Typically linear optical quantum computing (LOQC) models assume that all input photons are completely indistinguishable. In practice there will inevitably be non-idealities associated with the photons and the experimental setup which will introduce a degree of distinguishability between photons. We consider a non-deterministic optical controlled-NOT gate, a fundamental LOQC gate, and examine the effect of temporal and spectral distinguishability on its operation. We also consider the effect of utilizing non-ideal photon counters, which have finite bandwidth and time response.
We introduce a constructive procedure that maps all spatial correlations of a broad class of states into temporal correlations between general quantum measurements. This allows us to present temporal phenomena analogous to genuinely multipartite nonlocal phenomena, such as Greenberger-Horne-Zeilinger correlations, which do not exist if only projective measurements on qubits are considered. The map is applied to certain lattice systems in order to replace one spatial dimension with a temporal one, without affecting measured correlations. We use this map to show how repeated application of a 1d-…
Reservoir computing is a temporal information processing system that exploits artificial or physical dissipative dynamics to learn a dynamical system and generate the target time-series. This paper proposes the use of real superconducting quantum computing devices as the reservoir, where the dissipative property is served by the natural noise added to the quantum bits. The performance of this natural quantum reservoir is demonstrated in a benchmark time-series regression problem and a practical problem classifying different objects based on temporal sensor data. In both cases the proposed rese…
We study the consequence of the frequency errors of individual oscillators on the scalability of quantum computing based on nanomechanical resonators. We show the fidelity change of the quantum operation due to the frequency shifts numerically. We present a method to perfectly compensate for these negative effects. Our method is robust to whatever large frequency errors.
The observation of the so-called dispersion cancelation (Opt. Express 17, 19244, 2009) and temporal phase modulation (Phys. Rev. Lett. 103, 163601, 2009) of paired photons is generally attributed to the presence of frequency entanglement between two frequency anticorrelated photons. In this paper, it is shown that by introducing the appropriate amount of chromatic dispersion or phase modulation between non-entangled photons, it is also possible to observe these effects. Indeed, it is found that the relevant characteristic for the observation of dispersion cancelation or the cancelation of temp…
We report on coherent and multi-temporal mode storage of light using the full atomic frequency comb memory scheme. The scheme involves the transfer of optical atomic excitations in Pr3+:Y2SiO5 to spin-waves in the hyperfine levels using strong single-frequency transfer pulses. Using this scheme, a total of 5 temporal modes are stored and recalled on-demand from the memory. The coherence of the storage and retrieval is characterized using a time-bin interference measurement resulting in visibilities higher than 80%, independent of the storage time. This coherent and multimode spin-wave memory i…
High-Coherence and High-frequency Quantum Computing: The Design of a High-Frequency, High-Coherence and Scalable Quantum Computing Architecture
Sir Syed Science Park（Sir Syed 科学园）；Department of Physics, Faculty of Science, Jazan University（贾赞大学理学院物理系）；Physics Division, U. S. Jefferson National Laboratory and Accelerator Facility（美国杰斐逊国家加速器设施物理部）
We develop a scheme for time-frequency encoded continuous-variable cluster-state quantum computing using quantum memories. In particular, we propose a method to produce, manipulate and measure 2D cluster states in a single spatial mode by exploiting the intrinsic time-frequency selectivity of Raman quantum memories. Time-frequency encoding enables the scheme to be extremely compact, requiring a number of memories that is a linear function of only the number of different frequencies in which the computational state is encoded, independent of its temporal duration. We therefore show that quantum…
One-way quantum computing allows any quantum algorithm to be implemented easily using just measurements. The difficult part is creating the universal resource, a cluster state, on which the measurements are made. We propose a radically new approach: a scalable method that uses a single, multimode optical parametric oscillator (OPO). The method is very efficient and generates a continuous-variable cluster state, universal for quantum computation, with quantum information encoded in the quadratures of the optical frequency comb of the OPO.
This topical review introduces the theoretical and experimental advances in continuous-variable (CV) --- i.e., qumode-based in lieu of qubit-based --- large-scale, fault-tolerant quantum computing and quantum simulation. An introduction to the physics and mathematics of multipartite entangled CV cluster states is given, and their connection to experimental concepts is delineated. Paths toward fault tolerance are also presented. It is the hope of the author that this review attract more contributors to the field and promote its extension to the promising technology of integrated quantum photoni…
We report the successful design and experimental implementation of three coincident nonlinear interactions, namely ZZZ ("type-0"), ZYY (type-I), and YYZ/YZY (type-II) second harmonic generation of 780 nm light from a 1560 nm pump beam in a single, multigrating, periodically poled KTiOPO_4 crystal. The resulting nonlinear medium is the key component for making a scalable quantum computer over the optical frequency comb of a single optical parametric oscillator.
