Marcus P. da Silva

Symmetrized characterization of noisy quantum processes.

A major goal of developing high-precision control of many-body quantum systems is to realize their potential as quantum computers. A substantial obstacle to this is the extreme fragility of quantum systems to “decoherence” from environmental noise and other control limitations. Although quantum computation is possible if the noise affecting the quantum system satisfies certain conditions, existing methods for noise characterization are intractable for present multibody systems. We introduce a technique based on symmetrization that enables direct experimental measurement of some key properties of the decoherence affecting a quantum system. Our method reduces the number of experiments required from exponential to polynomial in the number of subsystems. The technique is demonstrated for the optimization of control over nuclear spins in the solid state.

Practical Characterization of Quantum Devices without Tomography

Quantum tomography is the main method used to assess the quality of quantum information processing devices. However, the amount of resources needed for quantum tomography is exponential in the device size. Part of the problem is that tomography generates much more information than is usually sought. Taking a more targeted approach, we develop schemes that enable (i) estimating the fidelity of an experiment to a theoretical ideal description, (ii) learning which description within a reduced subset best matches the experimental data. Both these approaches yield a significant reduction in resources compared to tomography. In particular, we demonstrate that fidelity can be estimated from a number of simple experiments that is independent of the system size, removing an important roadblock for the experimental study of larger quantum information processing units.

Robust Extraction of Tomographic Information via Randomized Benchmarking

Quantum processing tomography typically reconstructs an unknown quantum dynamical operation by measuring its effects on known states of a quantum device. Taking a different approach of comparing the operation of interest to a set of finite and easily implementable reference operations, a new method can reconstruct any quantum operation reliably.

Schemes for the observation of photon correlation functions in circuit QED with linear detectors

Correlations are important tools in the characterization of quantum fields, as they can be used to describe statistical properties of the fields, such as bunching and antibunching, as well as to perform field state tomography. Here we analyze experiments by Bozyigit et al. [Nat. Phys. (to appear), e-print arXiv:1002.3738] where correlation functions can be observed using the measurement records of linear detectors (i.e., quadrature measurements), instead of relying on intensity or number detectors. We also describe how large amplitude noise introduced by these detectors can be quantified and subtracted from the data. This enables, in particular, the observation of first- and second-order coherence functions of microwave photon fields generated using circuit quantum electrodynamics and propagating in superconducting transmission lines under the condition that noise is sufficiently low.

Research problems on numerical ranges in quantum computing

We describe some instances in quantum information processing where numerical range techniques arise. We focus on two basic settings: higher-rank numerical ranges and their relevance in theoretical quantum error correction, and the classical numerical range and its use for comparing quantum information processing operations. We present the basic theory, discuss examples and formulate open problems.

First-order sidebands in circuit QED using qubit frequency modulation

Sideband transitions have been shown to generate controllable interaction between superconducting qubits and microwave resonators. Up to now, these transitions have been implemented with voltage drives on the qubit or the resonator, with the significant disadvantage that such implementations only lead to second-order sideband transitions. Here we propose an approach to achieve first-order sideband transitions by relying on controlled oscillations of the qubit frequency using a flux-bias line. Not only can first-order transitions be significantly faster, but the same technique can be employed to implement other tunable qubit-resonator and qubit-qubit interactions. We discuss in detail how such first-order sideband transitions can be used to implement a high fidelity controlled-NOT operation between two transmons coupled to the same resonator.

Demonstration of quantum advantage in machine learning

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, limiting the obtained advantage. Here we solve an oracle-based problem, known as learning parity with noise, on a five-qubit superconducting processor. Executing classical and quantum algorithms using 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 significant quantum advantage already emerges in existing noisy systems.Large advantage in small quantum computersQuantum computing promises to revolutionize all fields of science by solving problems that are too complex for conventional computers. However, the realization of a full-fledged, universal quantum computer is still far ahead, requiring millions of quantum bits and very low error rates. Despite this, D. Ristè and colleagues at Raytheon BBN Technologies, with collaborators at IBM, have demonstrated that a quantum advantage already appears with only a few quantum bits and a highly noisy system. The team solved a particular problem, known as learning parity with noise, using a five-qubit superconducting quantum processor. Counting the number of times that the processor runs, they demonstrate that the implemented quantum algorithm finds the solution much faster than by classical methods

A direct approach to fault-tolerance in measurement-based quantum computation via teleportation

We discuss a simple variant of the one-way quantum computing model (Raussendorf R and Briegel H-J 2001 Phys. Rev. Lett. 86 5188), called the Pauli measurement model, where measurements are restricted to be along the eigenbases of the Pauli X and Y operators, while qubits can be initially prepared both in the state and the usual state. We prove the universality of this quantum computation model, and establish a standardization procedure which permits all entanglement and state preparation to be performed at the beginning of computation. This leads us to develop a direct approach to fault-tolerance by simple transformations of the entanglement graph and preparation operations, while error correction is performed naturally via syndrome-extracting teleportations.

Tomography via Correlation of Noisy Measurement Records

to measure N-body correlations from individual measurements scales exponentially with N, but with sucient signal-to-noise the approach remains viable for few-body correlations. We provide a new protocol to optimally account for the transient behavior of pulsed measurements. Despite single-shot measurement delity that is less than perfect, we demonstrate appropriate processing to extract and verify entangled states and processes. By engineering coherent manipulation of quantum states we hope to gain computational power not available to classical computers. The purported advantage of a quantum information processing system comes from its ability to create and control quantum correlations or entanglement [1]. As we work towards obtaining highdelity quantum control, the ability to measure, conrm

Stabilizer quantum error correction with quantum bus computation

In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators that generate the stabilizer group of a quantum code. First, we show how to measure a Pauli operator acting on physical qubits using a single coherent state with large average photon number, displacement operations, and photon detection. Second, we show how to measure the stabilizer operators fault-tolerantly by the deterministic preparation of coherent quantum superposition (“cat”) states along with one-bit teleportations between a qubitlike encoding of coherent states and physical qubits.