High Coherence in a Tileable 3D Integrated Superconducting Circuit Architecture

  1. Peter A. Spring,
  2. Shuxiang Cao,
  3. Takahiro Tsunoda,
  4. Giulio Campanaro,
  5. Simone D. Fasciati,
  6. James Wills,
  7. Vivek Chidambaram,
  8. Boris Shteynas,
  9. Mustafa Bakr,
  10. Paul Gow,
  11. Lewis Carpenter,
  12. James Gates,
  13. Brian Vlastakis,
  14. and Peter J. Leek
We report high qubit coherence as well as low crosstalk and single-qubit gate errors in a superconducting circuit architecture that promises to be tileable to 2D lattices of qubits.
The architecture integrates an inductively shunted cavity enclosure into a design featuring non-galvanic out-of-plane control wiring and qubits and resonators fabricated on opposing sides of a substrate. The proof-of-principle device features four uncoupled transmon qubits and exhibits average energy relaxation times T1=149(38) μs, pure echoed dephasing times Tϕ,e=189(34) μs, and single-qubit gate fidelities F=99.982(4)% as measured by simultaneous randomized benchmarking. The 3D integrated nature of the control wiring means that qubits will remain addressable as the architecture is tiled to form larger qubit lattices. Band structure simulations are used to predict that the tiled enclosure will still provide a clean electromagnetic environment to enclosed qubits at arbitrary scale.

Demonstrating Quantum Error Correction that Extends the Lifetime of Quantum Information

  1. Nissim Ofek,
  2. Andrei Petrenko,
  3. Reinier Heeres,
  4. Philip Reinhold,
  5. Zaki Leghtas,
  6. Brian Vlastakis,
  7. Yehan Liu,
  8. Luigi Frunzio,
  9. S. M. Girvin,
  10. Liang Jiang,
  11. Mazyar Mirrahimi,
  12. M. H. Devoret,
  13. and R. J. Schoelkopf
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 hope
for 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.

Violating Bell’s inequality with an artificial atom and a cat state in a cavity

  1. Brian Vlastakis,
  2. Andrei Petrenko,
  3. Nissim Ofek,
  4. Luayn Sun,
  5. Zaki Leghtas,
  6. Katrina Sliwa,
  7. Yehan Liu,
  8. Michael Hatridge,
  9. Jacob Blumoff,
  10. Luigi Frunzio,
  11. Mazyar Mirrahimi,
  12. Liang Jiang,
  13. M. H. Devoret,
  14. and R. J. Schoelkopf
The `Schr“odinger’s cat‘ thought experiment highlights the counterintuitive facet of quantum theory that entanglement can exist between microscopic and macroscopic
systems, 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.

Cavity State Manipulation Using Photon-Number Selective Phase Gates

  1. Reinier W. Heeres,
  2. Brian Vlastakis,
  3. Eric Holland,
  4. Stefan Krastanov,
  5. Victor V. Albert,
  6. Luigi Frunzio,
  7. Liang Jiang,
  8. and Robert J. Schoelkopf
The large available Hilbert space and high coherence of cavity resonators makes these systems an interesting resource for storing encoded quantum bits. To perform a quantum gate on
this encoded information, however, complex nonlinear operations must be applied to the many levels of the oscillator simultaneously. In this work, we introduce the Selective Number-dependent Arbitrary Phase (SNAP) gate, which imparts a different phase to each Fock state component using an off-resonantly coupled qubit. We show that the SNAP gate allows control over the quantum phases by correcting the unwanted phase evolution due to the Kerr effect. Furthermore, by combining the SNAP gate with oscillator displacements, we create a one-photon Fock state with high fidelity. Using just these two controls, one can construct arbitrary unitary operations, offering a scalable route to performing logical manipulations on oscillator-encoded qubits.

Universal Control of an Oscillator with Dispersive Coupling to a Qubit

  1. Stefan Krastanov,
  2. Victor V. Albert,
  3. Chao Shen,
  4. Chang-Ling Zou,
  5. Reinier W. Heeres,
  6. Brian Vlastakis,
  7. Robert J. Schoelkopf,
  8. and Liang Jiang
We investigate quantum control of an oscillator mode off-resonantly coupled to an ancillary qubit. In the strong dispersive regime, we may drive the qubit conditioned on number states
of the oscillator, which together with displacement operations can achieve universal control of the oscillator. Based on our proof of universal control, we provide explicit constructions for arbitrary state preparation and arbitrary unitary operation of the oscillator. Moreover, we present an efficient procedure to prepare the number state ∣∣n⟩ using only O(n‾‾√) operations. We also compare our scheme with known quantum control protocols for coupled qubit-oscillator systems. This universal control scheme of the oscillator can readily be implemented using superconducting circuits.

Confining the state of light to a quantum manifold by engineered two-photon loss

  1. Zaki Leghtas,
  2. Steven Touzard,
  3. Ioan M. Pop,
  4. Angela Kou,
  5. Brian Vlastakis,
  6. Andrei Petrenko,
  7. Katrina M. Sliwa,
  8. Anirudh Narla,
  9. Shyam Shankar,
  10. Michael J. Hatridge,
  11. Matthew Reagor,
  12. Luigi Frunzio,
  13. Robert J. Schoelkopf,
  14. Mazyar Mirrahimi,
  15. and Michel H. Devoret
Physical systems usually exhibit quantum behavior, such as superpositions and entanglement, only when they are sufficiently decoupled from a lossy environment. Paradoxically, a specially
engineered 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.

Observation of quantum state collapse and revival due to the single-photon Kerr effect

  1. Gerhard Kirchmair,
  2. Brian Vlastakis,
  3. Zaki Leghtas,
  4. Simon E. Nigg,
  5. Hanhee Paik,
  6. Eran Ginossar,
  7. Mazyar Mirrahimi,
  8. Luigi Frunzio,
  9. S. M. Girvin,
  10. and R. J. Schoelkopf
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 weak
interactions 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.

Black-box superconducting circuit quantization

  1. Simon E. Nigg,
  2. Hanhee Paik,
  3. Brian Vlastakis,
  4. Gerhard Kirchmair,
  5. Shyam Shankar,
  6. Luigi Frunzio,
  7. Michel Devoret,
  8. Robert Schoelkopf,
  9. and Steven Girvin
We present a semi-classical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions
coupled to electromagnetic environments made of an arbitrary combination of distributed and lumped elements. A convenient basis, capturing the multi-mode physics, is given by the quantized eigenmodes of the linearized circuit and is fully determined by a classical linear response function. The method is used to calculate numerically the low-energy spectrum of a 3D-transmon system, and quantitative agreement with measurements is found.