Entangling gates between qubits are a crucial component for performing algorithms in quantum computers. However, any quantum algorithm will ultimately have to operate on error-protectedlogical qubits, which are effective qubits encoded in a high-dimensional Hilbert space. A common approach is to encode logical qubits in collective states of multiple two-level systems, but algorithms operating on multiple logical qubits are highly complex and have not yet been demonstrated. Here, we experimentally realize a controlled NOT (CNOT) gate between two multiphoton qubits in two microwave cavities. In this approach, we encode a qubit in the large Hilbert space of a single cavity mode, rather than in multiple two-level systems. We couple two such encoded qubits together through a transmon, which is driven with an RF pump to apply the CNOT gate within 190 ns. This is two orders of magnitude shorter than the decoherence time of any part of the system, enabling high-fidelity operations comparable to state-of-the-art gates between two-level systems. These results are an important step towards universal algorithms on error-corrected logical qubits.
A central requirement for any quantum error correction scheme is the ability to perform quantum non-demolition measurements of an error syndrome, corresponding to a special symmetryproperty of the encoding scheme. It is in particular important that such a measurement does not introduce extra error mechanisms, not included in the error model of the correction scheme. In this letter, we ensure such a robustness by designing an interaction with a measurement device that preserves the degeneracy of the measured observable. More precisely, we propose a scheme to perform continuous and quantum non-demolition measurement of photon-number parity in a microwave cavity. This corresponds to the error syndrome in a class of error correcting codes called the cat-codes, which have recently proven to be efficient and versatile for quantum information processing. In our design, we exploit the strongly nonlinear Hamiltonian of a high-impedance Josephson circuit, coupling a high-Q cavity storage cavity mode to a low-Q readout one. By driving the readout resonator at its resonance, the phase of the reflected/transmitted signal carries directly exploitable information on parity-type observables for encoded cat-qubits of the high-Q mode.
The remarkable discovery of Quantum Error Correction (QEC), which can overcome the errors experienced by a bit of quantum information (qubit), was a critical advance that gives hopefor eventually realizing practical quantum computers. In principle, a system that implements QEC can actually pass a „break-even“ point and preserve quantum information for longer than the lifetime of its constituent parts. Reaching the break-even point, however, has thus far remained an outstanding and challenging goal. Several previous works have demonstrated elements of QEC in NMR, ions, nitrogen vacancy (NV) centers, photons, and superconducting transmons. However, these works primarily illustrate the signatures or scaling properties of QEC codes rather than test the capacity of the system to extend the lifetime of quantum information over time. Here we demonstrate a QEC system that reaches the break-even point by suppressing the natural errors due to energy loss for a qubit logically encoded in superpositions of coherent states, or cat states of a superconducting resonator. Moreover, the experiment implements a full QEC protocol by using real-time feedback to encode, monitor naturally occurring errors, decode, and correct. As measured by full process tomography, the enhanced lifetime of the encoded information is 320 microseconds without any post-selection. This is 20 times greater than that of the system’s transmon, over twice as long as an uncorrected logical encoding, and 10% longer than the highest quality element of the system (the resonator’s 0, 1 Fock states). Our results illustrate the power of novel, hardware efficient qubit encodings over traditional QEC schemes. Furthermore, they advance the field of experimental error correction from confirming the basic concepts to exploring the metrics that drive system performance and the challenges in implementing a fault-tolerant system.
The `Schr“odinger’s cat‘ thought experiment highlights the counterintuitive facet of quantum theory that entanglement can exist between microscopic and macroscopicsystems, producing a superposition of distinguishable states like the fictitious cat that is both alive and dead. The hallmark of entanglement is the detection of strong correlations between systems, for example by the violation of Bell’s inequality. Using the CHSH variant of the Bell test, this violation has been observed with photons, atoms, solid state spins, and artificial atoms in superconducting circuits. For larger, more distinguishable states, the conflict between quantum predictions and our classical expectations is typically resolved due to the rapid onset of decoherence. To investigate this reconciliation, one can employ a superposition of coherent states in an oscillator, known as a cat state. In contrast to discrete systems, one can continuously vary the size of the prepared cat state and therefore its dependence on decoherence. Here we demonstrate and quantify entanglement between an artificial atom and a cat state in a cavity, which we call a `Bell-cat‘ state. We use a circuit QED architecture, high-fidelity measurements, and real-time feedback control to violate Bell’s inequality without post-selection or corrections for measurement inefficiencies. Furthermore, we investigate the influence of decoherence by continuously varying the size of created Bell-cat states and characterize the entangled system by joint Wigner tomography. These techniques provide a toolset for quantum information processing with entangled qubits and resonators. While recent results have demonstrated a high level of control of such systems, this experiment demonstrates that information can be extracted efficiently and with high fidelity, a crucial requirement for quantum computing with resonators.
Physical systems usually exhibit quantum behavior, such as superpositions and entanglement, only when they are sufficiently decoupled from a lossy environment. Paradoxically, a speciallyengineered interaction with the environment can become a resource for the generation and protection of quantum states. This notion can be generalized to the confinement of a system into a manifold of quantum states, consisting of all coherent superpositions of multiple stable steady states. We have experimentally confined the state of a harmonic oscillator to the quantum manifold spanned by two coherent states of opposite phases. In particular, we have observed a Schrodinger cat state spontaneously squeeze out of vacuum, before decaying into a classical mixture. This was accomplished by designing a superconducting microwave resonator whose coupling to a cold bath is dominated by photon pair exchange. This experiment opens new avenues in the fields of nonlinear quantum optics and quantum information, where systems with multi-dimensional steady state manifolds can be used as error corrected logical qubits.
