Demonstration of quantum advantage in machine learning

  1. D. Ristè,
  2. Marcus P. da Silva,
  3. Colm A. Ryan,
  4. Andrew W. Cross,
  5. John A. Smolin,
  6. Jay M. Gambetta,
  7. Jerry M. Chow,
  8. and Blake R. Johnson
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage
involve the repeated use of a black box, or oracle, whose structure encodes the solution. One measure of the algorithmic performance is the query complexity, i.e., the scaling of the number of oracle calls needed to find the solution with a given probability. Few-qubit demonstrations of quantum algorithms, such as Deutsch-Jozsa and Grover, have been implemented across diverse physical systems such as nuclear magnetic resonance, trapped ions, optical systems, and superconducting circuits. However, at the small scale, these problems can already be solved classically with a few oracle queries, and the attainable quantum advantage is modest. Here we solve an oracle-based problem, known as learning parity with noise, using a five-qubit superconducting processor. Running classical and quantum algorithms on the same oracle, we observe a large gap in query count in favor of quantum processing. We find that this gap grows by orders of magnitude as a function of the error rates and the problem size. This result demonstrates that, while complex fault-tolerant architectures will be required for universal quantum computing, a quantum advantage already emerges in existing noisy systems

Digital feedback in superconducting quantum circuits

  1. D. Ristè,
  2. and L. DiCarlo
This chapter covers the development of feedback control of superconducting qubits using projective measurement and a discrete set of conditional actions, here referred to as digital
feedback. We begin with an overview of the applications of digital feedback in quantum computing. We then introduce an implementation of high-fidelity projective measurement of superconducting qubits. This development lays the ground for closed-loop control based on the binary measurement result. A first application of digital feedback control is fast and deterministic qubit reset, allowing the repeated initialization of a qubit more than an order of magnitude faster than its relaxation rate. A second application employs feedback in a multi-qubit setting to convert the generation of entanglement by parity measurement from probabilistic to deterministic, targeting an entangled state with the desired parity every time.

Detecting bit-flip errors in a logical qubit using stabilizer measurements

  1. D. Ristè,
  2. S. Poletto,
  3. M.-Z. Huang,
  4. A. Bruno,
  5. V. Vesterinen,
  6. O.-P. Saira,
  7. and L. DiCarlo
Quantum data is susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction
(QEC) to actively protect against both. In the smallest QEC codes, the information in one logical qubit is encoded in a two-dimensional subspace of a larger Hilbert space of multiple physical qubits. For each code, a set of non-demolition multi-qubit measurements, termed stabilizers, can discretize and signal physical qubit errors without collapsing the encoded information. Experimental demonstrations of QEC to date, using nuclear magnetic resonance, trapped ions, photons, superconducting qubits, and NV centers in diamond, have circumvented stabilizers at the cost of decoding at the end of a QEC cycle. This decoding leaves the quantum information vulnerable to physical qubit errors until re-encoding, violating a basic requirement for fault tolerance. Using a five-qubit superconducting processor, we realize the two parity measurements comprising the stabilizers of the three-qubit repetition code protecting one logical qubit from physical bit-flip errors. We construct these stabilizers as parallelized indirect measurements using ancillary qubits, and evidence their non-demolition character by generating three-qubit entanglement from superposition states. We demonstrate stabilizer-based quantum error detection (QED) by subjecting a logical qubit to coherent and incoherent bit-flip errors on its constituent physical qubits. While increased physical qubit coherence times and shorter QED blocks are required to actively safeguard quantum information, this demonstration is a critical step toward larger codes based on multiple parity measurements.

