dephasing times pose one of the main challenges in realizing a quantum computer. Different approaches have been devised to cure this problem for superconducting qubits, a prime example being the operation of such devices at optimal working points, so-called "sweet spots." This latter approach led to significant improvement of times in Cooper pair box qubits [D. Vion et al., Science 296, 886 (2002)]. Here, we introduce a new type of superconducting qubit called the "transmon." Unlike the charge qubit, the transmon is designed to operate in a regime of significantly increased ratio of Josephson energy and charging energy . The transmon benefits from the fact that its charge dispersion decreases exponentially with , while its loss in anharmonicity is described by a weak power law. As a result, we predict a drastic reduction in sensitivity to charge noise relative to the Cooper pair box and an increase in the qubit-photon coupling, while maintaining sufficient anharmonicity for selective qubit control. Our detailed analysis of the full system shows that this gain is not compromised by increased noise in other known channels.
A nanoparticle trapped and cooled
Cooling massive particles to the quantum ground state allows fundamental tests of quantum mechanics to be made; it would provide an experimental probe of the boundary between the classical and quantum worlds. Delić et al. laser-cooled an optically trapped solid-state object (a ∼150-nanometer-diameter silic a nanoparticle) into its quantum ground state of motion starting from room temperature. Because the object is levitated using optical forces, the experimental configuration can be switched to free fall, thereby providing a test bed for several macroscopic quantum experiments.
Science , this issue p. 892
We present a formalism that accounts for the interaction of a local quantum system, such as an atom or a cavity, with traveling pulses of quantized radiation. We assume Markovian coupling of the stationary system to the input and output fields and nondispersive asymptotic propagation of the pulses before and after the interaction. This permits derivation of a master equation where the input and output pulses are treated as single oscillator modes that both couple to the local system in a cascaded manner. As examples of our theory, we analyze reflection by an empty cavity with phase noise, stimulated atomic emission by a quantum light pulse, and formation of a Schrödinger-cat state by the dispersive interaction of a coherent pulse and a single atom in a cavity.
A challenge faced by experimenters exploring hybrid quantum systems is how to integrate and interconnect different materials and different substrates in a quantum-coherent fashion. Here, we present a simple and inexpensive flip-chip bonding process, suitable for integrating hybrid quantum devices on chips from different substrates. The process only requires equipment and materials used routinely for contact photolithography, and it is possible to undo the bonding and reuse the chips. The technique requires minimal compressive force, so it is compatible with a wide range of different substrates. Unlike indium-based bonding, this process does not establish a galvanic connection between the two chips, but as we show, in some situations this is not necessary. We demonstrate the technique using lithographically patterned quarter-wave coplanar waveguide resonators, fabricated on one chip, and couple these inductively to a transmission line patterned lithographically on a separate chip. The two chips have a vertical interchip gap of about 7 μm, and we can repeatedly achieve lateral alignments of better than 2 μm. We measure electromagnetic resonances with low-power (∼1 photon) internal quality factors Qi around 5 × 10⁵, comparable to single-chip performances, with as-designed coupling quality factors Qc ranging from 2 × 10² to 5 × 10⁵.
Good vibrations in quantum communication
Quantum information processing platforms typically require qubits to talk to each other. To date, photons (either optical or microwave) have been the carrier of choice to transfer quantum states between the qubits. For some solid-state systems, however, the vibrational properties of the materials themselves, phonons, could be advantageous. Bienfait et al. describe the deterministic emission and capture of itinerant phonons through an acoustic communication channel, enabling the phonon-based coherent transfer of quantum states from one superconducting qubit to another and the quantum entanglement of the two qubits over the acoustic channel. The results provide a route to couple hybrid quantum solid-state systems using surface acoustic waves.
Science , this issue p. 368
We propose and analyze a novel realization of a solid-state quantum network, where separated silicon-vacancy centers are coupled via the phonon modes of a quasi-one-dimensional diamond waveguide. In our approach, quantum states encoded in long-lived electronic spin states can be converted into propagating phonon wave packets and be reabsorbed efficiently by a distant defect center. Our analysis shows that under realistic conditions, this approach enables the implementation of high-fidelity, scalable quantum communication protocols within chip-scale spin-qubit networks. Apart from quantum information processing, this setup constitutes a novel waveguide QED platform, where strong-coupling effects between solid-state defects and individual propagating phonons can be explored at the quantum level.
