Related papers: Adaptive Quantum Homeopathy
In this work we give an efficient construction of unitary $k$-designs using $\tilde{O}(k\cdot poly(n))$ quantum gates, as well as an efficient construction of a parallel-secure pseudorandom unitary (PRU). Both results are obtained by giving…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
Suppose we want to implement a unitary $U$, for instance a circuit for some quantum algorithm. Suppose our actual implementation is a unitary $\tilde{U}$, which we can only apply as a black-box. In general it is an exponentially-hard task…
Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary…
Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing…
As quantum devices scale up, many-body quantum gates and algorithms begin to surpass what is possible to simulate classically. Validation methods which rely on such classical simulation, such as process tomography and randomized…
Quantum computers are expected to bring drastic acceleration to several computing tasks against classical computers. Noisy intermediate-scale quantum (NISQ) devices, which have tens to hundreds of noisy physical qubits, are gradually…
Quantum arithmetic computation requires a substantial number of scratch qubits to stay reversible. These operations necessitate qubit and gate resources equivalent to those needed for the larger of the input or output registers due to state…
Fault-tolerant quantum computing typically requires the transpilation of arbitrary quantum circuits into a finite, universal gate set, such as Clifford+T. As a baseline, Diagonal approximation can be used for synthesizing single-qubit Pauli…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
We consider the problem of deciding whether an $n$-qubit unitary (or $n$-bit Boolean function) is $\varepsilon_1$-close to some $k$-junta or $\varepsilon_2$-far from every $k$-junta, where $k$-junta unitaries act non-trivially on at most…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
At its core a $t$-design is a method for sampling from a set of unitaries in a way which mimics sampling randomly from the Haar measure on the unitary group, with applications across quantum information processing and physics. We construct…
There exist numerous problems in nature inherently described by finite $D$-dimensional states. Formulating these problems for execution on qubit-based quantum hardware requires mapping the qudit Hilbert space to that of multiqubit which may…
We develop an adaptive method for quantum state preparation that utilizes randomness as an essential component and that does not require classical optimization. Instead, a cost function is minimized to prepare a desired quantum state…
One of the main challenges for quantum computation is that while the number of gates required to perform a non-trivial quantum computation may be very large, decoherence and errors in realistic quantum architectures limit the number of…
While implementing a quantum algorithm it is crucial to reduce the quantum resources, in order to obtain the desired computational advantage. For most fault-tolerant quantum error-correcting codes the cost of implementing the non-Clifford…
We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a…
We study efficient generations of random diagonal-unitary matrices, an ensemble of unitary matrices diagonal in a given basis with randomly distributed phases for their eigenvalues. Despite the simple algebraic structure, they cannot be…
One of the primary objectives in the field of quantum state learning is to develop algorithms that are time-efficient for learning states generated from quantum circuits. Earlier investigations have demonstrated time-efficient algorithms…