Research

Quantum mechanics allows a new type of information represented by quantum states which may be in a superposition of 0 and 1 state. Quantum information processing seeks to perform tasks that are impossible or not effective with the use of conventional classical information, by manipulating quantum states to the limits of quantum theory. Examples are quantum computation, quantum cryptography, and quantum communication.
We consider that a quantum computer is not just a machine to run computational algorithms but also a machine to perform any operations allowed by quantum mechanics. We analyze what kinds of new properties and effects may appear in quantum systems by using quantum computers to improve our understanding of quantum mechanics from an operational point of view. We also investigate applications of quantum properties and effects such as entanglement for information processing, communication, quantum learning, and quantum manipulations by developing quantum algorithms and quantum protocols.
Our projects engaged in the academic year of 2022 were the following:

Quantum machine learning & Quantum learning

Quantum state generation via binary decision diagram

The Grover-Rudolph method [L. Grover et al, arXiv:quant-ph/0208112] using QRAM [O. D. Matteo et al, arXiv:1902.01329] is known as a method for generating the quantum superposition of an empirical distribution, whose generating circuit requires $\mathcal{O}(N)$ qubits or $\mathcal{O}(N)$ $T$-depth depending on how to construct the circuit, where $N$ is the number of data. To address this trade off problem, we introduce the data structure via binary decision diagram (BDD) to represent the empirical distribution and develop the algorithm generating the quantum superposition of the empirical distribution, which requires $\mathcal(|E|)$ queries to the BDD, where $E$ is the set of edges of the BDD, that is the algorithm does not depend on $N$ explicitly.

Quantum neural networks with coherent control over neurons

Quantum neural networks or variational quantum circuits have become the canonical generalisation of neural networks to the quantum level, where individual neurons are taken to be quantum gates that can act on superpositions of computational basis states. In this work, we formally define a new machine learning paradigm where the individual neurons can themselves be in a quantum superposition of different gates, and investigate its potential for performing standard machine learning tasks on quantum data.

Quantum simulation of unitary comparison

We implemented the optimal algorithm for unitary comparison, which determines whether unknown quantum circuits are the same or different, using Qiskit and executed it on the IBM Q quantum computer. Our experiments revealed that the decrease in success probability due to noise was small for small-scale circuits, indicating the practical feasibility of quantum machine learning tasks that extract specific information from unknown quantum systems using quantum computers.

Quantum Ridgelet Transform: Winning Lottery Ticket of Neural Networks with Quantum Computation

A significant challenge in the field of quantum machine learning (QML) is to establish applications of quantum computation to accelerate common tasks in machine learning such as those for neural networks. We develop a fast quantum algorithm for ridgelet transform and discover its application to find a sparse trainable subnetwork of large neural networks efficiently.

Distributed quantum computation

Distribution of non-local gates between networks of quantum computers

Given that quantum computers become hard to build in a robust way as the number of qubits increases, it is easy to imagine scenarios where a quantum computation might need to be distributed amongst many quantum computers in order to be executed, which is exactly the kind of scenario considered in this work. This work formalises an framework for automating the distribution of quantum circuits between two quantum computers which minimises the entanglement cost, and culminated in the production of a Python package that can implement this automated task.

Entanglement-efficient bipartite-distributed quantum computing with entanglement-assisted packing processes

We generalise the protocol by Eisert et. al. for the distribution of a single non-local controlled unitary gate such that a single process can be used for a number of non-local unitaries (the collection of which we define as the `kernel' of one use of the protocol). We then show how in this setting a bipartite graph can be formed, the minimum vertex cover for which minimises the entanglement cost of the distribution. This method was then extended to include other strategies for reducing the entanglement cost, such as embedding, as well as taking into account constraints that are imposed externally on the shape of the solution of the problem.

Higher-order algorithms

Deterministic exact algorithm for inverting qubit-unitary operations

We construct a deterministic exact algorithm for inverting unknown qubit-unitary operations. First, the problem of searching for a unitary inversion algorithm is formulated as semidefinite programming (SDP), and the SDP is simplified by using the unitary group symmetry of the problem. For the case the input unitary operation acts on a single-qubit system, the numerical results of the simplified SDP show a deterministic and exact unitary inversion algorithm. Using the numerical results, the unitary inversion algorithm is analytically constructed. It is also shown that the information of the input unitary operation is preserved in the output state of the auxiliary system in this algorithm, and that this information can be used as a catalyst in the unitary inversion algorithm.