We propose a general quantum theory of optical phase and instantaneous frequency in the time domain for slowly varying optical signals. Guided by classical estimation theory, we design homodyne phase-locked loops that enable quantum-limited measurements of temporal phase and instantaneous frequency. Standard and Heisenberg quantum limits to such measurements are then derived. For optical sensing applications, we propose multipass and Fabry-Pérot position and velocity sensors that take advantage of the signal-to-noise-ratio enhancement effect of wideband angle modulation without requiring noncl…
All classical and quantum technologies that encode in and retrieve information from optical fields rely on the ability to selectively manipulate orthogonal field modes of light. Such manipulation can be achieved with high selectivity for polarization modes and transverse-spatial modes. For the time-frequency degree of freedom, this could efficiently be achieved for a limited choice of approximately orthogonal modes, i.e. non-overlapping bins in time or frequency. We recently proposed a method that surmounts the selectivity barrier for sorting arbitrary orthogonal temporal modes [Opt. Lett. {\b…
In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle $ϕ(t)$ at the same time that it is inverted. For polynomial twist: $ϕ(t) \sim Bt^{n}$. We show that for $n \geq 3$, multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit trans…
We investigate the quantum optical response of antireflection temporal coatings, i.e., matching temporal layers that suppress the generation of backward waves in temporal boundaries. Our results reveal that quantum antireflection temporal coatings are characterized for inducing a frequency shift of the quantum state, while preserving all photon statistics intact. Thus, they might find application for fast quantum frequency shifting in photonic quantum networks. The quantum theory also provides additional insight on their classical mode of operation, clarifying which quantities are preserved th…
Lattice surgery protocols allow for the efficient implementation of universal gate sets with two-dimensional topological codes where qubits are constrained to interact with one another locally. In this work, we first introduce a decoder capable of correcting spacelike and timelike errors during lattice surgery protocols. Afterwards, we compute logical failure rates of a lattice surgery protocol for a biased circuit-level noise model. We then provide a new protocol for performing twist-free lattice surgery, where we avoid twist defects in the bulk of the lattice. Our twist-free protocol elimina…
We explore theoretically the feasibility of using frequency conversion by sum- or difference-frequency generation, enabled by three- wave-mixing, for selectively multiplexing orthogonal input waveforms that overlap in time and frequency. Such a process would enable a drop device for use in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second- order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process, a…
We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [Tsang, Shapiro, and Lloyd, Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to estimation, we design homodyne phase-locked loops that can measure the temporal phase with quantum-limited accuracy. We show that post-processing can further improve the estimation performance, if delay is allowed in the estimation. We also investigate the fundamental uncertainties in the simultaneous estimation of harmonic-oscillator position and momentum via continu…
Time-frequency (TF) filtering of analog signals has played a crucial role in the development of radio-frequency communications, and is currently being recognized as an essential capability for communications, both classical and quantum, in the optical frequency domain. How best to design optical time-frequency (TF) filters to pass a targeted temporal mode (TM), and to reject background (noise) photons in the TF detection window? The solution for coherent TF filtering is known, the quantum pulse gate, whereas the conventional, more common method is implemented by a sequence of incoherent spectr…
High-dimensional quantum entanglement is currently one of the most prolific fields in quantum information processing due to its high information capacity and error resilience. A versatile method for harnessing high-dimensional entanglement has long been hailed as an absolute necessity in the exploration of quantum science and technologies. Here we exploit Hong-Ou-Mandel interference to manipulate discrete frequency entanglement in arbitrary-dimensional Hilbert space. The generation and characterization of two-, four- and six-dimensional frequency entangled qudits are theoretically and experime…
One-way quantum computing is experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. Record-size, but non-universal, continuous-variable cluster states were recently demonstrated separately in the time and frequency domains. We propose to combine these approaches into a scalable architecture in which a single optical parametric oscillator and simple interferometer entangle up to ($3\times 10^3$ frequencies) $\times$ (unlimited number of temporal modes) into a new and computationally universal continuous-variable cluster state. We in…
