Steven Touzard

A practical guide for building superconducting quantum devices

  1. Yvonne Y. Gao,
  2. M. Adriaan Rol,
  3. Steven Touzard,
  4. and Chen Wang
Quantum computing offers a powerful new paradigm of information processing that has the potential to transform a wide range of industries. In the pursuit of the tantalizing promises
of a universal quantum computer, a multitude of new knowledge and expertise has been developed, enabling the construction of novel quantum algorithms as well as increasingly robust quantum hardware. In particular, we have witnessed rapid progress in the circuit quantum electrodynamics (cQED) technology, which has emerged as one of the most promising physical systems that is capable of addressing the key challenges in realizing full-stack quantum computing on a large scale. In this article, we present some of the most crucial building blocks developed by the cQED community in recent years and a précis of the latest achievements towards robust universal quantum computation. More importantly, we aim to provide a synoptic outline of the core techniques that underlie most cQED experiments and offer a practical guide for a novice experimentalist to design, construct, and characterize their first quantum device
arxiv pdf

The Kerr-Cat Qubit: Stabilization, Readout, and Gates

  1. Alexander Grimm,
  2. Nicholas E. Frattini,
  3. Shruti Puri,
  4. Shantanu O. Mundhada,
  5. Steven Touzard,
  6. Mazyar Mirrahimi,
  7. Steven M. Girvin,
  8. Shyam Shankar,
  9. and Michel H. Devoret
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 errors. However, several challenges have to be overcome in order 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 novel method for the generation and stabilization of Schrödinger cat states based on the interplay between Kerr nonlinearity and single-mode squeezing in a superconducting microwave resonator. We show an increase in transverse relaxation time of the stabilized, error-protected qubit over the single-photon Fock-state encoding by more than one order of magnitude. We perform all single-qubit gate operations on time-scales 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 with the robustness against errors intrinsic to stabilized macroscopic states and open up the possibility of using these states as resources in quantum information processing.
arxiv pdf

Bias-preserving gates with stabilized cat qubits

  1. Shruti Puri,
  2. Lucas St-Jean,
  3. Jonathan A. Gross,
  4. Alexander Grimm,
  5. N. E. Frattini,
  6. Pavithran S. Iyer,
  7. Anirudh Krishna,
  8. Steven Touzard,
  9. Liang Jiang,
  10. Alexandre Blais,
  11. Steven T. Flammia,
  12. and S. M. Girvin
The code capacity threshold for error correction using qubits which exhibit asymmetric or biased noise channels is known to be much higher than with qubits without such structured noise.However, it is unclear how much this improvement persists when realistic circuit level noise is taken into account. This is because implementations of gates which do not commute with the dominant error un-bias the noise channel. In particular, a native bias-preserving controlled-NOT (CX) gate, which is an essential ingredient of stabilizer codes, is not possible in strictly two-level systems. Here we overcome the challenge of implementing a bias-preserving CX gate by using stabilized cat qubits in driven nonlinear oscillators. The physical noise channel of this qubit is biased towards phase-flips, which increase linearly with the size of the cat, while bit-flips are exponentially suppressed with cat size. Remarkably, the error channel of this native CX gate between two such cat qubits is also dominated by phase-flips, while bit-flips remain exponentially suppressed. This CX gate relies on the topological phase that arises from the rotation of the cat qubit in phase space. The availability of bias-preserving CX gates opens a path towards fault-tolerant codes tailored to biased-noise cat qubits with high threshold and low overhead. As an example, we analyze a scheme for concatenated error correction using cat qubits. We find that the availability of CX gates with moderately sized cat qubits, having mean photon number <10, improves a rigorous lower bound on the fault-tolerance threshold by a factor of two and decreases the overhead in logical Clifford operations by a factor of 5. We expect these estimates to improve significantly with further optimization and with direct use of other codes such as topological codes tailored to biased noise.[/expand]
arxiv pdf

Multimode cat codes

  1. Victor V. Albert,
  2. Shantanu O. Mundhada,
  3. Alexander Grimm,
  4. Steven Touzard,
  5. Michel H. Devoret,
  6. and Liang Jiang
We introduce a driven-dissipative two-mode bosonic system whose reservoir causes simultaneous loss of two photons in each mode and whose steady states are superpositions of pair-coherent/Barut-Girardello
coherent states. We show how quantum information encoded in a steady-state subspace of this system is exponentially immune to phase drifts (cavity dephasing) in both modes. Additionally, it is possible to protect information from arbitrary photon loss in either (but not simultaneously both) of the modes by continuously monitoring the difference between the expected photon numbers of the logical states. Despite employing more resources, the two-mode scheme enjoys two advantages over its one-mode counterpart with regards to implementation using current circuit QED technology. First, monitoring the photon number difference can be done without turning off the currently implementable dissipative stabilizing process. Second, a lower average photon number per mode is required to enjoy a level of protection at least as good as that of the cat-codes. We discuss circuit QED proposals to stabilize the code states, perform gates, and protect against photon loss via either active syndrome measurement or an autonomous procedure. We introduce quasiprobability distributions allowing us to represent two-mode states of fixed photon number difference in a two-dimensional complex plane, instead of the full four-dimensional two-mode phase space. The two-mode codes are generalized to multiple modes in an extension of the stabilizer formalism to non-diagonalizable stabilizers. The M-mode codes can protect against either arbitrary photon losses in up to M−1 modes or arbitrary losses or gains in any one mode.
arxiv pdf

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.
arxiv pdf

Dynamically protected cat-qubits: a new paradigm for universal quantum computation

  1. Mazyar Mirrahimi,
  2. Zaki Leghtas,
  3. Victor V. Albert,
  4. Steven Touzard,
  5. Robert J. Schoelkopf,
  6. Liang Jiang,
  7. and Michel H. Devoret
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.
arxiv pdf