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Code switching is an established technique that facilitates a universal set of FT quantum gate operations by combining two QEC codes with complementary sets of gates, which each by themselves are easy to implement fault-tolerantly. In this…
We explore the design of quantum error-correcting codes for cases where the decoherence events of qubits are correlated. In particular, we consider the case where only spatially contiguous qubits decohere, which is analogous to the case of…
In order to compress quantum messages without loss of information it is necessary to allow the length of the encoded messages to vary. We develop a general framework for variable-length quantum messages in close analogy to the classical…
Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways,…
One of the essential building blocks of classical computer programs is the "if" clause, which executes a subroutine depending on the value of a control variable. Similarly, several quantum algorithms rely on applying a unitary operation…
Hybrid variational quantum algorithms are promising for solving practical problems, such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers.…
At its core, Quantum Mechanics is a theory developed to describe fundamental observations in the spectroscopy of solids and gases. Despite these practical roots, however, quantum theory is infamous for being highly counterintuitive, largely…
We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the…
The question of finding a lower bound on the number of Toffoli gates in a classical reversible circuit is addressed. A method based on quantum information concepts is proposed. The method involves solely concepts from quantum information -…
The causal structure of a stochastic process can be more efficiently transmitted via a quantum channel than a classical one, an advantage that increases with codeword length. While previously difficult to compute, we express the quantum…
We present a theory of quantum stabilizer turbo-encoders with unbounded minimum distance. This theory is presented under a framework common to both classical and quantum turbo-encoding theory. The main conditions to have an unbounded…
The divide-and-conquer framework, used extensively in classical algorithm design, recursively breaks a problem of size $n$ into smaller subproblems (say, $a$ copies of size $n/b$ each), along with some auxiliary work of cost…
The famous Shannon impossibility result says that any encryption scheme with perfect secrecy requires a secret key at least as long as the message. In this paper we provide its quantum analogue with imperfect secrecy and imperfect…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
In this correspondence we present a new proof of Holevo's coding theorem for transmitting classical information through quantum channels, and its strong converse. The technique is largely inspired by Wolfowitz's combinatorial approach using…
We prove that quantum expander codes can be combined with quantum fault-tolerance techniques to achieve constant overhead: the ratio between the total number of physical qubits required for a quantum computation with faulty hardware and the…
The amount of information transmissible through a communications channel is determined by the noise characteristics of the channel and by the quantities of available transmission resources. In classical information theory, the amount of…
We analyze utility of communication channels in absence of any short of quantum or classical correlation shared between the sender and the receiver. To this aim, we propose a class of two-party communication games, and show that the games…
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…
How can relevant information be extracted from a quantum process? In many situations, only some part of the total information content produced by an information source is useful. Can one then find an efficient encoding, in the sense of…