Reversing quantum trajectories with analog feedback

  1. G. de Lange,
  2. D. Ristè,
  3. M. J. Tiggelman,
  4. C. Eichler,
  5. L. Tornberg,
  6. G. Johansson,
  7. A. Wallraff,
  8. R. N. Schouten,
  9. and L. DiCarlo
We demonstrate the active suppression of transmon qubit dephasing induced by dispersive measurement, using parametric amplification and analog feedback. By real-time processing of the
homodyne record, the feedback controller reverts the stochastic quantum phase kick imparted by the measurement on the qubit. The feedback operation matches a model of quantum trajectories with measurement efficiency η~≈0.5, consistent with the result obtained by postselection. We overcome the bandwidth limitations of the amplification chain by numerically optimizing the signal processing in the feedback loop and provide a theoretical model explaining the optimization result.

Deterministic entanglement of superconducting qubits by parity measurement and feedback

  1. D. Ristè,
  2. M. Dukalski,
  3. C. A. Watson,
  4. G. de Lange,
  5. M. J. Tiggelman,
  6. Ya. M. Blanter,
  7. K. W. Lehnert,
  8. R. N. Schouten,
  9. and L. DiCarlo
The stochastic evolution of quantum systems during measurement is arguably the most enigmatic feature of quantum mechanics. Measuring a quantum system typically steers it towards a
classical state, destroying any initial quantum superposition and any entanglement with other quantum systems. Remarkably, the measurement of a shared property between non-interacting quantum systems can generate entanglement starting from an uncorrelated state. Of special interest in quantum computing is the parity measurement, which projects a register of quantum bits (qubits) to a state with an even or odd total number of excitations. Crucially, a parity meter must discern the two parities with high fidelity while preserving coherence between same-parity states. Despite numerous proposals for atomic, semiconducting, and superconducting qubits, realizing a parity meter creating entanglement for both even and odd measurement results has remained an outstanding challenge. We realize a time-resolved, continuous parity measurement of two superconducting qubits using the cavity in a 3D circuit quantum electrodynamics (cQED) architecture and phase-sensitive parametric amplification. Using postselection, we produce entanglement by parity measurement reaching 77% concurrence. Incorporating the parity meter in a feedback-control loop, we transform the entanglement generation from probabilistic to fully deterministic, achieving 66% fidelity to a target Bell state on demand. These realizations of a parity meter and a feedback-enabled deterministic measurement protocol provide key ingredients for active quantum error correction in the solid state.

Partial-measurement back-action and non-classical weak values in a superconducting circuit

  1. J. P. Groen,
  2. D. Ristè,
  3. L. Tornberg,
  4. J. Cramer,
  5. P. C. de Groot,
  6. T. Picot,
  7. G. Johansson,
  8. and L. DiCarlo
We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated
readout resonator. Accurate control of the interaction and ancilla measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit back-action is characterized through the distortion of a qubit Rabi oscillation imposed by ancilla measurement in different bases. Combining partial and projective qubit measurements, we provide the solid-state demonstration of the correspondence between a non-classical weak value and the violation of a Leggett-Garg inequality.

Feedback control of a solid-state qubit using high-fidelity projective measurement

  1. D. Ristè,
  2. C. C. Bultink,
  3. K. W. Lehnert,
  4. and L. DiCarlo
We demonstrate feedback control of a superconducting transmon qubit using discrete, projective measurement and conditional coherent driving. Feedback realizes a fast and deterministic
qubit reset to a target state with 2.4% error averaged over input superposition states, and cooling of the transmon from 16% spurious excitation to 3%. This closed-loop qubit control is necessary for measurement-based protocols such as quantum error correction and teleportation.

Initialization by measurement of a two-qubit superconducting circuit

  1. D. Ristè,
  2. J. G. van Leeuwen,
  3. H.-S. Ku,
  4. K. W. Lehnert,
  5. and L. DiCarlo
We demonstrate initialization by joint measurement of two transmon qubits in 3D circuit quantum electrodynamics. Homodyne detection of cavity transmission is enhanced by Josephson parametric
amplification to discriminate the two-qubit ground state from single-qubit excitations non-destructively and with 98.1% fidelity. Measurement and postselection of a steady-state mixture with 4.7% residual excitation per qubit achieve 98.8% fidelity to the ground state, thus outperforming passive initialization.