In the first work package, we analyzed the problem of dynamic cooling whereby a target qubit is cooled at the expense of heating up N-1 further identical qubits, by means of a global unitary operation. Quantum computers require qubits to be initialized in a pure (i.e. cold) state for successful computation. Dynamic cooling offers a route to effectively lower qubit temperatures beyond what is possible with direct, physical cooling techniques. While it was initially dismissed as impractical for the high-temperature NMR-based quantum computers available at the time of its inception, we show how dynamic cooling is substantially more effective and efficient on the low-temperature quantum computers available today. We further show that the associated work cost of cooling is exponentially more advantageous in the low temperature regime. We next examined how optimal dynamic cooling scales with total system size, in terms of the minimal achievable final temperature, the work cost, and the complexity of the associated quantum circuits. We then turned to implementation of dynamic cooling in terms of quantum circuits and examined the effects of hardware noise. We also successfully performed a demonstration of dynamic cooling with a 3-qubit system on a real quantum processor from IBM. Since the circuit size grows quickly with the number of qubits used for cooling, scaling dynamic cooling to larger systems on noisy devices poses a major challenge. We therefore derived a suboptimal cooling algorithm, whereby relinquishing a small amount of cooling capability results in a drastically reduced circuit complexity, greatly facilitating the implementation of dynamic cooling on near-future quantum computers. Specifically, our sub-optimal dynamic cooling scheme exhibits a fixed (low) complexity with system size, which we demonstrated can dramatically improve the feasibility of implementation on noisy quantum hardware. Finally, in order to make our results more broadly accessible to the research community, we developed an extensible, open-source software package, called QuL, which can be used to generate, analyze, and test quantum circuits for various computational cooling protocols. In its most basic usage, QuL enables a novice user to easily produce cooling circuits with minimal input or knowledge required. The programming library, however, offers flexibility to more advanced users to finely tune the cooling protocol used to generate the quantum circuit. Finally, QuL offers methods to assess and compare various cooling protocols for users interested in studying optimal implementation of computational cooling in general, or on specific quantum backends. It is our hope that QuL will not only facilitate the execution of computational cooling on current quantum computers, but also serve as a tool to investigate open questions in the optimal implementation of computational cooling.
In the second work package we developed and explored a technique for the experimental measurement of the work statistics of a genuinely open quantum system using a quantum computer. Such measurement has remained elusive thus far due to the inherent difficulty in measuring the total energy change of a system-bath compound (which is the work) in the open quantum system scenario. To overcome this difficulty, we extended the interferometric scheme, originally conceived for closed systems, to the open system case and implemented it on a superconducting quantum computer from IBM, taking advantage of the relatively high levels of noise on current quantum hardware to realize an open quantum system. We demonstrated that our method can be used as a diagnostic tool to probe physical properties of the system-bath compound, such as its temperature and specific transition frequencies in its spectrum. Finally, our experiments corroborate that the interferometric scheme is a promising tool to achieve the long-sought experimental validation of the Jarzynski equality for arbitrary open quantum systems.
In the third work package, we wrote a perspective and roadmap on research at the intersection of quantum thermodynamics (QT) and quantum computers (QCs). The piece focused on the core connections between QCs and QT, namely, dissipation. Dissipation is a central object of investigation in (quantum) thermodynamics. Meanwhile, dissipation is both essential and toxic to quantum computation. On the one hand, dissipation is required to cool/reset qubits to an initial fiducial state (one of DiVincenzo's criteria for QCs). Furthermore, it has been shown that the more accuracy is demanded of an information processing task, the more dissipation is required. On the other hand, dissipation tends to corrupt computational results. We posited that QT can be exploited for minimizing, mitigating, and even correcting dissipation-induced errors by providing a characterization of the dissipation channels, thereby improving the performance of QCs. In the reverse direction, QCs are proving to be fruitful playgrounds for implementing QT experiments. We identified major outstanding challenges in this area of research. The first major challenge is modeling the noise in quantum computers. Noisy quantum emulators attempt to emulate the performance of a computation on a noisy QC, but these results can differ substantially from those from the real machine. We conclude that central result in QT, specifically, fluctuation relations, can be used to build an accurate profile of the noise. The second major challenge is the initialization of the qubits into a pure fiducial state. For this, we propose that dissipation can be exploited to develop optimal techniques for generating pure (low-information/low-temperature) qubits, whereby their initial mixedness gets dumped into the thermal environment. Optimization of the dissipative channels will be necessary to minimizing the energetic cost of quantum computation, and can be achieved based on the principles of QT. A third major challenge is the difficulty in preparing thermal states on QCs in order to use them for QT experiments. We propose that perhaps some hardware-level operations could be developed that can automatically generate desired thermal states, in the spirit of how FPGA's perform specialized logic encoded in the hardware. We concluded by proposing a critical question for research in this area to address: can a quantum computational advantage be achieved at a reasonable energetic price? QT provides tools to connect information processing tasks with physical energetic exchanges, and is therefore precisely the right framework with which to answer such a question. Maximizing the impact of QCs across all possible applications will crucially depend on optimizing their energy consumption, which in turn will depend heavily on the peculiar physics of QT. In general, energy consumption is minimized when dissipation is minimized. However, as discussed above, dissipation is essential for quantum computation. QT, which characterizes dissipation in quantum systems, therefore must be employed to strike an optimal balance between performance and energy consumption of QCs.
Finally, in the fourth work package, we examined the efficiency of information in feedback-controlled quantum thermal engines. We first develop a general theory of quantum thermal machines interacting with a finite number of thermal baths and a Maxwell demon, which can make measurements of the system and perform feedback-control based on the information derived from the measurements. This allows the demon to induce operations of the machine that apparently violate the second law of thermodynamics, in accordance to the famous Maxwell paradox. We resolve the paradox by accounting for the energy cost of measurement used to obtain the necessary information used for feedback control. An intriguing observation was discovered, namely, that more information does not necessarily result in better thermodynamic performance: sometimes knowing less is better.
