Related papers: Pseudo-dimension of quantum circuits
Classical simulations of quantum circuits are limited in both space and time when the qubit count is above 50, the realm where quantum supremacy reigns. However, recently, for the low depth circuit with more than 50 qubits, there are…
We extend a recent method to detect lower bounds to the quantum capacity of quantum communication channels by considering realistic scenarios with general input probe states and arbitrary detection procedures at the output. Realistic…
The definition of a pseudo-dualizing complex is obtained from that of a dualizing complex by dropping the injective dimension condition, while retaining the finite generatedness and homothety isomorphism conditions. In the specific setting…
We investigate the power of non-deterministic circuits over restricted sets of base gates. We note that the power of non-deterministic circuits exhibit a dichotomy, in the following sense: For weak enough bases, non-deterministic circuits…
Quantum machine learning has shown promise for high-dimensional data analysis, yet many existing approaches rely on linear unitary operations and shared trainable parameters across outputs. These constraints limit expressivity and…
Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied…
We give a brief introduction to private quantum codes, a basic notion in quantum cryptography and key distribution. Private code states are characterized by indistinguishability of their output states under the action of a quantum channel,…
We investigate the quantum capacity of noisy quantum channels which can be represented by coupling a system to an effectively small environment. A capacity formula is derived for all cases where both system and environment are…
We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an…
Beyond computer science, quantum complexity theory can potentially revolutionize multiple branches of physics, ranging from quantum many-body systems to quantum field theory. In this paper, we investigate the relationship between the sample…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
The new and rapidly growing field of circuit QED offers extremely exciting prospects for learning about and exercising intimate control over quantum systems, providing flexible, engineerable design and strong nonlinearities and interactions…
Superconducting circuits are an extremely versatile platform to realize quantum information hardware and to emulate topological materials. We here show how a simple arrangement of capacitors and conventional…
Quantum resources like entanglement and magic are essential for characterizing the complexity of quantum states. However, when the number of copies of quantum states and the computational time are limited by numbers polynomial in the system…
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
We prove a quantum information-theoretic conjecture due to Ji, Liu and Song (CRYPTO 2018) which suggested that a uniform superposition with random \emph{binary} phase is statistically indistinguishable from a Haar random state. That is, any…
When considering a sequent-style proof system for quantum programs, there are certain elements of quantum mechanics that we may wish to capture, such as phase, dynamics of unitary transformations, and measurement probabilities. Traditional…
Quantum protocols including quantum key distribution and blind quantum computing often require the preparation of quantum states of known dimensions. Here, we show that, rather surprisingly, hidden multi-dimensional modulation is often…
Recently Bravyi, Gosset and K\"onig (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation. In this paper we show a similar separation in the…