In spin-encoded quantum information, a spin of magnitude s gives access to a (2s+1)-dimensional qudit. (In particular, s=1/2 yields a qubit). Quantum optics writ large as the quantum processing of boson fields has provided convenient experimental ways to generate effective, or "synthetic," spins by way of mathematical equivalences such as the Holstein-Primakoff transformation, which maps 1 boson field to 1 large, "linearized" spin, and the Schwinger transformation, which maps 2 boson fields to 1 spin. The latter is of particular interest as it also maps bijectively with two-mode Fock states, which have non-Gaussian Wigner functions and therefore enable, in principle, universal, fast-tolerant photonic quantum computing. The recent coming of age of high-efficiency photon-number-resolved detectors provided the missing experimental resource to work with Schwinger spins. In this talk, I will describe progress towards experimentally violating Mermin's inequality (the s>1/2 version of the Bell inequality) using superconducting transition edge sensors in our quantum optics laboratory.
We present numerical results from simulations using deep reinforcement learning to control a measurement-based quantum processor—a time-multiplexed optical circuit sampled by photon- number-resolving detection—and find it generates squeezed cat states quasi-deterministically, with an average success rate of 98%, far outperforming all other proposals. Since squeezed cat states are deterministic precursors to the Gottesman-Kitaev-Preskill (GKP) bosonic error code, this is a key result for enabling fault tolerant photonic quantum computing. Informed by these simulations, we also discovered a one-step quantum circuit of constant parameters that can generate GKP states with high probability, though not deterministically.
We present numerical simulations of deep reinforcement learning on a measurement-based quantum processor--a time-multiplexed optical circuit sampled by photon-number-resolving detection--and find it generates squeezed cat states with an average success rate of 98%, far outperforming all other similar proposals. Since squeezed cat states are deterministic precursors to the Gottesman-Kitaev-Preskill bosonic error code, this is a key result for enabling fault tolerant photonic quantum computing.
In the race to demonstrate a scalable and fault tolerant quantum computing (QC) platform, quantum photonics stands poised to have a major impact. In particular, by encoding quantum information over fields rather than photons (continuous-variable—CV, rather than discrete-variable—DV, quantum information), record-size quantum processors were demonstrated in spectral and in temporal quantum field combs. These demonstrations used the measurement-based QC paradigm, which is based on cluster entangled states. In this talk, I will outline two of our recent results: proposals for generating hypercubic cluster states by phase modulation of the quantum optical frequency comb and for generating fault-tolerant hybrid CV-DV encodings called Gottesman-Kitaev-Preskill states. The latter leverages CV cluster states along with our experimental ability to perform photon-number-resolving measurements up to 100 photons.
Continuous-variable quantum computing (CVQC) boasts, by way of quantum optics, one of the largest scalability potentials of all quantum computing platforms. In order to enable universal CVQC, i.e., exponential speedup as well as fault tolerance, one requires quantum resources (states and/or gates) with a non-Gaussian Wigner function. We present several state preparation techniques, using photon-number-resolving detection, that enable the generation of resource states such as GKP or binomial error encodings.
Characterization of quantum states and detectors is a key task in rapidly emerging optical quantum science and technology. First, we introduce and experimentally demonstrate a noise-robust quantum state characterization protocol using photon-number-resolving (PNR) measurements. Unlike conventional continuous variable state tomography methods, our method utilizes computationally efficient semi-definite programming (SDP) and can be used to accurately reconstruct the state even after loss a known loss. The protocol is demonstrated for a weak coherent state as well as a single-photon Fock state.
Next, we propose a method for characterizing a photodetector by directly reconstructing the Wigner functions of the detector’s Positive-Operator-Value-Measure (POVM) elements via weak-field homodyne technique. We also report our experimental progress on characterizing a superconducting transition-edge sensor for PNR measurements.
The practical implementation of quantum computing faces the two key requirements of achieving scalability and maintaining quantum coherence. While the latter has been reached by ion-trap and superconducting qubit platforms to the level required for quantum error correction to take place, the former has been reached to record levels (thousands of qubit equivalents, called qumodes) using the quantum optics of entangled electromagnetic fields. In this talk, I will present the experimental realization of quantum computing substrates called cluster entangled states in the optical frequency comb of a single parametric oscillator, and prospects for translation in integrated optics.
Quantum state engineering and state characterization is a key task in quantum information processing in both discrete and continuous variable systems in the optical domain. In particular, quantum states with non-Gaussian (i.e., non-positive) Wigner quasiprobability distribution functions are crucial to universal, fault-tolerant quantum computing with continuous variables. In this talk, we present our recent results on single-photon Fock state tomography using Photon-Number-Resolving (PNR) measurements. We generated a highly pure narrow-band single-photon Fock state by heralding cavity-enhanced spontaneous-parametric-downconversion from a PPKTP optical parametric oscillator. The Wigner function was reconstructed with photon statistics obtained using superconducting transition-edge sensors with an overall system efficiency of 58(2)%. We then discuss quantum state engineering for pure displaced single-photon Fock states, optical cat states, and approximate GKP states using coherent states and single-photon states along with linear optics and PNR measurements. We report our experimental progress for the same.
