The randomized measurement toolbox (2203.11374v1)

Abstract: Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large quantum systems is the source of their power, but also makes them difficult to control precisely or characterize accurately using measured classical data. We review recently developed protocols for probing the properties of complex many-qubit systems using measurement schemes that are practical using today's quantum platforms. In all these protocols, a quantum state is repeatedly prepared and measured in a randomly chosen basis; then a classical computer processes the measurement outcomes to estimate the desired property. The randomization of the measurement procedure has distinct advantages; for example, a single data set can be employed multiple times to pursue a variety of applications, and imperfections in the measurements are mapped to a simplified noise model that can more easily be mitigated. We discuss a range of use cases that have already been realized in quantum devices, including Hamiltonian simulation tasks, probes of quantum chaos, measurements of nonlocal order parameters, and comparison of quantum states produced in distantly separated laboratories. By providing a workable method for translating a complex quantum state into a succinct classical representation that preserves a rich variety of relevant physical properties, the randomized measurement toolbox strengthens our ability to grasp and control the quantum world.

• The paper introduces a set of randomized measurement protocols to accurately characterize complex many-qubit quantum states.
• It leverages classical shadows to extract multiple system properties from reduced measurement data, enhancing efficiency.
• Its applications in Hamiltonian simulation, quantum chaos, and noise mitigation pave the way for improved quantum computing techniques.

Summary of "The Randomized Measurement Toolbox"

The paper "The Randomized Measurement Toolbox" reviews advanced protocols for probing complex many-qubit quantum systems using today's programmable quantum simulators and quantum computers. These systems, characterized by their entangled states, present significant challenges for precise control and characterization via classical data. The researchers introduce a set of measurement protocols—collectively known as the randomized measurement toolbox—that leverage the randomness in measurement bases to access a wide range of system properties.

In essence, the paper presents a methodology where a quantum state is repeatedly prepared and measured in randomly chosen bases, and then a classical computer processes these results. This randomization has several advantages: it allows the reuse of a single dataset for multiple applications and simplifies noise mitigation by mapping imperfect measurements onto a noise model.

Key Concepts and Results

1. Randomized Measurements: Quantum states are measured after being transformed by randomly selected unitary operations from a unitary group or subset, often applied locally. The statistical correlations from these measurements can be used to estimate a variety of system properties efficiently.
2. Classical Shadows: The concept of classical shadows is central to the methodology. By sampling different random measurement bases, it becomes possible to construct classical shadows that provide succinct representations of quantum states. These shadows enable the estimation of multiple properties of the quantum system with a reduced number of measurements.
3. Applications: The paper discusses several applications verified in experiments including:
   • Hamiltonian Simulation: Randomized measurements facilitate efficient simulations of Hamiltonian dynamics.
   • Quantum Chaos: Correlations extracted from the measurement data are effective probes for quantum chaos, without requiring the inversion of time evolution.
   • Nonlocal Order Parameters: The toolbox can measure nonlocal parameters that characterize quantum order and phases, such as topological order.
   • Cross-Platform Comparisons: Randomized measurement techniques have been used to compare quantum states prepared on different platforms, providing a measure of their fidelity and reliability.

Implications and Future Directions

The implications of the randomized measurement toolbox extend both to practical applications and theoretical investigations:

• Quantum Computing and Simulation: By providing a mechanism to effectively interpret and manage large datasets from quantum experiments, these methods can streamline the testing and improvement of quantum algorithms and hardware.
• Noise Mitigation: The protocols naturally incorporate techniques for addressing noise, a crucial task in the era of noisy intermediate-scale quantum (NISQ) devices.
• Quantum Machine Learning: The potential for combining classical machine learning techniques with the shadow datasets opens new avenues for predicting properties of quantum systems beyond current capabilities.

The paper ultimately points towards a future where increasingly complex quantum systems can be harnessed and studied via these innovative methodologies. As hardware continues to develop, the principles outlined in this paper will likely play a crucial role in guiding the transition from small-scale demonstrations to large-scale quantum computation and simulation tasks.