New Method Measures nPoint Correlation Functions in Quantum Systems, Enhancing Quantum Simulations

A team of researchers from Georgetown University, Max Planck Institute for Solid State Research, Quantinuum, and North Carolina State University have developed a new method for measuring nPoint correlation functions in quantum systems. The method, which is robust and efficient, involves interrupting the time evolution of the system by interacting an ancilla qubit with the system and measuring the ancilla immediately afterward. This approach overcomes the limitations of existing methods, such as the Hadamard test, and is suitable for near-term quantum simulations of open quantum systems. The research could lead to more accurate and efficient quantum simulations in the future.

What is the New Method for Measuring nPoint Correlation Functions in Quantum Systems?

The article discusses a new method proposed by a team of researchers from Georgetown University, Max Planck Institute for Solid State Research, Quantinuum, and North Carolina State University. The team, led by Lorenzo Del Re and Brian Rost, has developed a unified hierarchical method to measure nPoint correlation functions in quantum systems. These systems can be driven dissipative, open, or nonequilibrium.

The method involves repeatedly interrupting the time evolution of the system by interacting an ancilla qubit with the system through a controlled operation and measuring the ancilla immediately afterward. The researchers compare this method’s robustness to other ancilla-based interferometric techniques, such as the Hadamard test, and highlight its advantages for near-term quantum simulations of open quantum systems.

The team implemented the method on a quantum computer to measure single-particle Green’s functions of a driven-dissipative fermionic system. The results show that dynamical correlation functions for driven-dissipative systems can be robustly measured with near-term quantum computers.

Why is this Method Important for Open Quantum Systems?

Open quantum systems, particularly driven-dissipative systems, are among the most challenging problems to study in many-body physics. However, they are also among the richest. The problem parameter space is vast, and the bath, as well as the system, have their own inherent dynamics. Their interaction can be complex.

Despite these complexities, there is a unification and emergent simplicity as the details often do not play a role when it comes to describing nonequilibrium steady or periodic states. These states can be captured with a few parameters, have lost all knowledge of their history, and are stable to perturbations away from their fixed point. In other words, they are remarkably robust.

This robustness has been exploited in simulations on quantum computers, either relying on the hardware intrinsic decoherence, by implementing Kraus maps and Lindblad operators, or by implementing non-Hermitian dynamics. In some cases, the existence of a fixed point has enabled quantum computers to perform the simulations far beyond the short coherence time of the qubits when the fidelity of one Trotter step is sufficiently high.

What are the Limitations of the Existing Methods?

The typical protocols for the measurement of correlation functions are based on the Hadamard test, where the correlation function is measured with an ancilla qubit. This approach does not robustly generalize to measuring correlation functions in open quantum systems.

The ancilla cannot capture the potentially long-time dynamics of the driven-dissipative open quantum systems because the ancilla has a short coherence time. For simulating closed quantum systems, this is not a problem because the system has an equally short coherence time and the region of inaccessibility by the Hadamard test approach has no information. However, for simulating open quantum systems, this is a problem because the now-stable dynamics of the driven-dissipative system are inaccessible due to the ancilla decoherence.

How Does the New Method Overcome These Limitations?

The new method proposed by the researchers is a full framework for computing nPoint correlation functions in open quantum systems and is suitable for the near term where we cannot rely on long ancilla coherence lifetimes. Its crux is a measurement of the ancilla right after it is entangled with the system and using the result of the measurement in post-processing to construct the desired nPoint correlation function.

For simulating closed quantum systems, this approach yields the same information as the standard Hadamard test. However, for open quantum systems, the region of inaccessibility by ancilla decoherence is now fully accessible.

The method is a simple strategy capable of measuring arbitrary unequal-time correlation functions between multi-qubit Pauli operators and works for both dissipative and unitary time evolution. As such, it subsumes and unifies the approaches of unequal-time commutators and unequal-time anticommutators. It is hierarchical in the sense that extracting the information of an nth order correlation function requires previous knowledge of lower-order correlation functions.

What are the Implications of this Research?

The research has significant implications for the field of quantum computing and many-body physics. The proposed method provides a robust and efficient way to measure nPoint correlation functions in quantum systems, which is crucial for understanding the dynamics of these systems.

The method’s ability to work with both dissipative and unitary time evolution and measure arbitrary unequal-time correlation functions between multi-qubit Pauli operators makes it a versatile tool for quantum simulations.

Moreover, the method’s successful implementation on a quantum computer to measure single-particle Green’s functions of a driven-dissipative fermionic system demonstrates its practical applicability and potential for near-term quantum simulations of open quantum systems. This could pave the way for more accurate and efficient quantum simulations in the future.