We investigate an acoustical analog of circuit quantum electrodynamics that facilitates compact high-Q () microwave-frequency cavities with dense spectra. We fabricate and characterize a device that comprises a flux tunable transmon coupled to a long surface acoustic wave resonator. For some modes, the qubit-cavity coupling reaches , exceeding the cavity loss rate (), qubit linewidth (), and the cavity free spectral range (), placing the device in both the strong coupling and strong multimode regimes. With the qubit detuned from the cavity, we show that the dispersive shift behaves according to predictions from a generalized Jaynes-Cummings Hamiltonian. Finally, we observe that the qubit linewidth strongly depends on its frequency, as expected for spontaneous emission of phonons, and we identify operating frequencies where this emission rate is suppressed.
We demonstrate ultra-sensitive measurement of fluctuations in a surface-acoustic-wave~(SAW) resonator using a hybrid quantum system consisting of the SAW resonator, a microwave (MW) resonator and a superconducting qubit. The nonlinearity of the driven qubit induces parametric coupling, which up-converts the excitation in the SAW resonator to that in the MW resonator. Thermal fluctuations of the SAW resonator near the quantum limit are observed in the noise spectroscopy in the MW domain.
Quantum information can be stored in micromechanical resonators, encoded as quanta of vibration known as phonons. The vibrational
motion is then restricted to the stationary eigenmodes of the resonator, which thus serves as local storage for phonons. In
contrast, we couple propagating phonons to an artificial atom in the quantum regime and reproduce findings from quantum optics,
with sound taking over the role of light. Our results highlight the similarities between phonons and photons but also point
to new opportunities arising from the characteristic features of quantum mechanical sound. The low propagation speed of phonons
should enable new dynamic schemes for processing quantum information, and the short wavelength allows regimes of atomic physics
to be explored that cannot be reached in photonic systems.
We demonstrate a planar, tunable superconducting qubit with energy relaxation times up to 44 μs. This is achieved by using a geometry designed to both minimize radiative loss and reduce coupling to materials-related defects. At these levels of coherence, we find a fine structure in the qubit energy lifetime as a function of frequency, indicating the presence of a sparse population of incoherent, weakly coupled two-level defects. We elucidate this defect physics by experimentally varying the geometry and by a model analysis. Our "Xmon" qubit combines facile fabrication, straightforward connectivity, fast control, and long coherence, opening a viable route to constructing a chip-based quantum computer.
It is shown that the usual amplitude and phase relations connecting the reflectance and transmittance of a stratified or continuous, nonabsorbing beam splitter can be derived by a simple energy balance argument relating to a Michelson interferometer.
We present an object-oriented open-source framework for solving the dynamics
of open quantum systems written in Python. Arbitrary Hamiltonians, including
time-dependent systems, may be built up from operators and states defined by a
quantum object class, and then passed on to a choice of master equation or
Monte-Carlo solvers. We give an overview of the basic structure for the
framework before detailing the numerical simulation of open system dynamics.
Several examples are given to illustrate the build up to a complete
calculation. Finally, we measure the performance of our library against that of
current implementations. The framework described here is particularly
well-suited to the fields of quantum optics, superconducting circuit devices,
nanomechanics, and trapped ions, while also being ideal for use in classroom
instruction.
A fourth-order interference technique has been used to measure the time intervals between two photons, and by implication the length of the photon wave packet, produced in the process of parametric down-conversion. The width of the time-interval distribution, which is largely determined by an interference filter, is found to be about 100 fs, with an accuracy that could, in principle, be less than 1 fs.
Linear optical quantum computing with photonic qubits
- P Kok
- W J Munro
- K Nemoto
- T C Ralph
- J P Dowling
- G J Milburn
P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P.
Dowling, and G. J. Milburn, Linear optical quantum
computing with photonic qubits, Reviews of Modern
Physics 79, 135 (2007).
- A M Brańczyk
A. M. Brańczyk, Hong-Ou-Mandel interference, (2017),
arXiv:1711.00080 [quant-ph].