Photon-number-resolving measurements allow one to address quantum optics from the corpuscular angle of quantum physics. A number of classically non-intuitive features are typically expected from working in the photon-number Fock eigenbasis, such as nonpositive Wigner functions. In this talk, we report on the progress of two applications of photon-number-resolving measurements in quantum optics: quantum interferometry with photon-subtracted twin beams and quantum state tomography of Fock states created by heralded parametric downconversion.
When it comes to practical quantum computing, the two main challenges are circumventing decoherence (devastating quantum errors due to interactions with the environmental bath) and achieving scalability (as many qubits as needed for a real-life, game-changing computation). We show that using, in lieu of qubits, the "qumodes" represented by the resonant fields of the quantum optical frequency comb of an optical parametric oscillator allows one to create bona fide, large scale quantum computing processors, pre-entangled in a cluster state. We detail our recent demonstration of 60-qumode entanglement (out of an estimated 3000) and present an extension to combining this frequency-tagged with time-tagged entanglement, in order to generate an arbitrarily large, universal quantum computing processor.
Quantum information can be encoded in a scalable manner over the continuous variables (CV) that are the canonically conjugate quantum amplitudes of the electromagnetic field, which are mathematical equivalents of the position and momentum of the quantum harmonic oscillator. Previous results in our group in Charlottesville and the groups of Akira Furusawa in Tokyo, of Nicolas Treps in Paris, and of Ping-Koy Lam in Canberra, have shown that CV quantum information is massively scalable. In addition, Nicolas Menicucci in Melbourne has shown that there exists a fault tolerance threshold for CV quantum computing with the Gottesman-Kitaev-Preskill qubit error encoding. Here, we report on our exploration of the extension of scalable CV encoding by way of intramode, rather than intermode, squeezing and entanglement. As is well known, single-mode squeezing can only be considered along with the "quasi-mode" approximation which assimilates the modes of the optical parametric oscillator cavity used in the experiment to delta functions. As Hans Bachor and Tim Ralph noted, when one ambles beyond this approximation, single-mode squeezing can be described as intramode two-mode squeezing. Here, we aim at generalizing this situation to the case of multipartite entangled cluster states.
The frequency comb of an optical resonator is a naturally large set of exquisitely well defined quantum systems,
such as in the broadband mode-locked lasers which have redefined time/frequency metrology and ultraprecise
measurements in recent years. High coherence can therefore be expected in the quantum version of the frequency
comb, in which nonlinear interactions couple different cavity modes, as can be modeled by different forms of graph
states. We show that is possible to thereby generate states of interest to quantum metrology and computing,
such as multipartite entangled cluster and Greenberger-Horne-Zeilinger states.
We investigate experimentally the number and phase quantum noises of the light emitted by an ultrastable nondegenerate optical parametric oscillator (OPO) above threshold. Strong intensity correlations at the photon level -- number-difference squeezing or twin beams -- have already been observed by several groups. We have recently observed the twin-beam interference of a classically phase-locked OPO and have shown that the phase-difference is antisqueezed, as expected from the number-phase Heisenberg (in)equality. In this paper we describe the realization of a stable classical measurement of the joint quadratures of an OPO, as part of our ongoing effort to generate ultrastable EPR light beams simultaneously squeezed in number difference and phase sum.
Following previous studies by Milburn and Braunstein, and Cochrane, Milburn, and Munro, we consider number-phase teleportation protocols. We investigate the use, as the teleportation quantum channel, of two-mode states with a perfectly well defined phase difference and number sum, which are also suitable for Heisenberg-limited interferometry. We show that intuition based on squeezing of these variables, which is commonly used to derive entangled states using the EPR paradox, can fail in this case to yield suitable teleportation channels. We show that the domain of failure is in fact of size 1/N, N being the total number of photons. We also point out another way of generating simpler analogs of number-sum/phase-difference eigenstates.
We report the realization of a classically phase-locked source of quantum twin beams. Theoretical work by Reid and Drummond, and more recently by van Loock and Braunstein, predicts that such a source is adequate for creating bipartite and multipartite continuous-variable entanglement. The source is a type-II optical parametric oscillator (OPO) above threshold. Its exceptional frequency and intensity stability is derived from careful design and from three servo loops. The OPO can stably emit on the frequency-degenerate mode, pumped a few percent above the threshold. We observe a preliminary number-difference squeezing of 5.5 dB (6.4 dB inferred) at 200 kHz. In order to enable future EPR measurements, the signal and idler fields must also be classically phase-locked: we measure a signal-idler-frequency-difference linewidth smaller than 300 Hz for our OPO.
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