We consider regimes of Spontaneous Parametric Down-Conversion both noncollinear and nondegenerate in frequencies. Parameters characterizing degrees of noncollinearity and of nondgeneracy are defined, and they are shown to be not independent of each other. At a given degree of nondegeneracy the emitted photons are shown to propagate along two different cones opening angles of which are determined by the degree of nondegeneracy. Based on this, the degree of nondegeneracy can be controlled by means of the angular selection of photons, e.g., with the help of appropriately installed slits. For such…
High-dimensional quantum information processing promises capabilities beyond the current state of the art, but addressing individual information-carrying modes presents a significant experimental challenge. Here we demonstrate effective high-dimensional operations in the time-frequency domain of non-classical light. We generate heralded photons with tailored temporal-mode structures through ultrafast pulse shaping of a parametric downconversion pump. We then implement a quantum pulse gate, enabled by dispersion-engineered sum-frequency generation, to project onto programmable temporal modes, r…
Single-photon wave packets can carry quantum information between nodes of a quantum network. An important general operation in photon-based quantum information systems is blind reversal of a photon's temporal wave-packet envelope, that is, the ability to reverse an envelope without knowing the temporal state of the photon. We present an all-optical means for doing so, using nonlinear-optical frequency conversion driven by a short pump pulse. This scheme allows for quantum operations such as a temporal-mode parity sorter. We also verify that the scheme works for arbitrary states (not only singl…
We demonstrate the ultranarrow temporal correlation (6 fs full width half maximum) of twin beams generated by parametric down-conversion, by using the inverse process of sum-frequency generation. The result relies on an achromatic imaging of a huge bandwith of twin beams and on a careful control of their spatial degrees of freedom. The detrimental effects of spatial filtering and of imperfect imaging are shown toghether with the theoretical model used to describe the results.
Orthogonal temporal modes (TMs) form a field-orthogonal, continuous-variable degree of freedom that is in principle infinite dimensional, and create a promising resource for quantum information science and technology. The ideal quantum pulse gate (QPG) is a device that multiplexes and demultiplexes temporally orthogonal optical pulses that have the same carrier frequency, spatial mode, and polarization. The QPG is the chief enabling technology for usage of orthogonal temporal modes as a basis for high-dimensional quantum information storage and processing. The greatest hurdle for QPG implement…
Quantum frequency conversion (QFC) in nonlinear optical media is a powerful tool for temporal-mode selective manipulation of light. Recent attempts at achieving high mode selectivities and/or fidelities have had to resort to multi-dimensional optimization schemes to determine the system's natural Schmidt modes. Certain combinations of relative-group velocities between the relevant frequency bands, medium length, and temporal pulse widths have been known to achieve good selectivities (exceeding 80%) for temporal modes that are nearly identical to pump pulse shapes, even for high conversion effi…
Learning Temporal Patterns in Financial Time Series: A Comparative Study of Quantum LSTM and Quantum Reservoir Computing
Centre of Finance, DHBW Stuttgart（斯图加特双元大学金融中心）；DHBW Stuttgart（斯图加特双元大学）；Zentrum für Digitale Innovationen, DHBW Ravensburg（拉文斯堡双元大学数字创新中心）；DHBW Ravensburg（拉文斯堡双元大学）；DATEV eG（DATEV股份合作公司）
In this work we propose and analyse a scheme where the full spatio-temporal correlation of twin photons/beams generated by parametric down-conversion is detected by using its inverse process, i.e. sum frequency generation. Our main result is that, by imposing independently a temporal delay Δt and a transverse spatial shift Δx between two twin components of PDC light, the up-converted light intensity provides information on the correlation of the PDC light in the full spatio-temporal domain, and should enable the reconstruction of the peculiar X-shaped structure of the correlation predicted in …
We demonstrate quantum interference of three photons that are distinguishable in time, by resolving them in the conjugate parameter, frequency. We show that the multiphoton interference pattern in our setup can be manipulated by tuning the relative delays between the photons, without the need for reconfiguring the optical network. Furthermore, we observe that the symmetries of our optical network and the spectral amplitude of the input photons are manifested in the interference pattern. Moreover, we demonstrate time-reversed HOM-like interference in the spectral correlations using time-bin ent…
All computing devices, including quantum computers, must exhibit that for a given input, an output is produced in accordance with the program. The outputs generated by quantum computers that fulfill these requirements are not temporally correlated, however. In a quantum-computing device comprising solid-state qubits such as superconducting qubits, any operation to rest the qubits to their initial state faces a practical problem. We applied a statistical analysis to a collection of random numbers output from a 20-qubit superconducting-qubit cloud quantum computer using the simplest random numbe…
