Nonlinear feedforward enabling quantum computation

Abstract

Measurement-based quantum computation with optical time-domain multiplexing is a promising method to realize a quantum computer from the viewpoint of scalability. Fault tolerance and universality are also realizable by preparing appropriate resource quantum states and electro-optical feedforward that is altered based on measurement results. While linear feedforward has been realized and become a common experimental technique, nonlinear feedforward was unrealized until now. In this paper, we demonstrate that a fast and flexible nonlinear feedforward realizes the essential measurement required for fault-tolerant and universal quantum computation. Using non-Gaussian ancillary states, we observed 10% reduction of the measurement excess noise relative to classical vacuum ancilla.

Deterministic Shaping of Quantum Light Statistics

“…The Hamiltonian H (3) from Equation ( 9) is responsible for two distinct photon number density-preserving processes, SPM and XPM, and a mode-mixing process, FWM. FWM is a rich effect, leading to optical frequency combs and soliton propagation in microresonators [43].…”

“…The corresponding Hamiltonian is diagonal in the Fock basis and, equivalently, conserves photon number for each mode. Our present objective is to solve for the time evolution of the field operator under photon number density-preserving Hamiltonian H 0 ≡ H (1) + H (3) such that H = H 0 + H (2) , where H (1) , H (2) , and H (3) are defined in Equations ( 7) and ( 9). We later show how this time evolution affects H (2) , producing a photon-number-selective interaction under the right conditions.…”

“…Systems that utilize quantum information resources generally take advantage of coherent macroscopic superposition and/or entanglement. The increased information density and sensitivity to measurements of such quantum states, compared to their classical counterparts, is central to their application in modern quantum information technologies like quantum key distribution [1,2], quantum computing [3][4][5], and metrology at the fundamental noise limit [6][7][8]. Efforts toward engineering the spatio-temporal profile of quantum states of light have already found great success [9][10][11].…”

“…where Γ (2) is the second-order displacement field susceptibility that is responsible for optical parametric oscillation (OPO)-often referred to as parametric down conversion. Γ (3) is the third-order displacement field susceptibility responsible for four effects: the two optical Kerr effects called self-phase modulation (SPM) and cross-phase modulation (XPM), a mode-mixing process called four-wave mixing (FWM), and a static-field-induced OPO. Both are defined by the power series expansion of the polarization field in terms of displacement field [40].…”

Logical states for fault-tolerant quantum computation with propagating light

“…By multiplexing of degrees of freedom such as time ( 20 , 21 ) or frequency ( 22 ) in the propagating wave, a large-scale quantum computation platform has already been demonstrated. Also, terahertz-bandwidth light source ( 23 ), 43-GHz optical homodyne measurement ( 24 ), and high-speed nonlinear feedforward ( 25 ), which are key components to high-speed optical quantum computation and error correction, have been demonstrated; this means that we can expect near-term optical quantum computation with a clock frequency of at least a few gigahertz, which surpasses other physical systems by several orders of magnitude. Despite these appealing features, however, the actual optical generation of GKP qubits in a propagating optical system has remained elusive because propagating electromagnetic systems lack viable strong nonlinearity, and even if we try to obtain nonlinearity by using a system such as cavity QED ( 26 ), a complex arrangement would be required to realize a complex quantum state.…”