## About

48

Publications

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Introduction

Yuan Su is a Senior Researcher at Microsoft Quantum. His current research focuses on quantum information and computation. He is particularly interested in the design, analysis, implementation, and application of quantum algorithms for quantum simulation. Website: http://yuansu.me/

## Publications

Publications (48)

With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical computers, but that requires the fewest resources for a quantum computer. We consider quantum simulation of spin...

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of prior approaches based on t...

Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different...

Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation n...

We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting the commutativity of Hamiltonian, the sparsity of interactions, and the prior knowledge of initial state. We achieve this using Trotterization for a class of interacting electrons that...

We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challenging to classically simulate in some...

We prove an entanglement area law for a class of 1D quantum systems involving infinite-dimensional local Hilbert spaces. This class of quantum systems include bosonic models such as the Hubbard-Holstein model, and both U(1) and SU(2) lattice gauge theories in one spatial dimension. Our proof relies on new results concerning the robustness of the gr...

Quantum many-body systems display rich phase structure in their low-temperature equilibrium states1. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases2–8 that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example...

While most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular properties can be expressed an energy derivative, including molecular forces, which are essential for applications suc...

Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition number $\kappa$ of the linear system, without requiring a complicated variable-time amplitude amplification p...

Quantum simulations of chemistry in first quantization offer some important advantages over approaches in second quantization including faster convergence to the continuum limit and the opportunity for practical simulations outside of the Born-Oppenheimer approximation. However, since all prior work on quantum simulation of chemistry in first quant...

Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation n...

We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challenging-to-classically-simulate in some...

Quantum simulations of chemistry in first quantization offer important advantages over approaches in second quantization including faster convergence to the continuum limit and the opportunity for practical simulations outside the Born-Oppenheimer approximation. However, as all prior work on quantum simulation in first quantization has been limited...

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of prior approaches based on t...

We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting the commutativity of Hamiltonian, the sparsity of interactions, and the prior knowledge of initial state. We achieve this using Trotterization for a class of interacting electrons that...

We study a sparse version of the Sachdev-Ye-Kitaev (SYK) model defined on random hypergraphs constructed either by a random pruning procedure or by randomly sampling regular hypergraphs. The resulting model has a new parameter, $k$, defined as the ratio of the number of terms in the Hamiltonian to the number of degrees of freedom, with the sparse l...

The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as $1/r^\alpha$ in the distance $r$ provide an experimentally realizable resource for information processing...

Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different...

Quantum computers can efficiently simulate the dynamics of quantum systems. In this Letter, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product-formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding...

The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For sparse Hamiltonian simulation, the gate complexity scales with the L1 no...

Magic-state distillation (or nonstabilizer state manipulation) is a crucial component in the leading approaches to realizing scalable, fault-tolerant, and universal quantum computation. Related to nonstabilizer state manipulation is the resource theory of nonstabilizer states, for which one of the goals is to characterize and quantify nonstabilizer...

Quantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a...

To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum ‘magic’ or non-stabilizerness of noisy quantum circuits. Fo...

Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and surprisingly efficient. We show that by simply randomizing how the summands are ordered, one can prove stronger...

We consider simulating an n-qubit Hamiltonian with nearest-neighbor interactions evolving for time t on a quantum computer. We show that this simulation has gate complexity (nt)1+o(1) using product formulas, a straightforward approach that has been demonstrated by several experimental groups. While it is reasonable to expect this complexity—in part...

The propagation of information in nonrelativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/r
α
. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique fo...

An n-qubit quantum circuit performs a unitary operation on an exponentially large, 2ⁿ-dimensional, Hilbert space, which is a major source of quantum speed-ups. We develop a new “Quantum singular value transformation” algorithm that can directly harness the advantages of exponential dimensionality by applying polynomial transformations to the singul...

The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For the case of sparse Hamiltonian simulation, the gate complexity scales wi...

To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum "magic" or non-stabilizerness of noisy quantum circuits. Fo...

Product formulas provide a straightforward yet surprisingly efficient approach to quantum simulation. We show that this algorithm can simulate an $n$-qubit Hamiltonian with nearest-neighbor interactions evolving for time $t$ using only $(nt)^{1+o(1)}$ gates. While it is reasonable to expect this complexity---in particular, this was claimed without...

Magic state manipulation is a crucial component in the leading approaches to realizing scalable, fault-tolerant, and universal quantum computation. Related to magic state manipulation is the resource theory of magic states, for which one of the goals is to characterize and quantify quantum "magic." In this paper, we introduce the family of thauma m...

The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance $r$ as a power law, $1/r^\alpha$. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a tec...

Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation" algorithm capable of harnessing this exponential advantage, that can apply polynomial transformations to the singular...

Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and surprisingly efficient. We show that by simply randomizing how the summands are ordered, one can prove stronger...

The ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer enables the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete logarithm over Abelian groups, and phase estimation. The standard fault-tolerant implementation of an $n$-qubit QFT appr...

The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a class of linear functions, defined on quantum strategy representations within this framework, that corresponds to...

The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a class of linear functions, defined on quantum strategy representations within this framework, that corresponds to...

We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection of fast algorithms capable of optimizing large-scale quantum circuits. For the suite of benchmarks considered,...

In this paper, we investigate the quantum state secure transmission in network communications. First of all, we propose new protocols of joint remote state preparation (RSP). A variety of situations are investigated, including N-to-two and N-to-M RSP of general 2-level states, N-to-M RSP of both equatorial and general d-level states. Compared with...

In this paper, the perfect secret sharing in quantum cryptography is investigated. On one hand, the security of a recent protocol [Adhikari et al. Quantum Inform. & Comput. 12 (2012) 0253-0261] is re-examined. We find that it violates the requirement of information theoretic security in the secret sharing and suffers from the information leakage. T...

Recently, a protocol is proposed for the quantum state sharing (QSTS) of an arbitrary three-photon state using four sets of W-class states. Unfortunately, its security analysis is inadequate. In this paper, we find the security loophole of this QSTS protocol. It is mainly caused by the fake quantum channel, whose security is not guaranteed by the l...

In this paper, several new protocols for the controlled remote state preparation (CRSP) by using the Brown state as the quantum channel are proposed. Firstly, we propose a CRSP protocol of an arbitrary two qubit state. Then, the CRSP protocol of an arbitrary three qubit state, which has rarely been considered by the previous papers, is investigated...

In this paper, the new protocol for quantum private comparison of equality (QPCE) is investigated. Instead of using the entanglement, we only utilize the single photon to efficiently realize the comparison of secret information. Furthermore, a more feasible QPCE protocol, which can be successfully performed via the collective amplitude damping chan...

Recently, Liu et al (2011 Phys. Scr. 84045015) pointed out that the multiparty quantum secret sharing (MQSS) protocol based on the GHZ state (Hwang et al 2011 Phys. Scr. 83045004) is insecure. They found that an inside participant can deduce half of the sender's secret information directly just by his piece of the secret. In order to resist this at...

We investigate novel protocols for the joint remote state preparation involving several senders and receivers. The highlight of our paper lies in two aspects. First, we focus on the distribution of information among multiple senders and receivers. Second, each receiver can simultaneously reconstruct a qubit state containing the joint information fr...