arXiv:2501.02929 · Physical Review Applied

Reducing circuit depth in quantum state preparation for quantum simulation using measurements and feedforward

Hyeonjun Yeo, Ha Eum Kim, IlKwon Sohn, Kabgyun Jeong

Published May 27, 2025• 5 citations

Abstract

Reducing circuit depth and identifying an optimal trade-off between circuit depth and width is crucial for successful quantum computation. In this context, midcircuit measurement and feedforward have been shown to significantly reduce the depth of quantum circuits, particularly in implementing logical gates. By leveraging these techniques, we propose several parallelization strategies that reduce quantum circuit depth at the expense of increasing width in preparing various quantum states relevant to quantum simulation. With measurements and feedforward, we demonstrate that utilizing unary encoding as a bridge between two quantum states substantially reduces the circuit depth required for preparing quantum states, such as sparse quantum states and sums of Slater determinants within the first quantization framework, while maintaining an efficient circuit width. Additionally, we show that a Bethe wave function, characterized by its high degree of freedom in its phase, can be probabilistically prepared in a constant-depth quantum circuit using measurements and feedforward. We anticipate that our study will contribute to the reduction of circuit depth in initial state preparation, particularly for quantum simulation, which is a critical step toward achieving quantum advantage.

DOI: 10.1103/physrevapplied.23.054066

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arXiv:2501.02929 · Physical Review Applied

Reducing circuit depth in quantum state preparation for quantum simulation using measurements and feedforward

Hyeonjun Yeo, Ha Eum Kim, IlKwon Sohn, Kabgyun Jeong

Published May 27, 2025• 5 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevapplied.23.054066

Related papers

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Mid-circuit measurements with feedforward reduce the optimal worst-case quantum depth for exact

n

-qubit unitary synthesis from

Θ(n)

O(1)

, using arbitrary one- and two-qubit gates and unrestricted ancillary space. Measurements and resets without feedforward remain subject to the circuit causal-cone bound. Our deterministic construction uses single-qubit measurements,

O(1)

rounds of parity feedforward, and

O(n4^n\log(n+2))

total qubits, with all ancillas starting and ending in

|0\rangle

. Classical processing is not counted in quantum depth. We teleport only the matrix error of an approximation by Nehoran and Yuen. An exactly prepared ancillary state encodes this error, whose action is added back by coherent interference. At operator-norm error

2^{-n}

, one step of amplitude amplification suffices. Coherent fanout circuits achieve the same constant-depth bound, while circuits using only one- and two-qubit gates attain depth

Θ(n)

with

O(4^n\log^2(n+2))

gates. Generic targets require

Ω(4^n/(h+1))

qubits at depth

h

, even under unrestricted classical control. Our depth-width trade-offs meet this bound within a factor

O(n^2)

for

1\le h\le2^n

O(n\log d)

, and another that reduces depth to

O(n)

. The latter leverages mid-circuit measurement and feedforward, where intermediate measurement outcomes are used to control subsequent quantum operations. Both constructions have size

O(dn)

and use

O(d)

ancilla qubits. Compared to the state-of-the-art SQSP algorithm in arXiv:2108.06150, which allows an arbitrary number of ancilla qubits

m>0

, both of our algorithms achieve lower circuit depth when

m=d

n

qubits with depth

O\left(M n^2\right)

, where

M = M(n)

is some function of

n

, can be transformed into a circuit with depth

O\left(\log_2(M) n^2\right)

operating on

O\left(M n\right)

qubits. This technique may be particularly useful in noisy environments, where recent findings indicate that only the final

O\left(\log n\right)

layers influence the expectation value of observables. It may also optimize Trotterization by exponentially reducing the number of Trotter steps. Additionally, the method may offer advantages for distributed quantum computing, and the intuition of treating quantum states as gates and operators as vectors used in this work may have broader applications in quantum computation.