Shadow process tomography of quantum channels

Abstract

Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scale exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements. In this work, we apply the concepts of shadow state tomography to the challenge of characterizing quantum processes. We make use of the Choi isomorphism to directly apply rigorous bounds from shadow state tomography to shadow process tomography, and we find additional bounds on the number of measurements that are unique to process tomography. Our results, which include algorithms for implementing shadow process tomography enable new techniques including evaluation of channel concatenation and the application of channels to shadows of quantum states. This provides a dramatic improvement for understanding large-scale quantum systems.

12 pages, 5 figures; Added citation to similar work; Errors corrected. Previous statements of main result first missed and then miscalculated an exponential cost in system size; Version accepted for publication

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Cited by in corpus (32)

• Shallow shadows: Expectation estimation using low-depth random Clifford circuits
• Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers
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• Classical shadows with Pauli-invariant unitary ensembles
• Analysing quantum systems with randomised measurements
• Learning quantum states and unitaries of bounded gate complexity
• Estimating gate-set properties from random sequences
• Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix
• Learning shallow quantum circuits
• Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows
• Group-theoretic error mitigation enabled by classical shadows and symmetries
• A Practical Introduction to Benchmarking and Characterization of Quantum Computers
• Enhanced estimation of quantum properties with common randomized measurements
• Classical shadows based on locally-entangled measurements
• Randomness-enhanced expressivity of quantum neural networks
• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• Quantum Computing Universal Thermalization Dynamics in a (2+1)D Lattice Gauge Theory
• Tensor network noise characterization for near-term quantum computers
• Randomized measurement protocols for lattice gauge theories
• Optimising quantum tomography via shadow inversion
• Extracting randomness from magic quantum states
• Exploring the Non-Markovian Dynamics in Depolarizing Maps
• Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains
• Learning Quantum Processes with Quantum Statistical Queries
• Holographic Classical Shadow Tomography
• Using non-convex optimization in quantum process tomography: Factored gradient descent is tough to beat
• Agnostic Process Tomography
• Nearly query-optimal classical shadow estimation of unitary channels
• Efficient and robust estimation of many-qubit Hamiltonians
• Reducing Complexity of Shadow Process Tomography with Generalized Measurements
• Efficient Characterization of Coherent and Correlated Low-Degree Noise in Layers of Gates
• Moments of Quantum Channel Ensembles