Characterizing quantum instruments: from non-demolition measurements to quantum error correction
arXiv:2110.06954 · doi:10.1103/PRXQuantum.3.030318
Abstract
In quantum information processing quantum operations are often processed alongside measurements which result in classical data. Due to the information gain of classical measurement outputs non-unitary dynamical processes can take place on the system, for which common quantum channel descriptions fail to describe the time evolution. Quantum measurements are correctly treated by means of so-called quantum instruments capturing both classical outputs and post-measurement quantum states. Here we present a general recipe to characterize quantum instruments alongside its experimental implementation and analysis. Thereby, the full dynamics of a quantum instrument can be captured, exhibiting details of the quantum dynamics that would be overlooked with common tomography techniques. For illustration, we apply our characterization technique to a quantum instrument used for the detection of qubit loss and leakage, which was recently implemented as a building block in a quantum error correction (QEC) experiment (Nature 585, 207-210 (2020)). Our analysis reveals unexpected and in-depth information about the failure modes of the implementation of the quantum instrument. We then numerically study the implications of these experimental failure modes on QEC performance, when the instrument is employed as a building block in QEC protocols on a logical qubit. Our results highlight the importance of careful characterization and modelling of failure modes in quantum instruments, as compared to simplistic hardware-agnostic phenomenological noise models, which fail to predict the undesired behavior of faulty quantum instruments. The presented methods and results are directly applicable to generic quantum instruments.
arXiv comment28 pages, 21 figures
References in corpus (72)
- Fault-tolerant quantum computation by anyons
- On the Measurement of Qubits
- Topological quantum memory
- An Open-System Quantum Simulator with Trapped Ions
- Randomized Benchmarking of Quantum Gates
- Multi-particle entanglement of hot trapped ions
- A Theory of Fault-Tolerant Quantum Computation
- State preservation by repetitive error detection in a superconducting quantum circuit
- Prescription for experimental determination of the dynamics of a quantum black box
- Topological Quantum Distillation
- Quantum correlations with no causal order
- Real-time quantum feedback prepares and stabilizes photon number states
- Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
- Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits
- Keldysh Field Theory for Driven Open Quantum Systems
- Quantum state estimation
- High-Fidelity Universal Gate Set for Be Ion Qubits
- Theoretical framework for quantum networks
- Realization of a scalable Shor algorithm
- Experimental Quantum Computations on a Topologically Encoded Qubit
- Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography
- Codes for the Quantum Erasure Channel
- A universal qudit quantum processor with trapped ions
- A quantum information processor with trapped ions
- 'Designer atoms' for quantum metrology
- Quantum back-action of variable-strength measurement
- Detecting bit-flip errors in a logical qubit using stabilizer measurements
- Tracking Photon Jumps with Repeated Quantum Non-Demolition Parity Measurements
- Characterizing large-scale quantum computers via cycle benchmarking
- A review of progress in the physics of open quantum systems: theory and experiment
- Repeated quantum error correction on a continuously encoded qubit by real-time feedback
- Quantum simulation of open-system dynamical maps with trapped ions
- Quantum error correction with only two extra qubits
- Implementation of the Five Qubit Error Correction Benchmark
- Topological Computation without Braiding
- Loss Tolerant Optical Qubits
- Assessing the progress of trapped-ion processors towards fault-tolerant quantum computation
- Quantum metrology enhanced by repetitive quantum error correction
- Three Qubit Randomized Benchmarking
- Thresholds for topological codes in the presence of loss
- Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
- Repeated multi-qubit readout and feedback with a mixed-species trapped-ion register
- A general framework for randomized benchmarking
- Simulating open quantum systems: from many-body interactions to stabilizer pumping
- Manipulating a qubit through the backaction of sequential partial measurements and real-time feedback
- Variational-State Quantum Metrology
- Coping with qubit leakage in topological codes
- Sequential random access codes and self-testing of quantum measurement instruments
- Experimental quantum process tomography of non trace-preserving maps
- Experimental quantum coding against photon loss error
- Quantum feedback with weak measurements
- Nondestructive detection of photonic qubits
- Characterizing quantum dynamics with initial system-environment correlations
- Understanding the effects of leakage in superconducting quantum error detection circuits
- Semi-device-independent self-testing of unsharp measurements
- Deterministic correction of qubit loss
- Leakage detection for a transmon-based surface code
- Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions
- Device-Independent Certification of a Nonprojective Qubit Measurement
- Benchmarking a high-fidelity mixed-species entangling gate
- Transversality and lattice surgery: exploring realistic routes towards coupled logical qubits with trapped-ion quantum processors
- Quantum Error Correction of a Qubit Loss in an Addressable Atomic System
- Fault-tolerant protection of near-term trapped-ion topological qubits under realistic noise sources
- Experimental certification of an informationally complete quantum measurement in a device-independent protocol
- Device-independent characterization of quantum instruments
- Eliminating Leakage Errors in Hyperfine Qubits
- Geometric measure of quantum discord for a two-parameter class of states in a qubit-qutrit system under various dissipative channels
- Information-Disturbance Tradeoff in Quantum State Discrimination
- Quantum instruments as a foundation for both states and observables
- Analytical percolation theory for topological color codes under qubit loss
- Quantum process tomography with informational incomplete data of two -coupled heterogeneous spins relaxation in a time window much greater than
- Measurement-Disturbance Tradeoff Outperforming Optimal Cloning