While dissipation is widely considered as being harmful for quantum coherence, it can, when properly engineered, lead to the stabilization of non-trivial pure quantum states. We proposea scheme for continuous generation and stabilization of Schr\“{o}dinger cat states in a cavity using dissipation engineering. We first generate non-classical photon states with definite parity by means of a two-photon drive and dissipation, and then stabilize these transient states against single-photon decay. The single-photon stabilization is autonomous, and is implemented through a second engineered bath, which exploits the photon number dependent frequency-splitting due to Kerr interactions in the strongly dispersive regime of circuit QED. Starting with the Hamiltonian of the baths plus cavity, we derive an effective model of only the cavity photon states along with analytic expressions for relevant physical quantities, such as the stabilization rate. The deterministic generation of such cat states is one of the key ingredients in performing universal quantum computation.
As the energy relaxation time of superconducting qubits steadily improves, non-equilibrium quasiparticle excitations above the superconducting gap emerge as an increasingly relevantlimit for qubit coherence. We measure fluctuations in the number of quasiparticle excitations by continuously monitoring the spontaneous quantum jumps between the states of a fluxonium qubit, in conditions where relaxation is dominated by quasiparticle loss. Resolution on the scale of a single quasiparticle is obtained by performing quantum non-demolition projective measurements within a time interval much shorter than T1, using a quantum limited amplifier (Josephson Parametric Converter). The quantum jumps statistics switches between the expected Poisson distribution and a non-Poissonian one, indicating large relative fluctuations in the quasiparticle population, on time scales varying from seconds to hours. This dynamics can be modified controllably by injecting quasiparticles or by seeding quasiparticle-trapping vortices by cooling down in magnetic field.
We present a new hardware-efficient paradigm for universal quantum computation which is based on encoding, protecting and manipulating quantum information in a quantum harmonic oscillator.This proposal exploits multi-photon driven dissipative processes to encode quantum information in logical bases composed of Schr\“odinger cat states. More precisely, we consider two schemes. In a first scheme, a two-photon driven dissipative process is used to stabilize a logical qubit basis of two-component Schr\“odinger cat states. While such a scheme ensures a protection of the logical qubit against the photon dephasing errors, the prominent error channel of single-photon loss induces bit-flip type errors that cannot be corrected. Therefore, we consider a second scheme based on a four-photon driven dissipative process which leads to the choice of four-component Schr\“odinger cat states as the logical qubit. Such a logical qubit can be protected against single-photon loss by continuous photon number parity measurements. Next, applying some specific Hamiltonians, we provide a set of universal quantum gates on the encoded qubits of each of the two schemes. In particular, we illustrate how these operations can be rendered fault-tolerant with respect to various decoherence channels of participating quantum systems. Finally, we also propose experimental schemes based on quantum superconducting circuits and inspired by methods used in Josephson parametric amplification, which should allow to achieve these driven dissipative processes along with the Hamiltonians ensuring the universal operations in an efficient manner.
Making a system state follow a prescribed trajectory despite fluctuations and
errors commonly consists in monitoring an observable (temperature,
blood-glucose level…) and reactingon its controllers (heater power, insulin
amount …). In the quantum domain, there is a change of paradigm in feedback
since measurements modify the state of the system, most dramatically when the
trajectory goes through superpositions of measurement eigenstates. Here, we
demonstrate the stabilization of an arbitrary trajectory of a superconducting
qubit by measurement based feedback. The protocol benefits from the long
coherence time ($T_2>10 mu$s) of the 3D transmon qubit, the high efficiency
(82%) of the phase preserving Josephson amplifier, and fast electronics
ensuring less than 500 ns delay. At discrete time intervals, the state of the
qubit is measured and corrected in case an error is detected. For Rabi
oscillations, where the discrete measurements occur when the qubit is supposed
to be in the measurement pointer states, we demonstrate an average fidelity of
85% to the targeted trajectory. For Ramsey oscillations, which does not go
through pointer states, the average fidelity reaches 75%. Incidentally, we
demonstrate a fast reset protocol allowing to cool a 3D transmon qubit down to
0.6% in the excited state.
Photons are ideal carriers for quantum information as they can have a long
coherence time and can be transmitted over long distances. These properties are
a consequence of their weakinteractions within a nearly linear medium. To
create and manipulate nonclassical states of light, however, one requires a
strong, nonlinear interaction at the single photon level. One approach to
generate suitable interactions is to couple photons to atoms, as in the strong
coupling regime of cavity QED systems. In these systems, however, one only
indirectly controls the quantum state of the light by manipulating the atoms. A
direct photon-photon interaction occurs in so-called Kerr media, which
typically induce only weak nonlinearity at the cost of significant loss. So
far, it has not been possible to reach the single-photon Kerr regime, where the
interaction strength between individual photons exceeds the loss rate. Here,
using a 3D circuit QED architecture, we engineer an artificial Kerr medium
which enters this regime and allows the observation of new quantum effects. We
realize a Gedankenexperiment proposed by Yurke and Stoler, in which the
collapse and revival of a coherent state can be observed. This time evolution
is a consequence of the quantization of the light field in the cavity and the
nonlinear interaction between individual photons. During this evolution
non-classical superpositions of coherent states, i.e. multi-component
Schroedinger cat states, are formed. We visualize this evolution by measuring
the Husimi Q-function and confirm the non-classical properties of these
transient states by Wigner tomography. The single-photon Kerr effect could be
employed in QND measurement of photons, single photon generation, autonomous
quantum feedback schemes and quantum logic operations.