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Science

Deterministically Encoding Quantum Information Using 100-Photon Schrödinger Cat States

Brian Vlastakis, Gerhard Kirchmair, Zaki Leghtas, Simon E. Nigg, Luigi Frunzio, S. M. Girvin, Mazyar Mirrahimi, Michel Devoret, Robert J. Schoelkopf

Published Sep 27, 2013• 642 citations
Publisher

Abstract

In contrast to a single quantum bit, an oscillator can store multiple excitations and coherences provided one has the ability to generate and manipulate complex multiphoton states. We demonstrate multiphoton control by using a superconducting transmon qubit coupled to a waveguide cavity resonator with a highly ideal off-resonant coupling. This dispersive interaction is much greater than decoherence rates and higher-order nonlinearities to allow simultaneous manipulation of hundreds of photons. With a tool set of conditional qubit-photon logic, we mapped an arbitrary qubit state to a superposition of coherent states, known as a "cat state." We created cat states as large as 111 photons and extended this protocol to create superpositions of up to four coherent states. This control creates a powerful interface between discrete and continuous variable quantum computation and could enable applications in metrology and quantum information processing.

DOI
10.1126/science.1243289

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In contrast to a single quantum bit, an oscillator can store multiple excitations and coherences provided one has the ability to generate and manipulate complex multiphoton states. We demonstrate multiphoton control by using a superconducting transmon qubit coupled to a waveguide cavity resonator with a highly ideal off-resonant coupling. This dispersive interaction is much greater than decoherence rates and higher-order nonlinearities to allow simultaneous manipulation of hundreds of photons. With a tool set of conditional qubit-photon logic, we mapped an arbitrary qubit state to a superposition of coherent states, known as a "cat state." We created cat states as large as 111 photons and extended this protocol to create superpositions of up to four coherent states. This control creates a powerful interface between discrete and continuous variable quantum computation and could enable applications in metrology and quantum information processing.
Schrödinger's cat originates from the famous thought experiment querying the counterintuitive quantum superposition of macroscopic objects. As a natural extension, several "cats" (quasi-classical objects) can be prepared into coherent quantum superposition states, which is known as multipartite cat states demonstrating quantum entanglement among macroscopically distinct objects. Here, we present a highly scalable approach to deterministically create flying multipartite Schrödinger's cat states by reflecting coherent-state photons from a microwave cavity containing a superconducting qubit. We perform full quantum state tomography on the cat states with up to four photonic modes and confirm the existence of quantum entanglement among them. We also witness the hybrid entanglement between discrete-variable states (the qubit) and continuous-variable states (the flying multipartite cat) through a joint quantum state tomography. Our work provides an enabling step for implementing a series of quantum metrology and quantum information processing protocols based on cat states.
A logical qubit is a two-dimensional subspace of a higher dimensional system, chosen such that it is possible to detect and correct the occurrence of certain errors. Manipulation of the encoded information generally requires arbitrary and precise control over the entire system. Whether based on multiple physical qubits or larger dimensional modes such as oscillators, the individual elements in realistic devices will always have residual interactions, which must be accounted for when designing logical operations. Here we demonstrate a holistic control strategy which exploits accurate knowledge of the Hamiltonian to manipulate a coupled oscillator-transmon system. We use this approach to realize high-fidelity (98.5%, inferred), decoherence-limited operations on a logical qubit encoded in a superconducting cavity resonator using four-component cat states. Our results show the power of applying numerical techniques to control linear oscillators and pave the way for utilizing their large Hilbert space as a resource in quantum information processing.A logical qubit is a two-dimensional subspace of a higher dimensional system, whose manipulation requires precise control over the whole system. Here the authors demonstrate a control strategy which exploits precise knowledge of the Hamiltonian to manipulate a coupled oscillator-transmon system.
Schr\{o}dinger cat states are crucial for exploration of fundamental issues of quantum mechanics and have important applications in quantum information processing. Here, we propose and experimentally demonstrate a method for manipulating cat states in a cavity with the Aharonov-Anandan phase acquired by a superconducting qubit, which is dispersively coupled to the cavity. Based on this dispersive coupling, the qubit can be forced to trace out a circuit in the projective Hilbert space conditional on one coherent state. By preparing the cavity in a superposition of two coherent states, the geometric phase associated with this transport is encoded to the relative probability amplitude of these two coherent states. We demonstrate the photon-number parity of a cat state in a cavity can be controlled by adjusting this geometric phase, which offers the possibility for protecting its quantum coherence from single-photon loss. Based on this geometric effect, we realize phase gates for one and two photonic qubits whose logical basis states are encoded in two quasi-orthogonal coherent states. We further demonstrate two-cavity gates with symmetric and asymmetric Fock state encoding schemes. Our method can be directly extended to implementation of controlled-phase gates between error-correctable logical qubits.
Abstract Quantum superpositions of macroscopically distinct classical states—so-called Schrödinger cat states—are a resource for quantum metrology, quantum communication and quantum computation. In particular, the superpositions of two opposite-phase coherent states in an oscillator encode a qubit protected against phase-flip errors1, 2. However, several challenges have to be overcome for this concept to become a practical way to encode and manipulate error-protected quantum information. The protection must be maintained by stabilizing these highly excited states and, at the same time, the system has to be compatible with fast gates on the encoded qubit and a quantum non-demolition readout of the encoded information. Here we experimentally demonstrate a method for the generation and stabilization of Schrödinger cat states based on the interplay between Kerr nonlinearity and single-mode squeezing1, 3 in a superconducting microwave resonator4. We show an increase in the transverse relaxation time of the stabilized, error-protected qubit of more than one order of magnitude compared with the single-photon Fock-state encoding. We perform all single-qubit gate operations on timescales more than sixty times faster than the shortest coherence time and demonstrate single-shot readout of the protected qubit under stabilization. Our results showcase the combination of fast quantum control and robustness against errors, which is intrinsic to stabilized macroscopic states, as well as the potential of these states as resources in quantum information processing5–8.
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.
Perfect deterministic amplification of arbitrary quantum states is prohibited by quantum mechanics, but determinism can be achieved by compromising between fidelity and amplification power. We propose a dynamical scheme for deterministically amplifying photonic Schrödinger cat states, which show great promise as a tool for quantum information processing. Our protocol is designed for strongly coupled circuit quantum electrodynamics and utilizes artificial atomic states and external microwave controls to engineer a set of optimal state transfers and achieve high fidelity amplification. We compare analytical results with full simulations of the open, driven Jaynes–Cummings model, using realistic device parameters for state of the art superconducting circuits. Amplification with a fidelity of 0.9 can be achieved for sizable cat states in the presence of cavity and atomic-level decoherence. This tool could be applied to practical continuous-variable information processing for the purification and stabilization of cat states in the presence of photon losses.