Higher-order Hamiltonian algorithms

Higher-order quantum algorithms, which take quantum gates as input, can be seen as the analogue of functional programming in classical algorithms. However, so far they have primarily been considered in situations where any quantum channels or unitary gates can be used as input. In this work, we formally extend the scope of higher-order algorithms to cases where the input gates are Hamiltonian evolutions, giving rise to new possibilities, such as a universal algorithm for linear transformations of Hamiltonian dynamics.

Catalytic supermaps

A quantum supermap (with definite causal order), which transforms quantum channels to quantum channels, can always be purified to a unitary supermap, by suitably adding auxiliary systems which are discarded at the end. In this work, we discover that the output of these auxiliary systems sometimes contains enough information to recover one of the input channels. We call such purifications catalytic supermaps, because the input channel which can be recovered from the auxiliary system essentially acts as a catalyst. We formally define the notion of catalytic supermaps in a resource-theoretic setting and discuss its potential applications in quantum information processing.

Indefinite causal order

Decomposition of unitarily extendable $n$-partite processes

The discovery of processes that admit an indefinite causal order between events has been a subject of great interest in recent years, however, the decomposition of such processes into elementary operations has remained an open problem. In this work, we aim to prove, or disprove, the conjecture proposed in [A. Vanrietvelde, et al., arXiv:2206.10042, 2022], that all process with any $n$ number of parties, can be decomposed into a routed circuit, provided that the process is unitarily extendable (which has been conjectured to correspond to the physically realisable processes). This work can be seen as a generalisation of the results found in [W. Yokojima, et al., Quantum, 2021], and is joint work by Yokojima, HK and Murao.

The simulatability of the quantum switch using definite causal order

The quantum switch is the most prominent example of a process with indefinite causal order. The action of the quantum switch on two unitary channels can be simulated using only definite causal order, if two copies of one of the unitaries is given, however, it is currently unknown whether any such a simulation is possible for the case of general quantum channels. In this work, we prove that the action of the quantum switch on two general quantum channels cannot be simulated given access to any finite number of copies of the channels if using only definite causal order.

Quantum error correction and fault-tolerant quantum computation

Low-depth random Clifford circuits for quantum coding against Pauli noise using a tensor-network decoder

Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the random circuits on $n$ qubits, embedded in one spatial dimension (1D), have a logarithmic depth $d=O(\log n)$; however, this was demonstrated only for a simple erasure noise model. In this work, we discover that this desired property indeed holds for the conventional Pauli noise model, by developing a tensor-network maximum-likelihood decoding algorithm that works efficiently for log-depth encoding circuits in 1D.

Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation

Constant-space-overhead fault-tolerant quantum computation (FTQC) using quantum low-density parity-check (LDPC) codes attracts considerable attention these days but suffers from a drawback: it incurs polynomially long time overhead. To address these problems, we here introduce an alternative approach using a concatenation of multiple small-size quantum codes for the constant-space-overhead FTQC rather than a single large-size quantum LDPC code, to achieve time-efficient constant-space-overhead FTQC.

Irreversibility of quantum entanglement

A long-standing problem in the characterization of quantum entanglement was to understand if it can be made reversible, which would resemble the properties of thermodynamics in the asymptotic (macroscopic) limit. We show that entanglement is fundamentally irreversible: there exist states which cannot be reversibly manipulated under any "free" operations do not generate entanglement, proving that laws such as the second law of thermodynamics cannot hold in the resource theory of entanglement in general. Our approach is based on introducing a new bound on the entanglement cost of any state --- the tempered negativity --- which can be efficiently computed and can be shown to improve on the best previously known bounds, e.g. those based on the quantum relative entropy. We generalize the results to quantum channels and show that the theory of quantum communication exhibits a similar type of irreversibility.

Tight constraints on the probabilistic convertibility of quantum states

We develop a general theoretical approach to understanding when quantum states can be converted to each other with some probability under the physical restrictions imposed by some quantum resource theory. In addition to a number of quantitative bounds and limitations, we study a new resource monotone --- the projective robustness --- which can improve on previously known results and reveal new restrictions governing the conversion of quantum states. This leads, in particular, to new, stronger bounds on the performance of important protocols such as distillation of entanglement or magic.

Foundations of Quantum Thermodynamics & Quantum resource theories

Landauer vs. Nernst: What is the True Cost of Cooling a Quantum System

The crucial role of control in physical processes is exemplified by the third law of thermodynamics, Nernst's unattainability principle, stating that infinite resources are required to cool a system to absolute zero temperature. But what are these resources and how should they be utilised? And how does this relate to Landauer's principle that famously connects information and thermodynamics? We answer these questions by providing a framework for identifying the resources that enable the creation of pure quantum states. We show that perfect cooling is possible with Landauer energy cost given infinite time or control complexity.